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Fundamentals of Fluid Mechanics

Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Chapter 5

Finite Control Volume Analysis - all with Video Answers

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Chapter Questions

06:22

Problem 1

Use the Reynolds transport theorem (Eq. 4.19 ) with $B=$ volume and, therefore, $b=$ volume/mass $=$ I/density to obtain the continuity equation for steady or unstcady incompressible flow through a fixed control volume: $\int_{0} \mathbf{V} \cdot \mathbf{n} d A=0$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:20

Problem 2

An incompressible fluid flows horizontally in the $x-y$ plane with a velocity given by
\[
u=30\left(1-e^{-4}\right) \mathrm{m} / \mathrm{s}, v=0
\]
where $y$ and $h$ are in meters and $a$ is a constant. Determine the average velocity for the portion of the flow between $y=0$ and $y=h$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
08:30

Problem 3

Water flows steadily through the horizontal piping system shown in Fig. P5.3. The velocity is uniform at section (1), the mass flowrate is 10 slugs/s at section $(2),$ and the velocity is nonuniform at section $(3) .(a)$ Determine the value of he quantity $\frac{D}{D t} \int_{\text {sys }} \rho d t$
where the system is the water contained in the pipe bounded by sections $(1),(2),$ and (3)
(b) Determine the mean velocity at section (2)
(c) Determine, if possible, the value of the integral
$\int_{(5)} \rho \mathrm{V} \cdot \hat{\mathbf{n}} d A$ over section $(3) .$ If it is not possible, explain what additional information is needed to do so.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:04

Problem 4

Water flows out through a set of thin, closely spaced blades as shown in Fig. P5.4 with a speed of $V=10 \mathrm{ft} / \mathrm{s}$ arsund the entire circumference of the outlet. Determine the mass flowrate through the inlet pipe.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
10:06

Problem 5

Estimate the rate (in gal/hr) that your car uses gasoline when it is being driven on an interstate highway. Determine how long it would take to empty a 12 -oz soft-drink container at this flowrate. List all assumptions and show calculations.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:43

Problem 6

The pump shown in Fig. P5.6 produces a steady flow of 10 gal/s through the nozzle. Determine the nozrle exit diameter, $D_{2}$, if the exit velocity is to be $V_{2}=100 \mathrm{ft} / \mathrm{s}$.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:45

Problem 7

The fluid axial velocities shown in Fig. $P S .7$ are the average velocities measured in $f t / s$ in each annular area of a duct. Find the volume flowrate for the flowing fluid.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
08:20

Problem 8

The human circulatory system consists of a complex branching pipe network ranging in diameter from the aorta (largest) to the capillaries (smallest). The average radii and the number of these vessels are shown in the table. Does the arerage blood velocity increase, decrease, or remain consiant as it travels from the aorta to the capillaries?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:52

Problem 9

Air flows steadily setween wo cross sections in a long. straight section of 0.1 -m-inside-diameter pipe. The static temperature and pressure at each section are indicated in Fig. P5.9. If the average air velocity at section (1) is $205 \mathrm{m} / \mathrm{s}$, determine the averge air velocity at scction (2).

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:19

Problem 10

A hydraulic jump (see Video $\mathbf{V} 10.11$ ) is in place downstream from a spillway as indicated in Fig. P5.10. Upstream of the jump, the depth of the stream is $0.6 \mathrm{ft}$ and the average stream velocity is $18 \mathrm{ft} / \mathrm{s}$. Just downstream of the junp, the average stream velocity is $3.4 \mathrm{ft} / \mathrm{s}$. Calculate the depth of the stream, $h$, just downsiream of the jump.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:58

Problem 11

A woman is cmptying her aquarium at a steady rate with a small pump. The water pumped to a 12 -in.-diameter cylindrical bucket, and its depth is increasing at the rate of 4.0 ir. per minute. Find the rate at which the aquarium water level is dropping if the aquarium measures 24 in. (wide) $\times 36$ in. (long) $x$ 18 in. (high)

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:46

Problem 12

An evaporative cooling tower (see Fig. $P 5.12$ ) is used to cool water from 110 to $80^{\circ} \mathrm{F}$. Water enters the tower at a rate of 250,000 Ibm, Dry air (no water vapor) flows into the tower at a rate of 151.000 lbm/hr. If the rate of wet airflow out of the tower is 156,900 Ibm $,$ he determine the rate of water evaporation in $16 \mathrm{m} / \mathrm{hr}$ and the rate of cooled water flow in $1 \mathrm{bm} / \mathrm{hr}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:38

Problem 13

At cruise conditions, air flows into a jet engine at a steady rate of 65 lbm/s. Fuel enters the engine at a sieady rate of $0.60 \mathrm{Ism} / \mathrm{s}$. The average velocity of the exhaust gases is 1500 ft/s relative to the engine. If the engine exhaust effective cross-sectional area is $3.5 \mathrm{ft}^{2}$, estimate the density of the exhaust gases in $\mathrm{lbm} / \mathrm{ft}^{3}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:38

Problem 14

Water at $0.1 \mathrm{m}^{3} / \mathrm{s}$ and alcohol $(S G=0.8)$ at $0.3 \mathrm{m}^{3}$ is are mixed in a $y$ -duct as shown in Fig. 5.14 . What is the average density of the mixture of alcohol and water?

Supratim Pal
Supratim Pal
Numerade Educator
05:51

Problem 15

In the vortex tube shown in Fig. P5.15, air enters at $202 \mathrm{kPa}$ absolute and $300 \mathrm{K}$. Hot air leaves at $150 \mathrm{kPa}$ absolute and $350 \mathrm{K}$ whereas cold air leaves at $101 \mathrm{kPa}$ absolute and $250 \mathrm{K}$. The hot air mass flow rate, $\dot{m}_{h},$ equals the cold air mass flow rate, $\dot{m}_{C}$. Find the ratio of the hot air exit area to cold air exit area for equal exit velocities.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:35

Problem 16

Molten plastic at a temperature of $510^{\circ} \mathrm{F}$ is angered through an extruder barrel by a screw oscupying $s$ of the tarrel's volume (Fig. $P 5.16$ ). The extruder is $16 \mathrm{ft}$ long and has an inner dianeter of 8 in. The barrel is connected to an adspter having a volume of $0.48 \mathrm{ft}^{3} .$ The adapter is then connected to a die of equal volume. The plastic exiting the die is immediately rolled into sheets. The line is producing 4 -ft widths of material at a rate of $30 \mathrm{ft} / \mathrm{min}$ and a gauge thickness of 187 mil. What is the axial velocity, $V_{1},$ of the plastic in the barrel' Assume that the plastic density is constant as it solidifies from a liquid (in the extruder) into a solid sheet.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:47

Problem 17

A water jet pump (see Fig. $P 5.17$ ) involves a jet cross-sectional area of $0.01 \mathrm{m}^{2}$, and a jet velociy of $30 \mathrm{m} / \mathrm{s}$. The jet is surrounded by entrained water. The total cross-secticnal area associated with the jet and entrained streams is $0.075 \mathrm{m}^{2}$. These two fluid streams leave the pump thoroughly mixed with an average velocity of $6 \mathrm{m} / \mathrm{s}$ through a cross-sectional area of $0.075 \mathrm{m}^{2}$. Determine the pumping rate (i.e., the entrained fluid flowrate) involved in liters/s.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
08:23

Problem 18

To measure the mass flowrate of ar through a 6 -in.-insidediameter pipe, local velocity data are cellected at different radii from the pipe axis (see Table). Determine the mass flowrate corresponding to the data listed in the following table, Plot the velocity profile and comment.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:09

Problem 19

Two rivers merge to form a larger river as shown in Fig. PS.19. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is $6 \mathrm{ft}$. Determine the value of $V$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:44

Problem 20

Warious types of attachments can be used with the shop vac shown in Video $\mathrm{V} 5.2 .$ Two such attachments are shown in Fig. $P 5.20-$ a nozzle and a brush. The flowrate is $1 \mathrm{ft}^{3} / \mathrm{s}$.
(a) Determine the average velocity through the nozzle entrance, $V_{n}$
(b) Assume the air cnters the brush attachment in a radial direction all around the brush with a velocity profile that varies linearly from 0 to $V_{b}$ along the length of the bristles as shown in the figure. Determine the value of $V_{b^{\prime}}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
07:53

Problem 21

An appropriate turbulent pipe flow velocity profile is
\[
\mathbf{V}=u_{c}\left(\frac{R-r}{R}\right)^{1 / n}
\]
where $u_{c}=$ centerline véocity, $r=$ local radius, $R-$ pipe radias, and $\hat{\mathbf{i}}=$ unit vector along pipe centerline. Determine the ratio of average velocity, $\bar{u},$ to centerline velocity, $u_{c},$ for $(\mathbf{a}) n=4$
(b) $n=6$
(c) $n=8$
(d) $n=10 .$ Compare the different velocity profiles.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:40

Problem 22

As shown in Fig. $P 5.22$, at the cntrance to a 3 -fl-wide channel the velocity distribution is uniform with a velocity $V$. Further downstream the velocity profile is given by $u=4 y-2 y^{2}$, where $u$ is in $\mathrm{ft} / \mathrm{s}$ and $y$ is in $\mathrm{ft}$. Determine the value of $V$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:19

Problem 23

The cross-sectional area of a rectangular duct is divided into 16 equal rectangular areas, as shown in Fig. P5.23. The axial fluid velocity measured in feet per second in each smaller area is given in the figure, Estimate the volume flowrate and average axial velocity.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:58

Problem 24

Oil for lubricating the thrust bearing shown in Fig. $\mathrm{P} 5.24$ flows into the space between the bearing surfaces through a circular inlet pipe with velocity
\[
u=U_{0}\left[1-\left(\frac{r}{R}\right)^{2}\right]
\]
where $R=1.5 \mathrm{mm}$. The oil has a specific gravity $S=0.86$ and flows in the inlet pipe at a rate o $0.006 \mathrm{kg} / \mathrm{s}$. Compute the average velocity $V_{\text {? }}$ of the oil in the inlet pipe and the average velocity $V_{2}$ at the outlet (plane 2 ) and the maximum velocity in the oil inlet pipe $\left(U_{0}\right) .$ Assume radial flow.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:13

Problem 25

Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in Fig. $\mathrm{P} 5.25$. This region of reduced flow is called a boundary layer. At the lcading edge of the plate, the velocity profile may be considered unformly distributed with a value $U$ All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also $U$. If the $x$ -dircction velocity profile at section (2) is
\[
\frac{u}{U}=\frac{3}{2}\left(\frac{y}{\delta}\right)-\frac{1}{2}\left(\frac{y}{\delta}\right)^{3}
\]
develop an expression for the volume flowrate through the edge of the boundary layer from the leading edge to a location downstream at $x$ where the boundary layer thickness is $\delta$.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:16

Problem 26

Air at standard conditions enters the compressor shown in Fig. $P 5.26$ at a rate of $10 \mathrm{ft}^{3} / \mathrm{s}$. It leaves the tank through a 1.2-in.- -diameter pipe with a density of 0.0035 slugs/ft' and a uniform speed of $700 \mathrm{ft} / \mathrm{s}$. (a) Determine the rate (slugsis) at which the mass of air in the tank is increasing or decreasing. (b) Determine the average time rate of change of air density within the tank.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:28

Problem 27

Estimate the time required to fill with water a cone-shaped container (see Fig. $P 5.27$ ) 5 ft high and 5 ft across at the top if the filling rate is 20 gal/min.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:12

Problem 28

For an automobile moving along a highway, descrite the control volume you would use to estimate the flowrate of air across the radiator. Explain how you would estimate the velocity of that air.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:35

Problem 29

A water jet leaves a fixed nozzle with a velacity of $10 \mathrm{m} / \mathrm{s}$. The jet diameter is $10 \mathrm{cm} .$ A $30^{\circ}$ cone is pushed into the water jet at a speed of $5 \mathrm{m} / \mathrm{s}$. The water impinges on the cone with the jet axis and the cone axis in perfect alignment so that the water is divided evenly by the cone. Bernoulli's equation suggests that because the pressure on the jet boundary is constant, the water velocity relative to the cone sirface is constant. Determine the thickness of the water stream when it reaches the base of the
cone.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:06

Problem 30

A hypodermic syringe (see Fig. $P 5.30$ ) is used to apply a vaccine. If the plunger is moved forward at the steady rate of $20 \mathrm{mm} / \mathrm{s}$ and if vaccine leaks past the plunger at 0.1 of the volume flowrate out the needle opening, calculate the average velocity of the needle exit flow. The inside diameters of the syringe ard the needle are $20 \mathrm{mm}$ and $0.7 \mathrm{mm}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:32

Problem 31

Figure $P 5.31$ shows a two-reservcir water supply system. The water level in reservoir 1 drops at the rate of $0.01 \mathrm{m} / \mathrm{min}$. and the water level in reservoir 2 drops at the rate of $0.015 \mathrm{m} /$ min. Calculate the average velocity $V_{3}$ in the 0.50 -m-diameter pipe.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:31

Problem 32

The Hoover Dam (see Video $V 2.4$ ) backs up the Colorado River and creates Lake Mead, which is approsimately 115 miles long and has a surface area of approximately 225 square miles. If during flcod conditions the Colorado River flows into the lake a: a rate of 45,000 cfs and the outflow from the dam is 8000 cfs, how many feet per 24 -hour day will the lake level rise?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:38

Problem 33

Storm sewer backup causes your basement to flood at the steady tate of 1 in. of depth per hour. The basement floor area is $1500 \mathrm{ft}^{2}$ What capacity (gal/min) pump would you rent to
(a) kecp the water eccumulated in your basement at a constant level urtil the storm sewer is blocked off. and
(b) reduce the water accumulation in ycur basement at a rate of 3 in fhr even while the backup problem exiss?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:33

Problem 34

(See The Wide World of Fluids erticle "Green' 1.6-gpf standards," Section 5.1.2.) When a toilet is flushed, the water deph, $h,$ in the tank as a function of time, $t$, is as given in the table. The size of the rectangular tank is 19 in. by 7.5 in.
(a) Determine the volume of water used per flush, gpf.
(b) Plot the flowrate for $0 \leq t \leq 6$ s.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:30

Problem 35

Find the force components $F_{x}$ and $F_{y}$ required to hold the box shown in Fig. P5.35 stationary. The fluid is oil and has specific gravity of $0.85 .$ Neglect gravity effects. Atmospheric pressure acts eround the entire bex. Steady flow conditions prevail.

Ajay Singhal
Ajay Singhal
Numerade Educator
View

Problem 36

When a bascball player catches a ball, the force of the ball on her glove is as shown as a function of time in Fig. $\mathrm{P} 5.36 .$ Describe how this situation is similar to the force generated by the deflection of a jet of water by a vane. Note: Consider many baseballs being caught in quick succession.

Victor Salazar
Victor Salazar
Numerade Educator
05:15

Problem 37

Find the horizontal and vertical forces to hold stationary the nozzle shown in Fig. P5.37. The fluid flowing through it is $10^{\circ} \mathrm{C}$ liquid water; $A_{1}=1.0 \mathrm{m}^{2}, A_{2}=0.25 \mathrm{m}^{2}, V_{1}=20 \mathrm{m} / \mathrm{s}, p_{2}=p_{\text {urm }}$ and $p_{1}=p_{\text {atm }}+30 \mathrm{kPa}$. Neglect gravity.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:18

Problem 38

Water flows through a horizontal bend and discharges into the atmosphere as showr in Fig. P5.38. When the pressure gage reads 10 psi, the resultant $x$ -direction anchoring force, $F_{A x}$ in the horizontal plane required to hold the bend in place is shown on the figure. Determine the flowrate through the bend and the $y$ -direction anchoring force, $F_{A v}$ required to hold the bend in place. The flow is not frictionless.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:38

Problem 39

Find the magnitude of the force $F$ required to hold the plate in Fig. $P 5.39$ stationary.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:44

Problem 40

Water enters the horizontal, circular cross-sectional, scdden contraction rozzle sketched in Fig. $\mathrm{P} 5.40$ at scction (1) with a uniformly distributed velocity of 25 ft 4 and a pressure of 75 psi. The water exits from the nozzle into the atmosphere at section (2) where the uniformly distribuied velocity is 100 IUs. Determine the axial component of the anchoring force required to hold the contruction in place.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:10

Problem 41

A trucs carrying chickens is too heavy for a bridge that it needs to cross. The empty truck is within the weight limits; with the chickens it is overweight. It is suggested that if one could get the chickens to fly around the truck (i.z.., by banging on the truck side) it would be safe to cross the bridge. Do you agree? Explain.

Narayan Hari
Narayan Hari
Numerade Educator
01:30

Problem 42

Exhaust (assumed to have the propertics of standard air) leaves the 4 -ft-diameter chimney shown in Video $V 5.4$ and Fig. $P 5.42$ with a speed of $6 \mathrm{ft} / \mathrm{s}$. Because of the wind, after a few diameters downstream the exhaust flows in a horizontal direction with the speed of the wind, 15 ft/s. Determine the horizontal component of the force that the blowing wind exerts on the exhaust gases.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:41

Problem 43

Air at $T_{1}=300 \mathrm{K}, p_{1}=303 \mathrm{kPa},$ and $V_{1}=0.5 \mathrm{m} / \mathrm{s}$ enters the Venturi shown in Fig. P5.43. The air leaves at $T_{2}=220 \mathrm{K}$ and $p_{2}=$ $101 \mathrm{kPa}: A_{1}=0.6 \mathrm{m}^{2}$ and $A_{2}=1.0 \mathrm{m}^{2}$. Calculate the horizontal
force required to hold the Venturi stationsry.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:41

Problem 44

Water flows steadily from a tank mcunted on a cart as shown in Fig. P5.44. After the water jet leaves the nozzle of the tank, it falls and strikes a vane attached to another cart. The cart's wheels are frictionless, and the fluid is inviscid. (a) Determine the speed of the water leaving the tank, $V_{1}$, and the water speed leaving the cart. $V_{2}$
(b) Determine the tension in rope $A$
(c) Determine the tension in rope $B$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:09

Problem 45

Detcrmine the magnitude and dircetion of the anchoring force needed to hold the horizontal elbow ard nozzle combimation shown in Fig. P5.45 in place. Atmospheric pressure is $100 \mathrm{kPa}(\mathrm{abs}) .$ The gage pressure at section (1) is $100 \mathrm{kPa}$. At sec tion $(2),$ the water exits to the atmosphere.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:04

Problem 46

Figure $\mathrm{PS} .46$ shows a lateral pipe fitting. This particular fitting has a mainline diameter of 4.0 in. The diameter of the lateral is 3.0 in. and the lateral angle is $45^{\circ} ; 60^{\circ} \mathrm{F}$ water is flowing in the lateral. Measurements show that the pressure at point 1 is 34.0 psig. the pressure at point 2 is 35.0 psig. the pressure at point 3 is 33.5 psig. and the flow rate at point 2 is $1.0 \mathrm{ft}^{3} / \mathrm{s}$. Determine the horizontal and vertical force components $\left(F_{x}$ and \right. $F_{y}$ ) required to hold the lateral fitting stationary. Neglect gravity. $Q_{1}=1.63 \mathrm{ft}^{3} / \mathrm{s}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:25

Problem 47

Water flows steadily between fixed vares, as shown in Fig. P5.47. Find the $x$ and $y$ components of the water's force on the vanes. The total volume flow rate is $100 \mathrm{m}^{3} / \mathrm{s}$, pressure $p_{1}=150 \mathrm{kPa},$ and pressure $p_{2}=101 \mathrm{kPa}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:00

Problem 48

The hydraulic dredge shown in Fig. P5.48 is used to drecige sand from a river bottom. Estimate the thrust needed from the propeller to hold the boat stationary. Assume the specific gravity of the sand/water mixture is $S G=1.4$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:19

Problem 49

A static thrust stand is to be designed for testing a specific jet engine, knowing the following conditions for a typical test.
\[
\begin{array}{c}
\text { intake air velocity }=700 \mathrm{ftfs} \\
\text { exhaust gas velocity }=1640 \mathrm{ft} \mathrm{s}
\end{array}
\]
intake cross section area $=10 \mathrm{ft}^{2}$
\[
\begin{aligned}
\text { intake static pressure } &=1.4 \mathrm{psia} \\
\text { intake static temperature } &=480^{\circ} \mathrm{R}
\end{aligned}
\]
exhaust gas pressure $=0 \mathrm{psi}$ Estimate a nominal thrust to design for.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:43

Problem 50

A vertical jet of water leaves a nozzle at a specd of $10 \mathrm{m} / \mathrm{s}$ and a diameter of $20 \mathrm{mm}$. It suspends a phate having a mass of $1.5 \mathrm{kg}$ as indicated in Fig. P5.50. What is the vertical distance $\mathrm{k}$ ?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:01

Problem 51

A horizontal, circular cross-sectional jet of air having a diameter of 6 in. strikes a conical deflector as shown in Fig. PS.51. A horizontal anchoring force of 5 lb is required to hold the cone in place. Estimate the nozzle flowrate in $\mathrm{ft}^{3} / \mathrm{s}$. The magnitude of the velocity of the air remains constant.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:11

Problem 52

Calculate the pressure change $\left(p_{2}-p_{1}\right)$ for the jet pump shown in Fig. P5.52. The fluid is $20^{\circ} \mathrm{C}$ watar. Assurre negligible friction at the walls and uniform pressure over each flow area.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:27

Problem 53

Air flows into the atmosphere from a nozzle and strikes a vertical plate as shown in Fig. P5.53. A horizontal force of 12 N is required to hold the plate in place. Determine the reading on the pressure gage. Assume the flow to be inconpressible and frictionless.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:14

Problem 54

Water flows from a large tank into a dish as shown in Fig. P5.54. (a) If at the instant shown the tank and the water in it weigh $W_{1}$ Ib, what is the tension, $T_{1},$ in the cable supporting the $\operatorname{ank} ?$
(b) If at the instant shown the dish and the water in it weigh $W_{2}$ Ib, what is the force, $F_{2}$, needed to support the dish?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:54

Problem 55

Figure $\mathrm{P} 5.55$ shows the configuration of the center (tailmounted) jet cngine on an airliner. The airliner is cruising at altitude, and the velocities shown are relative to an observer on board. Calculate the thrust force that the engine exerts on the airplane.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:07

Problem 56

The plate shown in Fig. $\mathrm{P} 5.56$ is $0.5 \mathrm{m}$ wide perpendicular to the paper. Calculate the velocity of the water jet required to hold the plate upright.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
08:43

Problem 57

Two water jets of equal size and speed strike each other as shown in Fig. $P 5.57 .$ Determine the speed, $V$, and direction, $\theta$, of the resulting combined jet. Gravity is negligible.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
00:52

Problem 58

Figure $P 5.58$ shows coal being dropped from a hopper onto a conveyor belt at a constant rate of $25 \mathrm{ft}^{3} / \mathrm{s}$. The coal has a specific gravity ranging from 1.12 to $1.50 .$ The balt has a speed of $5.0 \mathrm{ft} / \mathrm{s}$ and a loaded length of $15.0 \mathrm{ft}$. Estimate the torque required to turn the drive pulley of the conveyor belt. The drive pulley dianeter is $2.0 \mathrm{ft}$. Assume that there is no friction between the belt and the other rollers.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:57

Problem 59

Determine the magnitude of the horizontal componeat of the anchoring force required to hold in place the sluice gate shown in Fig. $5.59 .$ Compare this result with the size of the aorizontal component of the anchoring force required to hold in place the sluice gate when it is zlosed and the depth of water upstream is $10 \mathrm{ft}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:08

Problem 60

Water flows steadily into and oul of a tank that sits on frictionless wheels as stown in Fig. P5.60. Determine the diameter $D$ so that the tank remains motionless if $F=0$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:59

Problem 61

The rocket shown in Fig. P5.61 is held stationary by the horizontal force, $F_{s}$ and the vertical force, $F_{z}$. The velocity and pressure of the exhaust gas are 5000 flys and 20 psia at the nozzle ext, which has a cross section area of 60 in. $^{2}$. The exhaust mass flowrate is constant at $21 \mathrm{lbm} / \mathrm{s}$, Determine the value of the restraining force $F_{x}$ Assume the exhaust flow is essentially horizontal.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:14

Problem 62

Air discharges from a 2 -in.- -diameter nozyle and strikes a curved vane, which is in a vertical plane as shown in Fig. P5.62. A stagnation tube connected to a water U-tube menometer is located in the free air jet. Determine the horizortal component of the force that the air jet exerts on the vane. Neglec: the weight of the ar and all friction.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:24

Problem 63

Water is sprayed mdially outward over $180^{\circ}$ as indicated in Fig. $P 5.63 .$ The jet sheet is in the horizontal plare. If the jet velocity at the nozzle exit is $20 \mathrm{ft} / \mathrm{s}$, determine the direction and magnitude of the resultant horizontal anchoring force required to hold the nozzle in place.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:09

Problem 64

A sheet of water of uniform thickness $(h=0.01 \mathrm{m})$ flows from the device shown in Fig. P5.64. The water enters vertically through the inlet pipe and exits horizontally with a speed that varies linearly from 0 to $10 \mathrm{m} / \mathrm{s}$ alorg the 0.2 -m length of the slit. Determine the $y$ component of anchoring force necessary to hold this device stationary.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:13

Problem 65

The results of a wind tunnel test to determine the drag on a body (see Fig. $P 5.65$ ) are summarized below. The upstream [section $(1)]$ velocity is uniform at 100 ft/s. The static pressures are given by $p_{1}=p_{2}=14.7$ psia. The downstream velocity distribution, which is symmetrical about the centerline, is given by
\[
\begin{array}{ll}
u=100-30\left(1-\frac{|y|}{3}\right) & |y| \leq 3 \mathrm{ft} \\
u=100 & |y|>3 \mathrm{ft}
\end{array}
\]
where $u$ is the velocity in $f$ - $/$ s and $y$ is the distance on cither side of the centerline in feet (see Fig. $P 5.65$ ). Assume that the body shape does not change in the direction normal to the paper. Calculate the drag force (reaction force in $x$ direction) exerted on the air by the body per unit length normal to tice plane of the sketch.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:56

Problem 66

A variable mesh screen produces a linear and axisymmetric velocity profile as indicated in Fig. P5.66 in the airflow through a 2 -ft-diameter circular cross-sectional duct. The static pressures upsiream and downstream of the screen are 0.2 and 0.15 psi and are uniformly distributed over the flow cross-sectional area. Neglecting the force exerted by the duct wall on the flowing air, calculate the screen drag force.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:28

Problem 67

Consider unsteady flow in the constant diameter, horizontal pipe shown in Fig. P5.67. The velocity is uniform throughout the entire pipe, but it is a function of time: $\mathbf{V}=u(t)$ is the $x$ component of the unsteady momentum equation to determine the pressure difference $p_{1}-p_{2}$. Discuss how his result is related to $F_{x}=m a_{x}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:12

Problem 68

In a turbulent pipe flow that is fully developed, the axial velocity profile is.
\[
u=u_{c}\left[1-\left(\frac{r}{R}\right)\right]^{1 / 7}
\]
as is illustrated in Fig. $\mathrm{P} 5.68 .$ Compare the axial direction momentum flowrate calculated with the average velocity, $\bar{u},$ with the axial direction momentum flowrate calculated with the nonuniform velocity distribution taken into account.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:50

Problem 69

Water from a garden hose is sprayed against your car to rinse dirt from it. Estimate the force that the water exerts on the ca- List all assumptions and show calculations.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:42

Problem 70

A Pelton wheel vane directs a horizontal, circular cross sectional jet of water symmetrically as indicated in Fig. P5.70 and Video $V 5.6 .$ The jet leaves the nozzle with a velocity of $100 \mathrm{ft} / \mathrm{s}$. Determine the $x$ -direction component of anchoring force required to (a) hold the vane stationary.
(b) confine the speed of the vane to a value of 10 fus to the right. The fluid speed magnitude remains constant along the vane surface.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:28

Problem 71

The thrust developed to propel the jet ski shown in Video V9.18 and Fig. P5.71 is a result of water rumped through the vehicle and exiting as a high-speed water jet. For the conditions shown in the figure, what flowrate is needed to produce $=300$ -lb thrust? Assume the inlet and outlet jets of water are free jets.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:39

Problem 72

Thrust vector control is a technique that can be used to greatly improve the maneuverability of military fighter aircraft. It consists of using a set of vanes in the exit of a jet engine to deflect the exhaust gases as shown in Fig. P5.72.
(a) Determine the pitching moment (the moment tending to rotate the nose of the aircraft up) about the aircraft's mass center (cg) for the conditions indicated in the figure. (b) By how much is the thrust (force along the centerline of the aircraft) reduced for the case incicated compared to normal flight when the exhaust is parallel to the centerline?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:11

Problem 73

The exhaust gas from the rocket shown in Fig. P5.73 leaves the nozzle with a uriform velocity paralel to the $x$ axis. The gas is assumed to be discharged from the nozzle as a free jet. (a) Show that the thrust tat is developed is equal to $\rho A V^{2}$, where $A=\pi D^{2} / 4$. (b) The cxhaust gas from the rocket nozzle shown in Fig. $P 5.73 b$ is also uniform, but rather than being directed along the $x$ axis, it is directed along tays from point 0 as indicated. Determine the thrus for this rocket.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:57

Problem 74

(See The Wide World of Fluids article titled "Where the Plume goes," Section $5.2 .2 . .$ A flows into the jet engine shown in Fig. $P 5.74$ at a rate of 9 slugs/s and a speed of 300 fus. Upon Landing, the engine exhaust exits through the reverse thrust mechanism with a speed of $900 \mathrm{ft} / \mathrm{s}$ in the direction indicated. Determine the reverse thrust applied by the engine to the airplane. Assume the inlet and exit pressures are atmospheric and that the mass flowrate of fucl is negligible compared to the air flowrate through the engine.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:36

Problem 75

Figure $\mathrm{P} 5.75$ shows a sharp-edged splitter plate used to control the flow of a liquid jet $W$ units wide by $H_{1}$ units high. Write expressions for the deflection angle $\theta$ and he force $F$ of the jet on the splitter plate as a function cf the fluid density $\rho, H_{1}, W, V$ and plate insertion $h$. The force $F$ has no components parallel to the plate. Assume that the jet flow is inviscid, that the jet width $W$ remains constant, $H_{2} / H_{3}=H_{2}^{\prime} / H_{3}^{\prime}=h /\left(H_{1}-h\right),$ and constant fluid density.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:07

Problem 76

(See The Wide World of Fluids article titled "Motorized Surfboard," Section $5.2 .2 .$ ) The thrust to propel the powered surfboard shown in Fig. $\mathrm{P} 5.76$ is a reselt of water pumped through the board that exits as a high-speed 2.75 -in.- -diameter jet. Determine the flowrate and the velocity of the exiting jet if the thrust is to be 300 Ib, Neglect the momentum of the water entering the pump.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:43

Problem 77

(See The Wide World of Fluids article titled "Bow Thrusters," Section $5.2 .2 .$ ) The bow thruster on the boat shown in Fig. $P 5.77$ is used to turn the boat. The thruster produces a 1-m-diameter jet of water with a velocity of $10 \mathrm{m} / \mathrm{s}$, Determine the force produced by the thrusier. Assume that the inlet and outlet pressures are zero and that the momentum of the water enterirg the threster is negligible.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:27

Problem 78

Water flows from a two-dimensional open channel and is diverted by as inclined plate as illustrated in Fig. P5.78. When the velocity at section (1) is $10 \mathrm{ft} / \mathrm{s}$, what horizontal force (per unit width) is required to hold the plate in position? At section ( 1 ) the pressure distribution is hydrostatic, and the fluid acts as a free jet at section (2). Neglect friction.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
View

Problem 79

If a valve in a pipe is suddenly closed, a large pressure surge may develop. For example, when the electrically operated shutoff valve in a dishwasher closes quickly, the pipes supplying the dishwasher may rattle or "bang" because of this large pressure pulse. Explain the physical mechanism for this "water hammer" phenomenon. How could this phenomenon be analyzed?

James Kiss
James Kiss
Numerade Educator
02:23

Problem 80

A snowplow mounted on a truck clears a path 12 ft through heavy wet snow, as shown in Figure $\mathrm{P} 5.80$. The snow is 8 in. deep and its density is $10 \mathrm{lbm} / \mathrm{ft}^{3}$. The truck travels at $30 \mathrm{mph}$. The snow is discharged from the plow at an angle cf $45^{\circ}$ from the direction of travel and $45^{\circ}$ above the horizontal, as shown ir. Figure $\mathrm{PS} .80$. Estimate the force required to push the plow.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:48

Problem 81

An incompressible fluid flows outward through a blower as indicated in Fig. P5.81. The staff torque involved, $T$, is estimated with the following relationship:
\[
T_{\text {shan }}=\dot{m} r_{2} V_{p 2}
\]
where $\dot{m}=$ mass flowrate through the blower, $r_{2}=$ outer radius of blower, and $V_{a_{2}}=$ tangential component of absolute fluid velocity leaving the blower. State the flow conditions that make this formula valid.

Narayan Hari
Narayan Hari
Numerade Educator
00:51

Problem 82

Water at $60^{\circ} \mathrm{F}$ is flowing through the 2 -in. steel pipe shown in Fig. $\mathrm{P} 5.82$ at the rate of 90 gal/min. Determine the torque developed at the base where the pipe is supposed. Neglect the pipe and water weights. Steady-state conditions apply.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
08:34

Problem 83

Five liters/s of water enter the rotor shown in Video V5.10 and Fig. P5.83 along the axis of rotation. The crosssectional area of each of the three nozzle exits normal to the relative velocity is $18 \mathrm{mm}^{2}$. How large is the resisting torque required to hold the rotor stationary? How fast will the rotor spin steadily if the resisting torque is reduced to zero end
(a) $\theta=0^{\circ}$
(b) $\theta=30^{\circ}$
(c) $\theta=60^{\circ} ?$

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:34

Problem 84

Figure $P 5.84$ shows a simplificd skctch of a dist-washer water supply manifold. Find the resisting torque for a water temperature of $140^{\circ} \mathrm{F}, Q=0.25 \mathrm{gal} / \mathrm{min}$ and $\omega=3 \mathrm{rpm}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:43

Problem 85

The hydraulic turbine shown in Fig. $\mathrm{P} 5.85$ has a $10^{\circ} \mathrm{C}$ water flow rate of $36.4 \mathrm{m}^{3} / \mathrm{s},$ an inlet radius $R_{1}=1.0 \mathrm{n},$ an outlet radius $R_{2}=0.50 \mathrm{m},$ a blade depth (perpendicular to paper) $h=0.50 \mathrm{m}$ and a rotational speed $N=360 \mathrm{rpm} ; V_{1}=50 \mathrm{m} / \mathrm{s}, V_{2}=30 \mathrm{m} / \mathrm{s}$ $\alpha_{1}=13.4^{\circ},$ and $\alpha_{2}=40^{\circ} .$ Calculate the power iransferred by the fluid to the rotor, the inlet relative velocity $W_{1}$, and the direction $W_{1}$ makes with the radius at the inlet.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:57

Problem 86

A fan (see $\mathrm{Fi}_{2}$. $\mathrm{P} 5.86$ ) has a bladed rotor of 12 -in. outside diameter and 5 -in. inside diameter and runs at 1725 rpm. The width of each rotor blade is 1 in. from blade inlet to outlet. The volume flow rate is steady at $230 \mathrm{ft}^{3} / \mathrm{min}$, and the absolute velocity of the air at blade inlet, $V_{1},$ is purely adial. The blade discharge angle is $30^{\circ}$ measured with respect to the tangential direction at the outside diameter of the rotor.
(a) What would be a reasonable blade inlet angle (measured with respect to the tangential direction at the inside diameter of the rotor)?
(b) Find the power required to run the fan.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:36

Problem 87

Calculate the torque required to drive the pump shown in Fig. $P 5.87$ at $30 \mathrm{Hz}$ and to deliver $20^{\circ} \mathrm{C}$ water at $3.0 \mathrm{m}^{3} / \mathrm{min}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
04:17

Problem 88

An axial flow turbomachine rotor involves the upstream (1) and downstream (2) velocity triangles shown in Fig. P5.88. Is this turbomachine a turbine or a fan? Sketch an appropriate blade section and determine energy transferred per unit mass of fluid.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:42

Problem 89

An inward flow radial turbine (see Fig. P5.89) involves a nozzle angle, $\alpha_{1},$ of $60^{\circ}$ and an inlet rotor tip speed, $U_{1},$ of $6 \mathrm{m} / \mathrm{s}$. The ratio of rotor inlet to outlet diameters is 1.8 . The absolute velocity leavinz the rotor at section (2) is radial with a magnitude of $12 \mathrm{m} / \mathrm{s}$, Determine the energy transfer per unit mass of fluid flowing through this turbine if the fluid is
(a) air.
(b) water.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:25

Problem 90

A sketch of the arithmetic mean radius blade sections of an axial-flow water turbine stage is shown in Fig. P5.90. The rotor speed is 1000 rpm.
(a) Sketch and label velocity triangles for the flow entering and leaving the rotor row. Use $V$ for absolute velocity, $\mathbf{W}$ for relative velocity, and $\mathbf{U}$ for blade velocity. Assume flow enters and leaves each blade row at the blade angles stown.
(b) Calculate the work per unit mass delivered at the shaft.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
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Problem 91

Distinguish between shaft work and other kinds of work associated with a flowing fluid.

Nick Johnson
Nick Johnson
Numerade Educator
00:59

Problem 92

An incompressible fluid flows along a 0.20 -m-diameter pipe with a uniform velocity of $3 \mathrm{m} / \mathrm{s}$. If the pressure drop between the upsiream and downstream sections of the pipe is $20 \mathrm{kPa}$, determine the power transferred to the fluid due to fluid normal stresses.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:03

Problem 93

A horizontal Venturi flow meter consists of a convergingdiverging corduit as indicated in Fig. P5.93. The diameters of cross sections (1) and (2) are 6 and 4 in. The velocity and static pressure are uniformly distributed at cross sections (1) and $(2) .$ Determine the volume flowrate $\left(\mathrm{ft}^{3} / \mathrm{s}\right)$ through the meter if $p_{1}-p_{2}=3 \mathrm{psi}$ the flowing fluid is oil $\left(p=56 \mathrm{lbm} / \mathrm{ft}^{3}\right),$ and the loss per unit mass from (1) to (2) is negligibly $\operatorname{small}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:27

Problem 94

Figure $P 5.94$ shows the mixing of two streams. The shear stress between each fluid and its adjacent walls is negligible. Why can't Bernoulli's equation be applied between points in stream 1 and the mixed stream or between points in stream 2 and the mixed stream?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:50

Problem 95

Liquid water at $40^{\circ} \mathrm{F}$ flows down a vertical, thermally inselated. 2 -in. steel pipe. The temperature change of the water is related to its internal energy change by
\[
\tilde{u}_{2}-\tilde{u}_{1}=32.2 \mathrm{B} \mathrm{ta} / \mathrm{s} \operatorname{lug} \cdot^{\circ} \mathrm{F}\left(T_{2}-T_{1}\right)
\]
What is the temperature change of the water per $100 \mathrm{ft}$ of drop if the pressure drop $\left(p_{1}-p_{2}\right)$ per $100 \mathrm{ft}$ is $12.0 \mathrm{psi}$ ?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:08

Problem 96

A simplified schematic drawing of the carburetor of a gasoline $(S=0.75)$ engine is shown in Fig. $P 5.96 .$ The throat trea is 0.5 in. $^{2}$ The running engine draws air dowaward through the carburetor Venturi and maintains a throat pressure of 14.3 psia. The low throat pressure draws fuel from the float chamber and into the airstream. The chergy losses in the 0.07 -in.-diameter fuel metering line and valve are given by
\[
g h_{L}=\frac{K V^{2}}{2 g}
\]
where $\mathrm{K}=6.0$ and $V$ is the fuel velocty in the metering line. Assume that the air is an ideal fluid having a constant density $\rho_{A}$ $=0.075 \mathrm{lbm} / \mathrm{ft}^{3} .$ The atmospheric pressure is 14.7 psia. Calculate the air-to-fuel ratio $\left(\dot{m}_{2} / \dot{m}_{1}\right)$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:43

Problem 97

Oil $(S G=0.9)$ flows downward through a vertical pipe contraction as shown in Fig. P5.97. If the mercury manometer reading, $h$. is $100 \mathrm{mm}$, determine the volume flowrate for friction less flow. Is the actual flowrate more or less than the frictionless value? Explain.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:09

Problem 98

An incompressible liquid flows steadily along the pipe shown in Fig. P5.98. Determine the direction of flow and the head loss over the $6-m$ length of pipe.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:29

Problem 99

A siphon is used to draw water at $70^{\circ} \mathrm{F}$ from a large container as indicated in Fig. $P 5.99 .$ The inside Jiameter of the siphon line is 1 in. and the pipe centerline rises 3 ft above the essentially constant water level in the tank. Show that by varying the length of the siphon below the water level, $h$, the rate of flow through the siphon can be changed. Assuming frictionless flow, determine the maxi. mum flowrate possible through the siphon. The limiting condition is the occurrence of cavitation in the siphon. Will the actual maximum flow be more or less than the frictionless value? Explain.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
06:21

Problem 100

A water siphon having a constant inside diameter of 3 in. is arranged as shcwn in Fig. P5.100. If the friction loss between $A$ and $B$ is $0.8 V^{2} / 2,$ where $V$ is the velocity of flow in the siphon, determine the flowrate involved.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:56

Problem 101

Figure $P 5.101$ shows a test rig for evaluating the loss coefficient, $\mathrm{K}$, for a valve. Mechanical energy losses in valves are modeled by the equation:
\[
g h_{L}=K\left(\frac{V^{2}}{2}\right)
\]
where $g h_{L}$ is the mechancal energy loss and $V$ is the flow velocity entering the valve. In a particular test, the pressure gage reads $40 \mathrm{kPa},$ gage, and the $1.5-\mathrm{m}^{3}$ catch tank fills in $2 \mathrm{min}$ 55 s. Calculate the loss coefficient for a water temperature of $20^{\circ} \mathrm{C}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:11

Problem 102

For the $180^{\circ}$ elbow and nozzle flow shown in Fig. P5.102. determine the loss in available energy from section (1) to section
(2). How much additional available energy is lost from section (2) to where the water comes to rest?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
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Problem 103

An automobile engine will work test when the back pressure at the interface of the exhaust manifold and the engine block is minimized. Show how reduction of losses in the exhaust manifold. piping, and muffler will also reduce the back pressure. How could losses in the exhaust system be reduced? What primarily limits the minimization of exhaust system losses?

James Kiss
James Kiss
Numerade Educator
01:24

Problem 104

(Sec The Wide World of Fluids article titled "smart Shocks," Section $5.3 .3 . .$ A 200 -lb force epplied to the end of the piston of the shock absorber shown in Fig. P5.104 causes the two ends of the shock absorber to move toward each other with a speed of $5 \mathrm{ft} / \mathrm{s}$. Determine the head lossassociated with the flow of the oil through the channel. Neglect gravity and any friction force between the piston and cylinder walls.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:41

Problem 105

Based on flowrate and pressure rise information, estimate the power ou;put of a human heart.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:28

Problem 106

Oil $(S G=0.88)$ flows in an inclined pipe at a rate of $5 \mathrm{ft}^{3} / \mathrm{s}$ as shown in Fig. P5.106. If the differential reading in the mercury manometer is $3 \mathrm{ft}$, calculate the power that the punp supplies to the oil if head losses are negligible.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:33

Problem 107

The pumper truck shown in Fig. $P 5.107$ is to deliver $1.5 \mathrm{ft}^{3} / \mathrm{s}$ to a maximum elevation of $60 \mathrm{ft}$ above the hydrant. The pressure at the 4 -in. -diameter outlet of the hydrant is 10 psi. If head losses are negligibly small, determine the power that the pump must add to the water.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:47

Problem 108

The hydroelectric turbine shown in Fig. P5.108 passes 8 million gal/min across a head of 600 ft. What is the maximum amount of power output possible? Why will the actual amount be less?

Ajay Singhal
Ajay Singhal
Numerade Educator
01:08

Problem 109

A pump is to move water from a lake into a large, pressurized tank as shown in Fig. $\mathrm{P} 5.109$ at a rate of 1000 gal in 10 min or less. Will a pump that adds 3 hp to the water work for this purpose? Support your ansiver with appropriate calculations. Repeat the problem if the tank were pressurized to $3,$ rather than $2,$ atmospheres.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:28

Problem 110

Water is pumped from the tank shown in Fig. P5.110c. The head loss is known to be $1.2 \mathrm{V}^{2} / 2 \mathrm{g}$. where $V$ is the average velocity in the pipe. According to the pump manufacturer, the xelationship between the pump head and the flowrate is as shown in Fig. $\mathrm{P} 5.110 b: \mathrm{h}_{p}=20-2000 \mathrm{Q}^{2},$ where $h_{p}$ is in meters and $Q$ is in $\mathrm{m}^{3} / \mathrm{s}$. Detcrmine the flowrate, $Q$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:55

Problem 111

Water is pumped steadily through the apparatus shown in Fig. $P 5.111 .$ The pipe area and gage pressure are shown for both outlet sections 1 and $2 .$ Assume that the $40 \%$ water is frictionless and incorrpressible. Compute the horsepower input to the pump. The total volume flow rate $Q_{T}=1.0 \mathrm{ft}^{3} / \mathrm{s}, D_{a}=4.0 \mathrm{in.}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:56

Problem 112

Water is pumped from the large tank shown in Fig. P5.1 12 The head loss is known to be equal to $4 V^{2} / 2 g$ and the pump head is $h_{p}=2 C-4 Q^{2},$ where $h_{p}$ is in ft when $Q$ is in $\mathrm{ft}^{3} / \mathrm{s}$. Determine the flowrate.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:49

Problem 113

Water flows by gravity from one lake to another as sketched in Fig. $P 5.113$ at the steady rate of 80 gpm. What is the loss in available cnergy associated with this flow? If this same amount of loss is associated with pumping the fluid from the lower lake to the higher one at the same flowrate, estimate the amount of pumping power required.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:53

Problem 114

The turbine shown in Fig. P5.1 14 develops 100 hp when the flowrate of water is $20 \mathrm{ft}^{3} / \mathrm{s}$. If all losses are negligible, determine
(a) the elevation $h$
(b) the pressure difference across the turbine, and (c) the flowrate expected if the turbine were removed.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:55

Problem 115

Figure $\mathrm{P} 5.115$ shows a pump testing setup. Water is drawn from a sump and pumped through a pipe containing a valve. The water is discharged into a catch tank sitting on a scale. During a test run, 800 lb of water is collected in the catch tank in 15 s. The pump power input to the fluid during this period is $700 \mathrm{ft} \cdot \mathrm{lb} / \mathrm{s}$ Calculate the water velocity in the pipe and the mechanical energy loss $\left(\mathrm{ft} \cdot \mathrm{lb} / \mathrm{lb}_{\mathrm{m}}\right)$ in the pipe and valve.

Prashant Bana
Prashant Bana
Numerade Educator
01:37

Problem 116

Water is to be mored from one large reservoir so another at a higher elevation as indicated in Fig. $\mathrm{P} 5.116$. The loss of available energy associated with $2.5 \mathrm{ft}^{3} / \mathrm{s}$ being pumped from sections (1) to 2 ) is loss $=61 \mathrm{V}^{2} / 2 \mathrm{ft}^{2} / \mathrm{s}^{2}$, where $V$ is the average velocity of water in the 8 -in. inside-diameter piping involved. Determine the amount of shaft power required.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:31

Problem 117

Determine the volume flow rate and minimum power input to the water pump in Fig. $\mathrm{P} 5.117$. Determine the actual power if the hydraulic efficiency is $75 \%$ and losses in the motor and bearings are negligible.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:33

Problem 118

A pump moves water horizontally at a rate of $0.02 \mathrm{m}^{3} / \mathrm{s}$ Upstream of the pump where the pipe dianeter is $90 \mathrm{mm}$, the pressure is $120 \mathrm{kPa}$. Downstream of the pump where the pipe diameter is $30 \mathrm{mm}$, the pressure is $400 \mathrm{kPa}$. If the loss in energy across the purnp due to fluid friction effects is $170 \mathrm{N} \cdot \mathrm{m} / \mathrm{kg}$, determine the hydraulic efficiency of the pump.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:03

Problem 119

Water is to be pumped from the large tank shown ir Fig. P5.1 19 with an exit velocity of $6 \mathrm{m} / \mathrm{s}$. It was determined that the original pump (pump 1) that supplies 1 kW of power to the water did not produce the desired velocity. Hence, it is proposed that an additional pump (pump 2 ) be installed as indicated to increase the flowrate to the desired value. How much power must pump 2 add to the water? The head loss for this flow is $h_{l}=250 Q^{2}$, where $h_{l}$ is in $\mathrm{m}$ when $Q$ is in $\mathrm{m}^{3} / \mathrm{s}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:40

Problem 120

(See The Wide World of Fluids article titled "Curtain of Air." Section $5.3 .3 .$. The fan shown in Fig. P5.120 produces an air curtain to separate a loading dock from a cold storage room. The air curtain is a jet of air 10 ft wide, 0.5 ft thick moving with speed $V=30 \mathrm{ft} / \mathrm{s}$. The loss associated with this flow is loss $=K_{1} V^{2} / 2$. where $K_{L}=5 .$ How much power must the fan supply to the air to produce this flow?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:00

Problem 121

When the pump shown in Fig, $P \leqslant .121$ is stopped, there is no flow through the system and the spring force is zero. Wih the pump running, a 6 -in.- -diameter jet leaves the pipe, and the spring force is 420 lb. The water surface elevaticn in the tank is constant. Determine the water flow rate and the power consumed ty the pump. Assume quasi-steady flow.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
View

Problem 122

Air flows past an object in a pipe of 2 -m diameter and exits as a free jet as shown in Fig. $\mathrm{P} 5.122 .$ The velocity and pressure upstream are uniform at $10 \mathrm{m} / \mathrm{s}$ and $50 \mathrm{N} / \mathrm{m}^{2}$, respectively. At the pipe exit the velocity is nonuniform as indicated. The shear stress along the pipe wall is negligible.
(a) Determine the head loss associated with a particle as it flows from the uniform velocity upstream of the object to a location in the wake at the exit plane of the pipe.
(b) Determine the force that the air exerts on the object.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
View

Problem 123

Near the downstream end of a river spillway, a hydraulic jump often forms, as illustrated in Fig. P5.123 and Video V10.11. The velocity of the channel flow is reduced abruptly across the jump. Using the conservation of mass and linear momentum principles, derive the following expression for $h_{i}$
\[
h_{2}=-\frac{h_{1}}{2}+\sqrt{\left(\frac{h_{1}}{2}\right)^{2}+\frac{2 V_{1}^{2} h_{1}}{g}}
\]
The loss o " available energy across the jump can also be determined if energy conservation is considered. Derive the loss expression
\[
\text { jump loss }=\frac{g\left(h_{2}-h_{1}\right)^{3}}{4 h_{1} h_{2}}
\]

Victor Salazar
Victor Salazar
Numerade Educator
03:42

Problem 124

Water flows steadily down the inclined pipe as indicated in Fig P5.124. Determine the following:
(a) the difference in
(b) the loss between sections (1) and (2) pressure $p_{1}-p_{2}$
(c) the net axial force exerted by the pirce wall on the flowing water between sections (1) and (2)

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:24

Problem 125

When fluid flows through an abrupt expansion as indicated in Fig. $\mathrm{P} 5.125$, the loss in available energy across the expansion. $\operatorname{loss}_{c_{c}}$ is often expressed as
\[
\operatorname{loss}_{e x}=\left(1-\frac{A_{1}}{A_{2}}\right)^{2} \frac{V_{1}^{2}}{2}
\]
where $A_{1}=$ cross-sectional area upsiream of expansion, $A_{2}=$ cross-sectional area downstream of expansion, and $V_{1}=$ velocity of flow upstream of expansion. Derive this relationship.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
03:43

Problem 126

Water $\left(60^{\circ} \mathrm{F}\right)$ flows through an annular space formed by inserting a 1 -in.-radius solid cylinder into a 1.5 -in. -radius tube. The following axial velocities were measured in the arnular space.
Assume that the no-slip condition $(x=0)$ exists at the solid boundaries. What are the rates of mass, momentun, and kinetic energy flow through the annular space?

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
00:55

Problem 127

Find the acceleration of the cart shown in Fig. $\mathrm{P} 5.127$ as a function of the water height in the cart, which varies with time. The initial total mass is $m_{0},$ and the fluid density is $\rho_{0}$. Assume frictionless bearings, a frictionless surface, constant fluid density, uniform velocity over area $A_{N}$, all the fluid in the cart has the cart velocity. no air drag, and $A \gg A_{\mathrm{V}}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
11:55

Problem 128

Two water jets collide and form one homogeneous jet as shown in Fig. $P 5.128 .$ (a) Determine the speed, $V$, and direction. $\theta,$ of the combined jet. (b) Determine the less for a fluid particle flowing from (1) to (3), from (2) to (3). Gravity is negligible.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:30

Problem 129

Water flows vertically upward in a circular cross-sectional pipe. At section $(1),$ the velocity profile over the cross-sectional area is uniform. At section (2) , the velocity profile is
\[
\mathbf{V}=w_{r}\left(\frac{R-r}{R}\right)^{1 / n}
\]
where $\mathbf{V}=$ local velocity vector, $w_{c}=$ centerline velocity in the axial direction, $R=$ pipe inside radius, and $r=$ radius from pipe axis. Develop an expression for the loss in available energy between sections (1) and (2)

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
04:48

Problem 130

Calculate the kinetic energy correction factor for each of the following velocity profiles for a circular pipe:
(a) $u=u_{\max }\left(1-\frac{r}{R}\right)$
(b) $u=u_{\max }\left(1-\frac{r^{2}}{R^{2}}\right)$
(c) $u=u_{\max }\left(1-\frac{r}{R}\right)^{1 / 7}$

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
05:01

Problem 131

The cross-sectional area of a rectangular duct is divided into 16 equal rectangular areas, as shown in Fig. P5.131. The axial fluid velocity measured in feet per second in each smaller area is shown. Estimate the kinetic energy correction factor.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
04:14

Problem 132

$ \mathrm{A}$ small fan moves air $\mathrm{x}$, a mass flowrate of $0.004 \mathrm{lbm} / \mathrm{s}$ Upstream of the fan, the pipe diameter is 2.5 in.., the flow is laminar, the velocity distribution is parabolic, and the kinetic energy coefficient, $a_{1},$ is equal to $2.0 .$ Downstream of the fan, the pipe diameter is 1 in. the flow is turbulent, the velocity profile is quite flat, and the kinetic energy coefficient, $a_{2},$ is equal to $1.08 .$ If the rise in static pressure across the fan is 0.015 psi and the fan shaft draws 0.00024 hp, compare the value of loss calculated:
(a) assuming uniform velocity distributions,
(b) considering actual velocity distributions.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:15

Problem 133

Air enters a radial blower with zero angular momentum. It leaves with an absolute tangential velocity, $V_{a}$ of $200 \mathrm{fls}$, The roter blade speed at rotor exit is 170 fUs. If the stagnation pressure rise across the rotor is 0.4 psi, calculate the loss of arailable energy across the rotor and the rotor efficiency.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:17

Problem 134

Water enters a pump impeller radially, It leaves the impeller with a tangential component of absolute velocity of $10 \mathrm{m} / \mathrm{s}$. The impeller exit diameter is $60 \mathrm{mm}$, and the impeller speed is $1800 \mathrm{rpm}$. If the stagnation pressure rise across the impeller is 45 kpa, determine the loss of available energy across the impeller and the hydraulic efficiency of the pump.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
01:42

Problem 135

Water enters an axial-flow turbine rotor with an absolute velocity tangential component, $V_{\theta},$ of 15 fus. The corresponding blade velocity, $U,$ is $50 \mathrm{ft} / \mathrm{s}$. The water leaves the rotor blade row with no angular momentum. If the stagnation pressure drop across the turbine is 12 psi, determine the hydraulic efficiency of the turbine.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:24

Problem 136

An inward flow radial turbine (see Fig. P5.136) involves a nozzle angle, $a_{1},$ of $60^{\circ}$ and an inlet rotor tip speed, $U_{1},$ of 30 ft $/ \mathrm{s}$. The ratio of rotor inlet to outlet diameters is $2.0 .$ The radial component of velocity remains constant at 20 ft/s through the rotor, and the flow leaving the rotor at section (2) is without angular momentum. If the flowing fluid is water and the stagnation pressure drop across the rotor is 16 psi, determine the loss of available energy across the rotor and the hydraulic efficiency involved.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator