Fundamentals of Fluid Mechanics

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

Chapter 8

Viscous Flow in Pipes - all with Video Answers

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Chapter Questions

Problem 1

Under normal circumstances is the airflow though your trachea (your windpipe) laminar or furbulent? List all assumptions and show all calculations.

Chai Santi

Chai Santi

Numerade Educator

Problem 2

Rainwater runoff from a parking lot flows through a 3-ft-diameter pipe, completely filling it. Whether flow in a pipe is laminar or turbulent depends on the value of the Reynolds number. (See Video V8.2.) Would you expect the flow to be laminar or turbulent? Support your answer with appropriate calculations.

Narayan Hari

Numerade Educator

Problem 3

Blue and yellow streams of paint at $60^{\circ} \mathrm{F}$ (each with a density of 1.6 slugs/ft $^{3}$ and a viscosity 1000 times greater than water) enter a pipe with an average velocity of 4 ft as shown in Fig. P8.3. Would you expect the paint to exit the pipe as green paint or separate streams of blue and yellow paint? Explain. Repeat the problem if the paint were "thinned" so that it is only 10 times more viscous than water. Assume the density remains the same.

Narayan Hari

Numerade Educator

Problem 4

Air at $200^{\circ} \mathrm{F}$ flows at standard atmospheric pressure in a pipe at a rate of $0.08 \mathrm{lb} / \mathrm{s}$. Determine the minimum diameter allowed if the flow is to be laminar.

Narayan Hari

Numerade Educator

Problem 5

To cool a given room it is necessary to supply $4 \mathrm{ft}^{3} / \mathrm{s}$ of air through an 8 -in.-diameter pipe. Approximately how long is the entrance length in this pipe?

Narayan Hari

Numerade Educator

Problem 6

The flow of water in a 3 -mm-diameter pipe is to remain laminar. Plot a graph of the maximum flowrate allowed as a function of temperature for $0<T<100^{\circ} \mathrm{C}$

Chai Santi

Numerade Educator

Problem 7

The pressure distribution measured along a straight, horizontal portion of a 50 -mm-diameter pipe attached to a tank is shown in the table below, Approximately how long is the entrance length? In the fully developed portion of the flow, what is the value of the wall shear stress?

Chai Santi

Numerade Educator

Problem 8

(See The Wide World of Fluids article titled "Nanoscale Flows," Section $8.1 .1 .)$ (a) Water flows in a tube that has a diameter of $D=0.1 \mathrm{m} .$ Determine the Reynolds number if the average velocity is 10 diameters per second. (b) Repeat the calculations if the tube is a nanoscale tube with a diameter of $D=100 \mathrm{nm}$

Narayan Hari

Numerade Educator

Problem 9

For fully developed laminar pipe flow in a circular pipe, the velocity profile is given by $u(r)=2\left(1-r^{2} / R^{2}\right)$ in $\mathrm{m} / \mathrm{s},$ where $R$ is the inner radius of the pipe. Assuming that the pipe diameter is $4 \mathrm{cm},$ find the maximum and average velocities in the pipe as well as the volume flow rate.

Narayan Hari

Numerade Educator

Problem 10

A viscous fluid flows in a 0.10 -m-diameter pipe such that its velocity measured $0.012 \mathrm{m}$ away from the pipe wall is $0.8 \mathrm{m} / \mathrm{s}$ If the flow is laminar, determine the centerline velocity and the flowrate.

Narayan Hari

Numerade Educator

Problem 11

The wall shear stress in a fully developed flow portion of a 12-in.-diameler pipe carrying water is 1.85 Ib/ft? Determine the pressure gracient, $\partial p / \partial x,$ where $x$ is in the flow direction, if the pipe is (a) horizontal,
(b) vertical with flow up, or
(c) vertical with flow down.

Narayan Hari

Numerade Educator

Problem 12

The pressure drop needed to force water through a horizontal 1 -in.-tiameter pipe is 0.60 psi for every 12 -ft length of pipe. Determine the shear stress on the pipe wall. Determine the shear stress at distances 0.3 and 0.5 in. away from the pipe wall.

Narayan Hari

Numerade Educator

Problem 13

Repeat Problem 8.12 if the pipe is on a $20^{\circ}$ till. Is the flow up or down the hill? Explain.

Narayan Hari

Numerade Educator

Problem 14

Water flows in a constant-diameter pipe with the following conditions measured: At section (a) $p_{a}=32.4$ psi and $z_{a}=56.8 \mathrm{ft}$ at section
(b) $p_{b}=29.7$ psi and $z_{b}=68.2 \mathrm{ft}$. Is the flow from
(a) to (b) or from (b) to (a)? Explain.

Chai Santi

Numerade Educator

Problem 15

For laminar flow in a round pipe of diameter $D,$ at what distance from the centerline is the actual velocity equal to the average velocity?

Narayan Hari

Numerade Educator

Problem 16

Glycerin at $20^{\circ} \mathrm{C}$ flows upward in a vertical 75 -mm-diameter pipe with a centerline velocity of $1.0 \mathrm{m} / \mathrm{s}$. Determine the head loss and pressure drop in a 10 -m length of the pipe.

Chai Santi

Numerade Educator

Problem 17

Water at $60^{\circ} \mathrm{F}$ flows at a rate of $4.0 \mathrm{gal} / \mathrm{min}$ through a $6-\mathrm{in}$ I.D. plastic pipe. The pipe is 500 ft long and rises a vertical height of $40 \mathrm{ft}$ over the $500 \mathrm{ft}$. Find the pressure drop.

Narayan Hari

Numerade Educator

Problem 18

At time $t=0$ the level of water in tank $A$ shown in Fig. P8.1 8 is 2 ft above that in $\tan k B$. Plot the elevation of the water in $\tan \mathrm{k} A$ as a function of time until the free surfaces in both tanks are at the same elevation. Assume quasisteady conditions that is, the steady pipe flow equations are assumed valid at any time, even though the flowrate does change (slowly) in time. Neglect minor losses, Note: Verify and use the fact that the flow is laminar.

Keshav Singh

Numerade Educator

Problem 19

A fluid flows through a horizontal 0.1-in.-diameter pipe. When the Reynolds number is $1500,$ the head loss over a $20-f t$ lenzth of the pipe is $6.4 \mathrm{ft}$. Determine the fluid velocity.

Narayan Hari

Numerade Educator

Problem 20

Asphalt at $120^{\circ} \mathrm{F}$, considered to be a Newtonian fluid with a viscosity 80,000 times that of water and a specific gravity of 1.09 flows through a pipe of diameter 2.0 in. If the pressure gradient is 1.6 psi/ft determine the flowrate assuming the pipe is
(a) horizontal;
(b) vertical with flow up.

Chai Santi

Numerade Educator

Problem 21

Oil of $S G=0.87$ and a kinematic viscosity $\nu=2.2 \times 10^{-4}$ $\mathrm{m}^{2} / \mathrm{s}$ flows through the vertical pipe shown in Fig. $\mathrm{P} 8.21$ at a rate of $4 \times 10^{-4} \mathrm{m}^{3} / \mathrm{s}$. Determine the manometer reading, $h$

Chai Santi

Numerade Educator

Problem 22

A liquid with $S G=0.96, \mu=9.2 \times 10^{-4} \mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2},$ and vapor pressure $p_{\nu}=1.2 \times 10^{4} \mathrm{N} / \mathrm{m}^{2}(\text { abs })$ is drawn into the syringe as is indicated in Fig $\mathrm{P} 8.22 .$ What is the maximum flowrate if cavitation is not to occur in the syringe?

Rashmi Sinha

Numerade Educator

Problem 23

A 3 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.) carries 210 'F SAE 40 crankcase oil at the rate of 6.0 gal/min. The oil specific gravity is $0.89,$ and the absolute viscosity is $6,6 \times 10^{-7} 1 \mathrm{b} \cdot$ sec/ft $^{2}$. For the same pressure drop, what must the acw pipe size be to carry the oil at 10.7 gal/min?

Vipender Yadav

Numerade Educator

Problem 24

A 3 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.) carries $210^{\circ} \mathrm{F}$ SAE 40 crankcase oil at the rate of 6.0 gal/min. The oil specific gravity is $0.89,$ and the absolute viscosity is $6.6 \times 10^{-7} 1 \mathrm{b} \cdot \mathrm{sec} / \mathrm{ft}^{2} .$ Calculate the pipe size required to carry the same flow rate at approximately one-half the pressure drop of the 3 -in. pipe. Both pipes are horizontal.

Narayan Hari

Numerade Educator

Problem 25

Water at $20^{\circ} \mathrm{C}$ flows down a vertical pipe with no pressure drop. Find the range of pipe diameters $D$ (if any) for which the flow is definitely laminar

Narayan Hari

Numerade Educator

Problem 26

A person is donating blood. The pint bag in which the blood is collected is initially flat and is at atmospheric pressure. Neglect the initial mass of air in the $1 / 8$ -in. I.D., 4 ft-long plastic tube carrying blood to the bag. The average blood pressure in the vein is $40 \mathrm{mm}$ Hg above atmospheric pressure. Estimate the time required for the person to donate one pint of blood. Assume that blood has a specific gravity of 1.06 and a viscosity of $1.0 \times$ $10^{-4} 1 b \cdot \sec / f t^{2},$ The needle's I.D. is $1 / 16$ inch and the needle length is 2.0 in. The bag is $1.0 \mathrm{ft}$ below the needle inlet and the vein's I.D. is $1 / 8$ in. Optional: Donate a pint of blood and check your answer.

Ameer Said

Numerade Educator

Problem 27

For oil $\left(S G=0.86, \mu=0.025 \mathrm{Ns} / \mathrm{m}^{2}\right)$ flow of $0.2 \mathrm{m}^{3} / \mathrm{s}$ through a round pipe with diameter of $500 \mathrm{mm}$, determine the Reynolds number. Is the flow laminar or turbulent?

Narayan Hari

Numerade Educator

Problem 28

As shown in Video V8.10 and Fig. P8.28, the velocity profile for laminar flow in a pipe is quite different from that for turbulent flow. With laminar flow the velocity profile is parabolic; with turbulent flow at $\mathrm{Re}=10.000$ the velocity profile can be approximated by the power-law profile shown in the figure.
(a) For laminar flow, determine at what radial location you would place a Pitot tube if it is to measure the average velocity in the pipe.
(b) Repeat part (a) for turbulent flow with $\mathrm{Re}=10,000$

Chai Santi

Numerade Educator

Problem 29

Water at $10^{\circ} \mathrm{C}$ flows through a smooth 60 -mm-diameter pipe with an average velocity of $8 \mathrm{m} / \mathrm{s}$. Would a layer of rust of height $0.005 \mathrm{mm}$ on the pipe wall protrude through the viscous sublayer? Justify your answer with appropriate calculations.

Chai Santi

Numerade Educator

Problem 30

When soup is stirred in a bowl, there is considerable turbulence in the resulting motion (see Video $\mathrm{V} 8.7$ ). From a very simplistic standpoint, this turbulerce consists of numerous intertwined swirls, each involving a characteristic diameter and velocity. As time goes by, the smaller swirls (the fine scale structure) die out relatively quickly, leaving the large swirls that continue for quite some time. Explain why this is to be expected.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 31

Water at $60^{\circ} \mathrm{F}$ flows through a 6 -in.-diameter pipe with an average velocity of $15 \mathrm{ft} / \mathrm{s}$. Approximately what is the height of the largest roughness element allowed if this pipe is to be classified as smooth?

Narayan Hari

Numerade Educator

Problem 32

Water is pumped between two tanks as shown in Fig. P8.32. The energy line is as indicated. Is the fluid being pumped from $A$ to $B$ or $B$ to $A$ ? Explain. Which pipe has the larger diameter: A to the pump or $B$ to the pump? Explain.

Narayan Hari

Numerade Educator

Problem 33

A person with no experience in fluid mechanics wants to estimate the friction factor for 1 -in.-diameter galvanized iron pipe at a Reynolds number of 8,000 . The person stumbles across the simple equation of $f=64 / \mathrm{Re}$ and uses this to calculate the friction factor. Explain the problem with this approach and estimate the error.

Narayan Hari

Numerade Educator

Problem 34

During a heavy rainstorm, water from a parking lot completely fills an 18 -in.-diameter, smooth, concrete storm sewer. If the flowrate is $10 \mathrm{ft}^{3} / \mathrm{s}$, determine the pressure drop in a $100-\mathrm{ft}$ horizontal section of the pipe. Repeat the problem if there is a $2-f t$ change in elevation of the pipe per 100 ft of its length.

Ameer Said

Numerade Educator

Problem 35

Water flows through a horizontal plastic pipe with a diameter of $0.2 \mathrm{m}$ at a velocity of $10 \mathrm{cm} / \mathrm{s}$. Determine the pressure drop per meter of pipe and the power lost to the friction per meter of pipe.

Narayan Hari

Numerade Educator

Problem 36

Water flows downward through a vertical 10 -mm-diameter galvanized iron pipe with an average velocity of $5.0 \mathrm{m} / \mathrm{s}$ and exits as a free jet. There is a small hole in the pipe $4 \mathrm{m}$ above the outlet. Will water leak out of the pipe through this hole, or will air enter into the pipe through the hole? Repeat the problem if the average velocity is $0.5 \mathrm{m} / \mathrm{s}$

Ameer Said

Numerade Educator

Problem 37

Air at standard conditions flows through an 8 -in.-diameter 14.6-ft-long, straight duct with the velocity versus head loss data indicated in the following table. Determine the average friction factor over this range of data.

Ameer Said

Numerade Educator

Problem 38

Water flows through a horizontal 60 -mm-diameter galvanized iron pipe at a rate of $0.02 \mathrm{m}^{3} / \mathrm{s}$. If the pressure drop is 135 kPa per $10 \mathrm{m}$ of pipe, do you think this pipe is (a) a new pipe,
(b) an old pipe with a somewhat increased roughness due to aging, or (c) a very old pipe that is partially clogged by deposits? Justify your answer.

Ameer Said

Numerade Educator

Problem 39

Water flows at a rate of 10 gallons per minute in a new horizontal 0.75 -in.- diameter galvanized iron pipe. Determine the pressure gradient, $\Delta p / \ell,$ along the pipe.

Narayan Hari

Numerade Educator

Problem 40

Carbon dioxide at a temperature of $0^{\circ} \mathrm{C}$ and a pressure of $600 \mathrm{kPa}(\text { abs })$ flows through a horizontal $40-\mathrm{mm}$ -diameter pipe with an average velocity of $2 \mathrm{m} / \mathrm{s}$. Determine the friction factor if the pressure drop is $235 \mathrm{N} / \mathrm{m}^{2}$ per 10 -m length of p pe.

Narayan Hari

Numerade Educator

Problem 41

{ Blood iassume } \mu=4.5 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}, S G=1.0\right)$ flows
through an artery in the neck of a giraffe from its heart to its head at a rate of $2.5 \times 10^{-4} \mathrm{ft}^{3} / \mathrm{s}$. Assume the length is $10 \mathrm{ft}$ and the diameter is 0.20 in. If the pressure at the beginning of the artery (outlet of the heart) is equivalent to $0.70 \mathrm{ft}$ Hg, determine the pressure at the end of the artery when the head is (a) 8 ft above the heart, or
(b) 6 ft below the heart. Assume steady flow. How much of this pressure difference is due to elevation effects, and how much is due to frictional effects?

Ameer Said

Numerade Educator

Problem 42

A 40 -m-long, 12 -mm-diameter pipe with a friction factor of 0.020 is used to siphon $30^{\circ} \mathrm{C}$ water from a tank as shown in Fig. P8.42. Determine the maximum value of $h$ allowed if there is to be no cavitation within the hose. Neglect minor losses

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 43

Gasolire flows in a smooth pipe of $40-\mathrm{mm}$ diameter at a rate of $0.001 \mathrm{m}^{3} / \mathrm{s}$. If it were possible to prevent turbulence from occurring, what would be the ratio of the head loss for the actual turbulent flow compared to that if it were laminar flow?

Narayan Hari

Numerade Educator

Problem 44

A 3 -ft-diameter duct is used to carry ventilating air into a vehicular tunnel at a rate of $9000 \mathrm{ft}^{3} / \mathrm{min}$. Tests show that the pressure drop is 1.5 in. of water per 1500 ft of duct. What is the value of the friction factor for this duct and the approximate size of the equivalent roughness of the surface of the duct?

Ameer Said

Numerade Educator

Problem 45

H. Blasius correlated data on turbulent friction factor in smooth pipes. His equation $f_{\text {smooth}}=0.3164 \mathrm{Re}^{-1 / 4}$ is reasonably accurate for Reynolds numbers between 4000 and $10^{5}$. Use this information for the following scenario. Water at $20^{\circ} \mathrm{C}$ is to flow through a $3-\mathrm{cm}$ I.D. plastic pipe at the rate of $0.001 \mathrm{m}^{3} / \mathrm{s}$. Find the inc ine angle of the pipe needed to make the static pressure constant along the pipe.

Ameer Said

Numerade Educator

Problem 46

Von Karman suggested that the whclly turbulent friction factor be expressed by the equation $$f=\frac{1}{4[0.57-\log (\varepsilon / D)]^{2}}$$ where $\varepsilon$ is the absolute roughness of the pipe. Compare the values preticted by this equation and those indicated on the Moody chart.

Narayan Hari

Numerade Educator

Problem 47

The Swamee and Jain formula for the friction factor is $$f=\frac{0.25}{\left[\log \left(\varepsilon / 3.7 D+5.74 / \mathrm{Re}^{0.9}\right)\right]^{2}}$$ Compare this equation for $\varepsilon / D=0.00001,0.0001,0.001,$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.

Ameer Said

Numerade Educator

Problem 48

The Haaland formula for the friction factor is $$f=\frac{0.3086}{\left\{\log \left[6.9 / \mathrm{Rc}+(\varepsilon / 3.7 D)^{1.11}\right]\right\}^{2}}$$ Compare this equation for $f$ for $\varepsilon / D=0.00001,0.0001,0.001$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.

Ameer Said

Numerade Educator

Problem 49

The Churchill formula for the friction factor is $$f=8\left[\left(\frac{8}{\mathrm{Re}}\right)^{12}+\frac{1}{(A+B)^{15}}\right]^{1 / 12}$$ where $$\begin{array}{l}
A=\left\{-2.457 \ln \left[\left(\frac{7}{\mathrm{Re}}\right)^{0.9}+\frac{\varepsilon}{3.7 D}\right]\right\}^{16} \\
B=\left(\frac{37.530}{\mathrm{Re}}\right)^{16}
\end{array}$$
Compare this equation for $f$ for both the laminar and turbulent regimes for $\varepsilon / D=0.00001,0.0001,0.001,$ and 0.01 and Reynolds numbers of $10,10^{2}, 10^{3}, 10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.

Ameer Said

Numerade Educator

Problem 50

Air at standard temperature and pressure flows through a 1-in.-diameter galvanized iron pipe with an average velocity of $8 \mathrm{ft} / \mathrm{s} .$ What length of pipe produces a head loss equivalent to
(a) a flanged $90^{\circ}$ elbow,
(b) a wide-open angle valve, or (c) sharp-edged entrance?

Narayan Hari

Numerade Educator

Problem 51

Given $90^{\circ}$ threaded elbows used in conjunction with copper pipe (drawn tubing) of 0.75 -in. diameter, convert the loss for a single elbow to equivalent length of copper pipe for wholly turbulant flow.

Narayan Hari

Numerade Educator

Problem 52

To conserve water and energy, a "flow reducer" is installed in the shower head as shown in Fig. P8.52. If the pressure at point (1) remains constant and all losses except for that in the flow redacer are neglected, determine the value of the loss coefficient (based on the velocity in the pipe) of the flow reducer if its presence is to reduce the flowrate by a factor of $2 .$ Neglect gravity.

Ameer Said

Numerade Educator

Problem 53

Water flows at a rate of $0.040 \mathrm{m}^{3} / \mathrm{s}$ in a 0.12 -m-diameter pipe that contains a sudden contraction to a 0.06 -m-diameter pipe. Determine the pressure drop across the contraction section. How much of this pressure difference is due to losses and how much is due to kinetic energy changes?

Ameer Said

Numerade Educator

Problem 54

Water flows from the container shown in Fig. P8.54. Determine the loss coefficient needed in the valve if the water is to "bubble up" 3 in. above the outlet pipe. The entrance is slightly rounded.

Ameer Said

Numerade Educator

Problem 55

(See The Wide World of Fluids article titled "New Hi-tech Fountains," Section $8.5 .$.) The fountain shown in Fig. $\mathrm{Pg} .55$ is designed to provide a stream of water that rises $h=10 \mathrm{ft}$ to $h=20 \mathrm{ft}$ above the nozzle exit in a periodic fashion. To do this the water from the pool enters a pump, passes through a pressure regulator that maintains a constant pressure ahead of the flow control valve. The valve is electronically adjusted to provide the desired water height. With $h=10 \mathrm{ft}$ the loss coefficient for the valve is $K_{L}=$
50. Determine the valve loss coefficient needed for $h=20 \mathrm{ft}$. All losses except for the flow control valve are negligible. The area of the pipe is 5 times the area of the exit nozzle.

Ameer Said

Numerade Educator

Problem 56

Water flows through the screen in the pipe shown in Fig. P8.56 as indicated. Determine the loss coefficient for the screen.

Ameer Said

Numerade Educator

Problem 57

Air flows though the mitered bend shown in Fig. $\mathrm{P} 8.57$ at a rate of 5.0 cfs. To help straighten the flow after the bend, a set of 0.25 -in.-diameter drinking straws is placed in the pipe as shown. Estimate the extra pressure drop between points (1) and (2) caused by these straws.

Ameer Said

Numerade Educator

Problem 58

As shown in Fig. $\mathrm{P} 8.58,$ water flows from one tank to another through a short pipe whose length is $n$ times the pipe diameter. Head losses occur in the pipe and at the entrance and exit. (See Video V8.10.) Determine the maximum value of $n$ if the major loss is to be no more than $10 \%$ of the minor loss and the friction factor is 0.02

Narayan Hari

Numerade Educator

Problem 59

Water flows steadily through the 0.75 -in.-diameter galvanized iron pipe system shown in Video V8.16 and Fig. P8.59 at a rate of 0.020 cfs. Your boss suggests that friction losses in the straight pipe sections are negligible compared to losses in

Narayan Hari

Numerade Educator

Problem 60

Given two rectangular ducts with equal cross-sectional area but different aspect ratios (width/height) of 2 and $4,$ which will have the greater frictional losses? Explain your answer

Ameer Said

Numerade Educator

Problem 61

A viscous oil with a specific gravity $S G=0.85$ and a viscosity of 0.10 Pa $\cdot$ s flows from tank $A$ to tank $B$ through the six rectangular slots indicated in Fig. P8.61. If the total flowrate is $30 \mathrm{mm}^{3} / \mathrm{s}$ and minor losses are negligible, determine the pressure in $\tan \mathrm{k} A$

Anand Jangid

Numerade Educator

Problem 62

Air at standard temperature and pressure flows at a rate of 7.0 cfs through a horizontal, galvanized iron duct that has a rectangular cross-sectional shape of 12 in. by 6 in. Estimate the pressure drop per 200 ft of duct.

Narayan Hari

Numerade Educator

Problem 63

Water at $20^{\circ} \mathrm{C}$ flows through a concentric annulus of inner diameter $D_{1}=2.0 \mathrm{cm}$ and outer diameter $D_{2}=4.0 \mathrm{cm} .$ The surface roughness is $0.002 \mathrm{cm} .$ Calculate the frictional pressure loss per unit length for a flow rate of $0.01 \mathrm{m}^{3} / \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 64

Air at standard conditions flows through a horizontal 1 ft by 1.5 ft rectangular wooden duct at a rate of $5000 \mathrm{ft}^{3} / \mathrm{min}$. Determine the head loss, pressure drop, and power supplied by the fan to overcome the flow resistance in 500 ft of the duct.

Ameer Said

Numerade Educator

Problem 65

Assume a car's exhaust system can be approximated as $14 \mathrm{ft}$ of 0.125 -ft-diameter cast-iron pipe with the equivalent of six $90^{\circ}$ flanged elbows and a muffler. (See Video V8.14.) The muffler acts as a resistor with a loss coefficient of $K_{t}=8.5 .$ Determine the pressure at the beginning of the exhaust system if the flowrate is $0.10 \mathrm{cfs},$ the temperature is $250^{\circ} \mathrm{F}$, and the exhaust has the same properties as air.

Ameer Said

Numerade Educator

Problem 66

The pressure at section (2) shown in Fig. $\mathrm{P} 8.66$ is not to fall below 60 psi when the flowrate from the tank varies from 0 to 1.0 cfs and the branch line is shut off. Determine the minimum height, $h,$ of the water tank under the assumption that (a) minor losses are negligible, (b) minor losses are not negligible.

Ameer Said

Numerade Educator

Problem 67

Repeat Problem 8.66 with the assimption that the branch line is open so that half of the flow from the tank goes into the branch, and half continues in the main line.

Ameer Said

Numerade Educator

Problem 68

The $\frac{1}{2}$ -in.- diameter hose shown in Fig. $P 8.68$ can withstand a maximum pressure of 200 psi without rupturing. Determine the maximum length, $\ell,$ allowed if the friction factor is 0.022 and the flowrate is 0.010 cfs. Neglect minor losses.

Ameer Said

Numerade Educator

Problem 69

The hose shown in Fig. P8.69 will collapse if the pressure within it is lower than 10 psi below atmospheric pressure. Determine the maximum length, $\ell$, allowed if the friction factor is 0.015 and the flowrate is 0.010 cfs. Neglect minor losses.

Ameer Said

Numerade Educator

Problem 70

According to fire regulations in a town, the pressure drop in a commercial steel horizontal pipe must not exceed 1.0 psi per 150 ft of pipe for flowrates up to 500 gal/min. If the water temperature is above $50^{\circ} \mathrm{F}$, can a 6 -in.-diameter pipe be used?

Ameer Said

Numerade Educator

Problem 71

As shown in Video $V 8.15$ and Fig. $P 8.71,$ water "bubbles up" 3 in. above the exit of the vertical pipe attached to three horizontal pipe segments. The total length of the 0.75 -in. diameter galvanized iron pipe between point (1) and the exit is 21 in. Determine the pressure needed at point
(1) to produce this flow.

Ameer Said

Numerade Educator

Problem 72

Water at $10^{\circ} \mathrm{C}$ is pumped from a lake as shown in Fig. P8.72. If the flowrate is $0.011 \mathrm{m}^{3} / \mathrm{s}$, what is the maximum length inlet pipe, $\ell,$ that can be used without cavitation occurring?

Ameer Said

Numerade Educator

Problem 73

At a ski resort, water at $40^{\circ} \mathrm{F}$ is pumped through a $3-\mathrm{in}$. diameter, 2000 -ft-long steel pipe from a pond at an elevation of $4286 \mathrm{ft}$ to a snow-making machine at an elevation of $4623 \mathrm{ft}$ at a rate of $0.26 \mathrm{ft}^{3} / \mathrm{s}$. If it is necessary to maintain a pressure of $180 \mathrm{psi}$ at the snow-making machine, determine the horsepower added to the water by the pump. Neglect minor losses.

Ameer Said

Numerade Educator

Problem 74

Crude oil having a specific gravity of 0.80 and a viscosity of $6.0 \times 10^{-5} \mathrm{ft}^{2} / \mathrm{sec}$ flows through a pumping station at a rate of 10,000 barrels/hr. The oil then flows through 120,000 ft of 24 -in.
ID, horizontal, commercial steel pipe, enters another pumping station at 20 psig, and leaves at a discharge pressure equal to the discharge pressure of the previous pumping station. Calculate the discharge pressures and the power supplied to the crude oil at the second pumping station. See Fig. P8.74.

Ameer Said

Numerade Educator

Problem 75

A motor-driven centrifugal pump delivers $15^{\circ} \mathrm{C}$ water at the rate of $10 \mathrm{m}^{3} / \mathrm{min}$ from a reservoir, through a 2500 -m-long, $30-\mathrm{cm} 1 . \mathrm{D} .$ plastic pipe, to a second reservoir. The water level in the second reservoir is $40 \mathrm{m}$ above the water level in the first reservoir. The pump efficiency is $75 \% .$ Find the motor output power. The pipe entrance is square edged.

Rashmi Sinha

Numerade Educator

Problem 76

An emergency flooding system for a nuclear reactor core is shown in Fig. P8.75. Find the power input required to flood the core at the rate of 5000 gal/min. Assume a square-edged entrance, $60^{\circ} \mathrm{F}$ water, and threaded connections.

Ameer Said

Numerade Educator

Problem 77

A hydraulic turbine takes water from a lake with the piping system shown in Figure $\mathrm{P} 8.77$. Find the head $h_{f}$ available to the turbine for flow rates of $0,5000,10,000,15,000,$ and $20,000 \mathrm{ft}^{3} / \mathrm{min}$

Ameer Said

Numerade Educator

Problem 78

Water flows through a 2 -in.-diameter pipe with a velocity of $15 \mathrm{ft} / \mathrm{s}$ as shown in Fig. $\mathrm{P} 8.78 .$ The relative roughness of the pipe is 0.004 , and the loss coefficient for the exit is $1.0 .$ Determine the height, $h,$ to which the water rises in the piezometer tube.

Narayan Hari

Numerade Educator

Problem 79

Figure $P 7.79$ shows the $60^{\circ} \mathrm{F}$ water flow rates from the branches of a main supply line. Find the total pressure drop $\left(p_{A}-p_{F}\right)$ for soldered copper pipe. Assume that the loss coefficient for each tee is based on the threaded type.

Penny Riley

Numerade Educator

Problem 80

Water is pumped through a $60-\mathrm{m}$ -long, 0.3 -m-diameter pipe from a lower reservoir to a higher reservoir whose surface is $10 \mathrm{m}$ above the lower one. The sum of the minor loss cocfficient for the system is $K_{L}=14.5 .$ When the pump adds $40 \mathrm{kW}$ to the water the flowrate is $0.20 \mathrm{m}^{3} / \mathrm{s}$. Determine the pipe roughness.

Ameer Said

Numerade Educator

Problem 81

Natural gas $\left(\rho=0.0044 \mathrm{slugs} / \mathrm{ft}^{3} \text { and } \nu=5.2 \times 10^{-5} \mathrm{ft}^{2} / \mathrm{s}\right)$ is pumped through a horizontal 6 -in.- -diameter cast-iron pipe at
a rate of 800 lb/hr. If the pressure at section (1) is 50 psi (abs), determine the pressure at section (2) $8 \mathrm{mi}$ downstream if the flow is assumed incompressible. Is the incompressible assumption reasonable? Explain.

Ameer Said

Numerade Educator

Problem 82

As shown in Fig. $P 8.82,$ a standard household water meter is incorporated into a lawn irrigation system to measure the volume of water applied to the lawn. Note that these meters measure volume, not volume flowrate. (See Video V8.16.) With an upstream pressure of $p_{1}=50$ psi the meter registered that $120 \mathrm{ft}^{3}$ of water was delivered to the lawn during an "on" cycle. Estimate the upstream pressure, $p_{1},$ needed if it is desired to have $150 \mathrm{ft}^{3}$ delivered during an "on" cycle. List any assumptions needed to arrive at your answer.

Ameer Said

Numerade Educator

Problem 83

A fan is to produce a constant air speed of $40 \mathrm{m} / \mathrm{s}$ throughout the pipe loop shown in Fig. $\mathrm{P} 8.83 .$ The 3 -m-diameter pipes are smooth, and each of the four $90^{\circ}$ elbows has a loss coefficient of $0.30 .$ Determine the power that the fan adds to the air.

Narayan Hari

Numerade Educator

Problem 84

A fan is to produce a constant air speed of $40 \mathrm{m} / \mathrm{s}$ throughout the pipe loop shown in Fig. $\mathrm{P} 8.83 .$ The 3 -m-diameter pipes are smooth, and each of the four $90^{\circ}$ elbows has a loss coefficient of $0.30 .$ Determine the power that the fan adds to the air.

Narayan Hari

Numerade Educator

Problem 85

The turbine shown in Fig. $\mathrm{P} 8.85$ develops $400 \mathrm{kW}$. Determine the flowrate if (a) head losses are negligible or (b) head loss due to friction in the pipe is considered. Assume $f=0.02 .$ Note: There may be more than one solution or there may be no solution to this problem.

Ameer Said

Numerade Educator

Problem 86

Water flows from the nozzle attached to the spray tank shown in Fig. $\mathrm{P} 8.86 .$ Determine the flowrate if the loss coefficient for the nozzle (based on upstream conditions) is 0.75 and the friction factor for the rough hose is 0.11

Ameer Said

Numerade Educator

Problem 87

Water flows through the pipe shown in Fig. $P 8.87 .$ Determine the net tension in the bolts if minor losses are neglected and the wheels on which the pipe rests are frictionless.

Ameer Said

Numerade Educator

Problem 88

When the pump shown in Fig. $\mathrm{P} 8.88$ adds 0.2 horsepower to the flowing water, the pressures indicated by the two gages are equal. Determine the flowrate.

Narayan Hari

Numerade Educator

Problem 89

The pump shown in Fig. $P 8.89$ adds $25 \mathrm{kW}$ to the water and causes a flowrate of $0.04 \mathrm{m}^{3} / \mathrm{s}$. Determine the flowrate expected if the pump is removed from the system. Assume $f=0.016$ for either case and neglect minor losses.

Ameer Said

Numerade Educator

Problem 90

The vented storage tank shown in Fig. $\mathrm{P} 8.90$ is used to refuel race cars at a race track. A total of $40 \mathrm{ft}$ of steel pipe $(\mathrm{I.D},=0.957 \text { in. })$ two $90^{\circ}$ regular elbows, and a globe valve make up the system. Calculate the time needed to put 20 gal of fuel in a car tank. The pressures, $p_{2}$ and $p_{1},$ are aqual, the connections are threaded, and the fuel has the properties of $68^{\circ} \mathrm{F}$ normal octane $\left(\nu=8.31 \times 10^{-6} \mathrm{ft}^{2} / \mathrm{s}\right)$

Ajay Singhal

Numerade Educator

Problem 91

Gasoline is unloaded from the tanker truck shown in Fig. P8.91 through a 4 -in.-diameter rough-surfaced hose. This is a "gravity dump" with no pump to enhance the flowrate. It is claimed that the 8800 -gallon capacity truck can be unloaded in 28 minutes. Do you agree with this claim? Support your answer with appropriate calculations.

Narayan Hari

Numerade Educator

Problem 92

Calculate the water flow rate in the system shown in Fig. P8.92. The piping system includes four gate valves, two half-open globe valves, fourteen $90^{\circ}$ regular elbows, and 250 ft of 2 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 2.067 in.). Assume threaded connections and a square-edged pipe entrance.

Rashmi Sinha

Numerade Educator

Problem 93

The pump shown in Fig. $P 8.93$ delivers a head of 250 ft to the water. Determine the power that the pump adds to the water. The difference in elevation of the two ponds is $200 \mathrm{ft}$

Ajay Singhal

Numerade Educator

Problem 94

For the standpipe system shown in Fig. $\mathrm{P} 8.94$, calculate the flow rate for $H=4.0 \mathrm{ft}, D=6.77$ in. $, d=0.125$ in. $,$ and $L=48$ in. The fluid is $70^{\circ} \mathrm{F}$ water. Assume steady flow and neglect the energy loss in the entrance nozzle. The pipe is commercial steel.

Ameer Said

Numerade Educator

Problem 95

Water flows through two sections of the vertical pipe shown in Fig. $\mathrm{P} 8.95$. The bellows connection cannot support any force in the vertical direction. The 0.4-ft-diameter pipe weights 0.2 $1 \mathrm{b} / \mathrm{ft}$ and the friction factor is assumed to be $0.02 .$ At what velocity will the force, $F$, required to hold the pipe be zero?

Ameer Said

Numerade Educator

Problem 96

Water is circulated from a large tank, through a filter, and back to the tank as shown in Fig. $\mathrm{P} 8.96 .$ The power added to the water by the pump is $200 \mathrm{ft} \cdot 1 \mathrm{b} / \mathrm{s}$. Determine the flowrate through the filter.

Ajay Singhal

Numerade Educator

Problem 97

A thief siphoned 15 gal of gasoline from a gas tank in the middle of the night. The gas tank is 12 in. wide, 24 in. long, and 18 in. high and was full when the thief started. The siphoning plastic tube has an inside diameter of 0.5 in. and a length of $4.0 \mathrm{ft}$. Assume that at any instant of time, the steady-state mechanical energy equation is adequate to predict the gasoline flow rate through the tube. As 15 gal is 3465 in $^{3}$, the gasoline level in the tank will drop 12.0 in. You may use the gasoline level after it has dropped 6.0 in. to estimate the average gasoline flow rate. Use this flow rate to estimate the time needed to siphon the 15 gal of gasoline. Compare your answer with the answer of 190 sec found in problem 3.107 using Bernoulli's equation. The siphon cischarges at the level of the bottom of the gasoline tank. You may find it useful to use the Blasius equation for smooth pipes found in problem 8.45

Hast Aggarwal

Numerade Educator

Problem 98

Estimate the time required for the water depth in the reservoir shown in Fig. $\mathrm{P} 8.98$ to drop from a height of $25 \mathrm{m}$ to $5 \mathrm{m}$. The connections are threaded.

Ameer Said

Numerade Educator

Problem 99

Sheldon and Leonard come home from a long day of studying to discover that their basement is flooded with water. They have a submersible pump for such an emergency and connect the pump discharge to a 12 -ft-long garden hose, as shown in Fig. P8.99. The garden hose may be considered a smooth plastic pipe with a 1.0 -in. indside diameter. If the initial water depth is 6.0 in. and the pump has an input power of 0.25 hp and an overall efficiency of $0.60,$ how long will it take to pump out the basement? The pump inlet piping length is negligible, and the garden hose outlet is $7.0 \mathrm{ft}$ above the basement floor.

Ameer Said

Numerade Educator

Problem 100

A company markets ethylene glycol antifreeze in halfgal bottles. A machine fills and caps the bottles at a rate of 60 per minute. The $68^{\circ} \mathrm{F}$ ethylene glycol $\left(\rho=69.3 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}, v=1.93 \times\right.$ $\left.10^{-4} \mathrm{ft}^{2} / \mathrm{s}\right)$ is pumped to the machine from a tank $36 \mathrm{ft}$ away. The pressure at the discharge of the pump is 35 psig, and the pressure at the inlet to the filling machine must be at least 15 psig. Determine the diameter necessary for drawn copper pipe. The pipe has no elevation change.

Ronald Prasad

Numerade Educator

Problem 101

A certain process requires 2.3 cfs of water to be delivered at a pressure of 30 psi. This water comes from a large-diameter supply main in which the pressure remains at 60 psi. If the galvanized iron pipe connecting the two locations is 200 ft long and contains six threaded $90^{\circ}$ elbows, determine the pipe diameter. Elevation differences are negligible.

Ameer Said

Numerade Educator

Problem 102

Water is pumped between two large open reservoirs through $1.5 \mathrm{km}$ of smooth pipe. The water surfaces in the two reservoirs are at the same elevation. When the pump adds $20 \mathrm{kW}$ to the water, the flowrate is $1 \mathrm{m}^{3}$ is. If minor losses are negligible, determine the pipe diameter.

Narayan Hari

Numerade Educator

Problem 103

Determine the diameter of a steel pipe that is to carry 2000 gal/min of gasoline with a pressure drop of 5 psi per 100 ft of horizontal pipe.

Narayan Hari

Numerade Educator

Problem 104

Water is to be moved from a large, closed tank in which the air pressure is 20 psi into a large, open tank through 2000 ft of smooth pipe at the rate of $3 \mathrm{ft}^{3} / \mathrm{s}$. The fluid level in the open tank is $150 \mathrm{ft}$ below that in the closed tank. Determine the required diameter of the pipe. Neglect minor losses.

Ameer Said

Numerade Educator

Problem 105

A commercial steel flow channel in a heat exchanger has an equilateral triangle cross section with each side measuring 5.0 in. and a length measuring 96.0 in. Water at $60^{\circ} \mathrm{F}$ flowing through the channel has a pressure loss of 0.10 psi. Find the water flow rate.

Ameer Said

Numerade Educator

Problem 107

Repeat Problem 8.106 if the downspout is circular.

Ameer Said

Numerade Educator

Problem 108

For a given head loss per unit length, what effect on the flowrate does doubling the pipe diameter have if the flow is (a) laminar, or (b) completely turbulent?

Narayan Hari

Numerade Educator

Problem 109

It is necessary to deliver $270 \mathrm{ft}^{3} / \mathrm{min}$ of water from reservoir $A$ to reservoir $B,$ as shown in Fig. $\mathrm{P} 8.109 .$ The connecting piping consists of four fully open gate valves, twelve regular $90^{\circ}$ elbows, one swing check valve, two fully open globe valves, and 3000 ft of commercial steel pipe. Find the minimum diameter for steel pipe needed to obtain this flow rate. All fittings and valves have flanged connections. Assume a square-edged entrance.

Ameer Said

Numerade Educator

Problem 110

A 10 -m-long $, 5.042$ -cm I.D. copper pipe has two fully open gate valves, a swing check valve, and a sudden enlargement to a $9.919-\mathrm{cm}$ I.D. copper pipe. The $9.919 \mathrm{cm}$ copper pipe is $5.0 \mathrm{m}$ Iong and then has a sudden contraction to another 5.042 -cm copper pipe. Find the head loss for a $20^{\circ} \mathrm{C}$ water flow rate of $0.05 \mathrm{m}^{3} / \mathrm{s}$

Chai Santi

Numerade Educator

Problem 111

Air, assumed incompressible, flows through the two pipes shown in Fig. P8.11 1. Determine the flowrate if minor losses are neglected and the friction factor in each pipe is $0.015 .$ Determine the flowrate if the 0.5 -in.-diameter pipe were replaced by a 1 -in. diameter pipe. Comment on the assumption of incompressibility.

Ameer Said

Numerade Educator

Problem 112

Repeat Problem 8.111 if the pipes are galvanized iron and the friction factors are not known a priori.

Ameer Said

Numerade Educator

Problem 113

Estimate the power that the human heart must impart to the blood to pump it through the two carotid arteries from the heart to the brain. List all assumptions and show all calculations.

Ameer Said

Numerade Educator

Problem 114

Normal octane at $68^{\circ} \mathrm{F}\left(\nu=8.31 \times 10^{-6} \mathrm{ft}^{2} / \mathrm{s}\right)$ is to be delivered at a flow rate of 3.0 gal/min through a 2.0 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 2.067 in.). Energy losses are important, so consideration is being given to expanding the pipe to a 3.0 -in. schedule 40 commercial steel pipe (with an actual inside diameter of 3.068 in.), using a $10^{\circ}$ conical expansion. After a length $\ell$ of the 3.0 -in. pipe, it is decreased to a 2.0 - in. schedule 40 commercial steel pipe with a gradual contraction $(\mathbf{K}=0.10,$ based on the smaller diameter pipe flow). Find the minimem length $\ell$ so that the energy loss will be the same as in a 2.0 -in. pipe of length $\ell+2(5.7 \text { in })$ See Fig. $P 8.114$

Ajay Singhal

Numerade Educator

Problem 115

The flowrate between tank $A$ and tank $B$ shown in Fig. P8.1 15 is to be increased by $30 \%$ (i.e., from $Q$ to $1.30 Q$ ) by the addition of a second pipe (indicated by the dotted lines) running from node $C$ to tank $B$. If the elevation of the free surface in tank $A$ is 25 ft above that in $\operatorname{tank} B,$ determine the diameter, $D,$ of this new pipe. Neglect minor losses and assume that the friction factor for each pipe is 0.02

Ameer Said

Numerade Educator

Problem 116

A 250 ft-high building has a 6.065 -in.-diamcter steel standpipe and a 100 -ft-long $2 \frac{9}{16}$ -in. diameter fire hose on each floor. The nearest fireplag is $100 \mathrm{ft}$ from the standpipe's ground-level connection. Assume that fire-fighters connect a 6 -in.- -diameter, 50 -ft-long fire hose from the fireplug to the fire truck and a 4-in.- -diameter. 50-ft-long fire hose from the fire truck to the standpipe's groundlevel connection. The National Fire Protection Association (NFPA) requires that a minimum pressure of 65 psig be meintained at the connection of the $2 \frac{9}{16}$ -in.- -diameter hose and the standpipe while maintaining a flow rate of 500 gal/min through the fire hose. What pressure rise must the pump on the fire engine supply to satisfy the NFPA requirement for this building? The fire hydrant water pressure is 80 psiz and the water temperature is $60^{\circ} \mathrm{F}$. The connections are threaded.

Chai Santi

Numerade Educator

Problem 117

With the valve closed, water flows from tank $A$ to $\tan k B$ as shown in Fig. $\mathrm{P} 8.117 .$ What is the flowrate into $\tan \mathrm{k} B$ when the valve is opened to allow water to flow into tank $C$ also? Neglect all minor losses and assume that the friction factor is 0.02 for all pipes.

Ameer Said

Numerade Educator

Problem 118

Repeat Problem 8.117 if the friction factors are not known. but the pipes are steel pipes.

Ameer Said

Numerade Educator

Problem 119

The three water-filled tanks shown in Fig. $P 8.119$ are connected by pipes as indicated. If minor losses are neglected, determine the flowrate in each pipe.

Ameer Said

Numerade Educator

Problem 120

(See The Wide World of Fluids article titled "Deepwater Pipeline," Section $8.5 .2 .$ ) Five oil fields, each producing an output of $Q$ barrels per day, are connected to the 28 -in.- -diameter "mainline pipe" $(A-B-C)$ by 16 -in. -diameter "lateral pipes" as shown in Fig. $\mathrm{P} 8.120 .$ The friction factor is the same for each of the pipes and elevation effects are negligible. (a) For section $A-B$ determine the ratio of the pressure drop per mile in the mainline pipe to that in the lateral pipes.
(b) Repeat the calculations for section $B-C$

Ameer Said

Numerade Educator

Problem 121

As shown in Fig. $\mathrm{P} 8.121,$ cold water $\left(T=50^{\circ} \mathrm{F}\right)$ flows from the water meter to either the shower or the hot water heater. In the hot water heater it is heated to a temperature of $150^{\circ} \mathrm{F}$ Thus, with equal amounts of hot and cold water, the shower is at a comfortable $100^{\circ} \mathrm{F}$. However, when the dishwasher is turned on. the shower water becomes too cold. Indicate how you would predict this new shower temperature (assume the shower faucet is not adjusted). State any assumptions needed in your analysis.

Victor Salazar

Numerade Educator

Problem 123

Water flows through the orifice meter shown in Fig $\mathrm{P} 8.122$ such that $h=1.6 \mathrm{ft}$ with $d=1.5$ in. Determine the flowrate.

Narayan Hari

Numerade Educator

Problem 124

Water flows through the orifice meter shown in Fig. $\mathrm{P} 8.122$ at a rate of $0.10 \mathrm{cfs} .$ If $h=3.8 \mathrm{ft},$ determine the value of $d$

Ameer Said

Numerade Educator

Problem 125

Water flows through a 40 -mm-diameter nozzle meter in a 75-mm-diameter pipe at a rate of $0.015 \mathrm{m}^{3} / \mathrm{s}$. Determine the pressure difference across the nozzle if the temperature is
(a) $10^{\circ} \mathrm{C}$
or
(b) $80^{\circ} \mathrm{C}$

Ameer Said

Numerade Educator

Problem 126

Gasoline flows through a 35 -mm-diameter pipe at a rate of $0.0032 \mathrm{m}^{3} / \mathrm{s}$. Determine the pressure drop across a flow nozzle placed in the line if the nozzle diameter is $20 \mathrm{mm}$

Narayan Hari

Numerade Educator

Problem 127

Air at $200^{\circ} \mathrm{F}$ and 60 psia flows in a 4-in.-diameter pipe at a rate of 0.52 Ib/s. Determine the pressure at the 2 -in.- -diameter throat of a Venturi meter placed in the pipe.

Narayan Hari

Numerade Educator

Problem 128

A 2.5 -in.-diameter flow nozzle meter is installed in a 3.8 -in.- diameter pipe that carries water at $160^{\circ} \mathrm{F}$. If the air-water manometer used te measure the pressure difference across the meter indicates a reading of $3.1 \mathrm{ft}$, determine the flowrate

Narayan Hari

Numerade Educator

Problem 129

A 0.064 -m-diameter nozzle meter is installed in a 0.097 -m-diameter pipe that carries water at $60^{\circ} \mathrm{C}$. If the inverted air-water U-tube manometer used to measure the pressure difference across the meter indicates a reading of $1 \mathrm{m}$, determine the flowrate.

Ameer Said

Numerade Educator

Problem 130

A 50 -mm-diameter nozzle meter is installed at the end of a $80-\mathrm{mm}$ -diameter pipe through which air flows. A manometer attached to the static pressure tap just upstream from the nozzle indicates a pressure of $7.3 \mathrm{mm}$ of water. Determine the flowrate.

Ameer Said

Numerade Educator

Problem 131

Water flows through the Venturi meter shown in Fig. P8.131. The specific gravity of the manometer fluid is 1.52 Determine the flowrate.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 132

If the fluid flowing in Problem 8.131 were air, what would the flowrate be? Would compressibility effects be important? Explain.

Narayan Hari

Numerade Educator

Problem 133

The scale reading on the rotameter shown in Fig. $\mathrm{P} 8.133$ and Video $\vee 8.15$ (also see Fig. 8.44 ) is directly proportional to the volumetric flowrate. With a scale reading of 2.6 the water bubbles up approximately 3 in. How far will it bubble up if the scale reading is $5.0 ?$

Narayan Hari

Numerade Educator