Fluid Mechanics in SI Units

R. C. Hibbeler, Kai Beng Yap

Chapter 5

Work and Energy of Moving Fluids - all with Video Answers

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Chapter Questions

Problem 1

Water flows through a $5 \mathrm{~m}$ long horizontal pipe. Determine the average decrease in pressure along a horizontal streamline so that the water has an acceleration of $0.3 \mathrm{~m} / \mathrm{s}^{2}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 2

An ideal fluid having a density $\rho$ flows with a velocity $V$ through the horizontal pipe bend. Plot the pressure variation within the fluid as a function of the radius $r,$ where $r_{i} \leq r \leq r_{o}$ and $r_{o}=2 r_{i} .$ For the calculation assume the velocity is constant over the cross section.

James Kiss

Numerade Educator

Problem 3

There is a cylinder-piston arrangement. Determine the pressure within the cylinder and the power required to move the piston, if piston $C$ moves outwards (to the right) at a constant speed of $7 \mathrm{~m} / \mathrm{s}$, and as it does, outside air at atmospheric pressure flows into the circular cylinder through the opening at $B$. Take $\rho_{a}=1.23 \mathrm{~kg} / \mathrm{m}^{3}$. Hint: Recall that power is force $F$ times velocity $V$, where $F=p A$.

Penny Riley

Numerade Educator

Problem 4

A plunger $(A)$ moves inside a syringe $(B)$ with a velocity of $25 \mathrm{~mm} / \mathrm{s}$. If the fluid inside the syringe has a density of $\rho_{s}=1060 \mathrm{~kg} / \mathrm{m}^{3},$ determine the pressure developed inside the syringe at $B$.

Penny Riley

Numerade Educator

Problem 5

A plunger $(A)$ moves inside a syringe $(B)$ with a velocity of $25 \mathrm{~mm} / \mathrm{s}$. If the fluid inside the syringe has a density of $\rho_{s}=1060 \mathrm{~kg} / \mathrm{m}^{3}$, and the pressure developed inside the syringe is $80 \mathrm{kPa}$, determine the average velocity of the solution through the needle.

Penny Riley

Numerade Educator

Problem 6

A plunger $(A)$ moves inside a syringe $(B)$ with a velocity of $V_{s}$. If the fluid inside the syringe has a density of $\rho_{s}=1060 \mathrm{~kg} / \mathrm{m}^{3}$. Show that the average velocity of the fluid passing through the needle is the function of the force applied on the plunger $F$.

Penny Riley

Numerade Educator

Problem 7

An airplane is flying at an altitude of $5 \mathrm{~km}$ with a velocity of $100 \mathrm{~m} / \mathrm{s}$ in still air $A$. Determine the absolute stagnation pressure at the leading edge $B$ of the wing.

Penny Riley

Numerade Educator

Problem 8

An airplane is flying at an altitude of $5 \mathrm{~km}$ with a velocity of $100 \mathrm{~m} / \mathrm{s}$ in still air $A$. If the air flows past point $C$ near the wing at $110 \mathrm{~m} / \mathrm{s}$, measured difference in pressure between the air near the leading edge $B$ of the wing and point $C$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 9

Water is discharged through the drain pipe at $B$ from the large basin at $0.03 \mathrm{~m}^{3} / \mathrm{s}$. If the diameter of the drainpipe is $d=60 \mathrm{~mm},$ determine the pressure at $B$ just inside the drain when the depth of the water is $h=2 \mathrm{~m}$.

Penny Riley

Numerade Educator

Problem 10

Water is discharged through the drain pipe at $B$ from the large basin at $0.03 \mathrm{~m}^{3} / \mathrm{s}$. Determine the pressure at $B$ just inside the drain as a function of the diameter $d$ of the drainpipe. The height of the water is maintained at $h=2 \mathrm{~m} .$ Plot the pressure (vertical axis) versus the diameter for $60 \mathrm{~mm}<d<120 \mathrm{~mm}$. Give values for increments of $\Delta d=20 \mathrm{~mm}$.

James Kiss

Numerade Educator

Problem 11

The mercury in the manometer has a difference in elevation of $h=0.15 \mathrm{~m}$. Determine the volumetric discharge of gasoline through the pipe. Take $\rho_{g a s}=726 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 12

The average human lung takes in about 0.6 liter of air with each inhalation, through the mouth and nose, $A$. This lasts for about 1.5 seconds. Determine the power required to do this if it occurs through the trachea $B$ having a cross-sectional area of $125 \mathrm{~mm}^{2}$. Take $\rho_{a}=1.23 \mathrm{~kg} / \mathrm{m}^{3}$. Hint: Recall that power is force $F$ times velocity $V$, where $F=p A$.

Penny Riley

Numerade Educator

Problem 13

A fountain is produced by water that flows up the tube at $Q=0.08 \mathrm{~m}^{3} / \mathrm{s}$ and then radially through two cylindrical plates before exiting to the atmosphere. Determine the velocity and pressure of the water at point $A$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 14

A fountain is produced by water that flows up the tube at $Q=0.08 \mathrm{~m}^{3} / \mathrm{s}$ and then radially through two cylindrical plates before exiting to the atmosphere. Determine the pressure of the water as a function of the radial distance $r$. Plot the pressure (vertical axis) versus $r$ for $200 \mathrm{~mm} \leq r \leq 400 \mathrm{~mm}$. Give values for increments of $\Delta r=50 \mathrm{~mm}$

James Kiss

Numerade Educator

Problem 15

A fountain ejects water through the four nozzles, which have inner diameters of $10 \mathrm{~mm}$. Determine the pressure in the pipe and the required volumetric flow through the supply pipe so that the water stream always reaches a height of $h=4 \mathrm{~m}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 16

A fountain ejects water through the four nozzles, which have inner diameters of $10 \mathrm{~mm}$. Determine the maximum height $h$ of the water stream passing through the nozzles as a function of the volumetric flow rate into the 60 -mm-diameter pipe at $E$. Also, what is the corresponding pressure at $E$ as a function of $h ?$

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 17

If water flows into the pipe at a constant rate of $30 \mathrm{~kg} / \mathrm{s}$, determine the pressure acting at the inlet $A$ when $y=0.5 \mathrm{~m} .$ Also, what is the rate at which the water surface at $B$ is rising when $y=0.5 \mathrm{~m}$ ? The container is circular.

Penny Riley

Numerade Educator

Problem 18

A tapered channel is used to divert the sea water into a reservoir. As a wave approaches the shore through the closed tapered channel at $A,$ its height will begin to increase until it begins to spill over the sides and into the reservoir. The water in the reservoir then passes through a turbine in at $C$ to generate power and is returned to the sea at $D$. If the speed of the water at $A$ is $V_{A}=3 \mathrm{~m} / \mathrm{s}$, and the water depth is $h_{A}=3.5 \mathrm{~m},$ determine the minimum height of the channel to prevent water from entering the reservoir.

James Kiss

Numerade Educator

Problem 19

Blood flows from the left ventricle (LV) of the heart, which has an exit diameter of $d_{1}=16 \mathrm{~mm},$ through the stenotic aortic valve of diameter $d_{2}=8 \mathrm{~mm}$, and then into the aorta $A$ having a diameter of $d_{3}=20 \mathrm{~mm}$. If the cardiac output is 4 liters per minute, the heart rate is 90 beats per minute, and each ejection of blood lasts $0.31 \mathrm{~s}$, determine the pressure change over the valve. Take $\rho_{b}=1060 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 20

There is a conical tepee with door $A$ and air outlet at $\mathrm{B}$. Air enters the tepee door at $A$ with an average speed of $3 \mathrm{~m} / \mathrm{s}$ and exits at the top $B$. Determine the pressure difference between these two points and find the average speed of the air at $B$. The areas of the openings are $A_{A}=0.25 \mathrm{~m}^{2}$ and $A_{B}=0.08 \mathrm{~m}^{2} .$ The density of the air is $\rho_{a}=1.20 \mathrm{~kg} / \mathrm{m}^{3} .$

Penny Riley

Numerade Educator

Problem 21

An air pump is used to exit the water from a tank. Water comes out from the hose at $B$ at the rate of $5 \mathrm{~m} / \mathrm{s}$ when the water level in the tank is $0.8 \mathrm{~m}$. Determine the pressure of air that has been pumped into the top of the $\operatorname{tank}$ at $A$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 22

An air pump is used to exit the water from a tank. If the pressure of air that has been pumped into the top of the tank at $A$ is $200 \mathrm{kPa},$ determine the discharge of the water comes out from the hose of diameter $12 \mathrm{~mm}$ at $B$. The water level in the tank is $0.8 \mathrm{~m}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 23

Determine the flow of oil through the pipe if the difference in height of the water column in the manometer is $h=100 \mathrm{~mm}$. Take $\rho_{o}=875 \mathrm{~kg} / \mathrm{m}^{3}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 24

Determine the difference in height $h$ of the water column in the manometer if the flow of oil through the pipe is $0.04 \mathrm{~m}^{3} / \mathrm{s}$. Take $\rho_{o}=875 \mathrm{~kg} / \mathrm{m}^{3}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 25

Air enters into a nozzle at $A$ at a temperature of $30^{\circ} \mathrm{C}$ at $5 \mathrm{~m} / \mathrm{s}$ and then exits to the atmosphere at $B,$ where the temperature is $0^{\circ} \mathrm{C}$. Determine the pressure at $A$.

Penny Riley

Numerade Educator

Problem 26

The fuel elements in the form of plates are spaced $5 \mathrm{~mm}$ apart and of length $1000 \mathrm{~mm}$ are used in a water-cooled nuclear reactor. During the test, water enters at the bottom of the reactor (plates) and flows upwards at $1 \mathrm{~m} / \mathrm{s}$. Determine the pressure difference in the water between $A$ and $B$. Take the average water temperature to be $90^{\circ} \mathrm{C}$.

Penny Riley

Numerade Educator

Problem 27

Water is flowing through a pipe and a manometer is attached with this pipe. Determine the velocity of water through the pipe. Take $\rho_{\mathrm{Hg}}=13550 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 28

The discharge of kerosene oil required through a drain pipe is $0.15 \mathrm{~m}^{3} / \mathrm{s}$ once the valve at $A$ is opened. Determine the air pressure that must be exerted at the top of the kerosene in the large tank at $B$ to maintain the required discharge through the drain pipe.

James Kiss

Numerade Educator

Problem 29

Determine the discharge of kerosene oil through a drain pipe at valve $A$. If the air pressure at the top of the kerosene in the large tank at $B$ is $60 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 30

A bent pipe is used to supply the water. Determine the pressure at $A$ if the average velocity of water at $B$ is $5 \mathrm{~m} / \mathrm{s}$

James Kiss

Numerade Educator

Problem 31

Water flows up through the vertical pipe such that when it is at $A$, it is subjected to a pressure of $150 \mathrm{kPa}$ and has a velocity of $3 \mathrm{~m} / \mathrm{s}$. Determine the pressure and its velocity at $B$. Set $d=75 \mathrm{~mm}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 32

Water flows through the vertical pipe such that when it is at $A,$ it is subjected to a pressure of $150 \mathrm{kPa}$ and has a velocity of $3 \mathrm{~m} / \mathrm{s}$. Determine the pressure and velocity at $B$ as a function of the diameter $d$ of the pipe at $B .$ Plot the pressure and velocity (vertical axis) versus the diameter for $25 \mathrm{~mm} \leq d \leq 100 \mathrm{~mm} .$ Give values for increments of $\Delta d=25 \mathrm{~mm}$. If $d_{B}=25 \mathrm{~mm}$, what is the pressure at $B$ ? Is this lower region of the graph reasonable? Explain.

James Kiss

Numerade Educator

Problem 33

Water flows in a rectangular channel over the $1-\mathrm{m}$ drop. If the width of the channel is $1.5 \mathrm{~m}$, determine the volumetric flow in the channel.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 34

Water flows through the pipe at $A$ with a velocity of $6 \mathrm{~m} / \mathrm{s}$ and at a pressure of $280 \mathrm{kPa}$. Determine the velocity of the water at $B$ and the difference in elevation $h$ of the mercury in the manometer.

Sanat Mukherjee

Sanat Mukherjee

Numerade Educator

Problem 35

Carbon dioxide at $20^{\circ} \mathrm{C}$ flows past the Pitot tube $B$ such that mercury within the manometer is displaced $50 \mathrm{~mm}$ as shown. Determine the mass flow if the duct has a crosssectional area of $0.18 \mathrm{~m}^{2}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 36

Water flows along the rectangular channel such that after it falls to the lower elevation, the depth becomes $h=0.3 \mathrm{~m}$. Determine the volumetric discharge through the channel. The channel has a width of $1.5 \mathrm{~m}$.

Penny Riley

Numerade Educator

Problem 37

Water flows at $3 \mathrm{~m} / \mathrm{s}$ at $A$ along the rectangular channel that has a width of $1.5 \mathrm{~m}$. If the depth at $A$ is $0.5 \mathrm{~m}$, determine the depth at $B$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 38

The change in velocity between two sections $A$ and $B$ is $12 \mathrm{~m} / \mathrm{s}$ to $5 \mathrm{~m} / \mathrm{s}$. Determine the pressure difference between $A$ and $x$.

James Kiss

Numerade Educator

Problem 39

The change in velocity between two sections $A$ and $B$ is $12 \mathrm{~m} / \mathrm{s}$ to $5 \mathrm{~m} / \mathrm{s}$. Determine the pressure difference between $A$ and $x=2 \mathrm{~m}$.

James Kiss

Numerade Educator

Problem 40

Oil flows through the horizontal pipe under a pressure of $400 \mathrm{kPa}$ and at a velocity of $2.5 \mathrm{~m} / \mathrm{s}$ at $A$. Determine the pressure in the pipe at $B$ if the pressure at $C$ is $150 \mathrm{kPa}$. Neglect any elevation difference. Take $\rho_{o}=880 \mathrm{~kg} / \mathrm{m}^{3}$.

Narayan Hari

Numerade Educator

Problem 41

Oil flows through the horizontal pipe under a pressure of $100 \mathrm{kPa}$ and at a velocity of $2.5 \mathrm{~m} / \mathrm{s}$ at $A$. Determine the pressure in the pipe at $C$ if the pressure at $B$ is $95 \mathrm{kPa}$. Take $\rho_{o}=880 \mathrm{~kg} / \mathrm{m}^{3}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 42

Air at $15^{\circ} \mathrm{C}$ and an absolute pressure of $275 \mathrm{kPa}$ flows through the 200 -mm-diameter duct at $V_{A}=4 \mathrm{~m} / \mathrm{s}$. Determine the absolute pressure of the air after it passes through the transition and into the 400 -mm-diameter duct $B$. The temperature of the air remains constant.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 43

Air at $15^{\circ} \mathrm{C}$ and an absolute pressure of $250 \mathrm{kPa}$ flows through the 200-mm-diameter duct at $V_{A}=20 \mathrm{~m} / \mathrm{s}$. Determine the rise in pressure, $\Delta p=p_{B}-p_{A},$ when the air passes through the transition and into the 400 -mm-diameter duct. The temperature of the air remains constant.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 44

The open cylindrical tank is filled with linseed oil. A crack having a length of $50 \mathrm{~mm}$ and average height of $2 \mathrm{~mm}$ occurs at the base of the tank. How many liters of oil will slowly drain from the tank in eight hours? Take $\rho_{o}=940 \mathrm{~kg} / \mathrm{m}^{3}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 45

Water drains from the fountain cup $A$ to cup $B$. Determine the depth $h$ of the water in $B$ in order for steady flow to be maintained. Take $d=25 \mathrm{~mm}$.

James Kiss

Numerade Educator

Problem 46

Water drains from the fountain $\operatorname{cup} A$ to cup $B$. If the depth in cup $B$ is $h=50 \mathrm{~mm}$, determine the velocity of the water at $C$ and the diameter $d$ of the opening at $D$ so that steady flow occurs.

James Kiss

Numerade Educator

Problem 47

As air flows downward through the venturi constriction, it creates a low pressure $A$ that causes ethyl alcohol to rise in the tube and be drawn into the air stream. If the air is then discharged to the atmosphere at $C$, determine the smallest volumetric flow of air required to do this. Take $\rho_{e a}=789 \mathrm{~kg} / \mathrm{m}^{3}$ and $\rho_{a}=1.225 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 48

As air flows downward through the venturi constriction, it creates a low pressure at $A$ that causes ethyl alcohol to rise in the tube and be drawn into the air stream. Determine the velocity of the air as it passes through the tube at $B$ in order to do this. The air is discharged to the atmosphere at $C .$ Take $\rho_{e a}=789 \mathrm{~kg} / \mathrm{m}^{3}$ and $\rho_{a}=1.225 \mathrm{~kg} / \mathrm{m}^{3}$.

Anand Jangid

Numerade Educator

Problem 49

Determine the volumetric flow and the pressure in the pipe at $A$ if the height of the water column in the Pitot tube is $0.3 \mathrm{~m}$ and the height in the piezometer is $0.1 \mathrm{~m}$.

James Kiss

Numerade Educator

Problem 50

Determine the velocity of the flow out of the vertical pipes at $A$ and $B$, if water flows into the Tee at $8 \mathrm{~m} / \mathrm{s}$ and under a pressure of $40 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 51

At the instant shown, the level of water in the conical funnel is $y=200 \mathrm{~mm} .$ If the stem has an inner diameter of $5 \mathrm{~mm}$, determine the rate at which the surface level of the water is dropping.

James Kiss

Numerade Educator

Problem 52

If the stem of the conical funnel has a diameter of $5 \mathrm{~mm},$ determine the rate at which the surface level of the water is dropping as a function of the depth $y$. Assume steady flow. Note: For a cone, $V=\frac{1}{3} \pi r^{2} h$.

Penny Riley

Numerade Educator

Problem 53

Determine the kinetic energy coefficient $\alpha$ if the velocity distribution for laminar flow in a smooth pipe has a velocity profile defined by $u=U_{\max }\left(1-(r / R)^{2}\right)$

James Kiss

Numerade Educator

Problem 54

Determine the kinetic energy coefficient $\alpha$ if the velocity distribution for turbulent flow in a smooth pipe is assumed to have a velocity profile defined by Prandtl's oneseventh power law, $u=U_{\max }(1-r / R)^{1 / 7}$

James Kiss

Numerade Educator

Problem 55

Water at a pressure of $80 \mathrm{kPa}$ and a velocity of $2 \mathrm{~m} / \mathrm{s}$ at $A$ flows through the transition. Determine the velocity and the pressure at $B$. Draw the energy and hydraulic grade lines for the flow from $A$ to $B$ using a datum at $B$.

James Kiss

Numerade Educator

Problem 56

Water at a pressure of $80 \mathrm{kPa}$ and a velocity of $2 \mathrm{~m} / \mathrm{s}$ at $A$ flows through the transition. Determine the velocity and the pressure at $C .$ Plot the pressure head and the gravitational head for $A B$ using a datum at $B$.

James Kiss

Numerade Educator

Problem 57

Oil flows through the constant-diameter pipe such that at $A$ the pressure is $50 \mathrm{kPa}$, and the velocity is $2 \mathrm{~m} / \mathrm{s}$. Determine the pressure and velocity at $B$. Draw the energy and hydraulic grade lines for $A B$ using a datum at $B$. Take $\rho_{o}=900 \mathrm{~kg} / \mathrm{m}^{3}$.

James Kiss

Numerade Educator

Problem 58

Oil flows through the constant-diameter pipe such that at $A$ the pressure is $50 \mathrm{kPa}$, and the velocity is $2 \mathrm{~m} / \mathrm{s}$. Plot the pressure head and the gravitational head for $A B$ using a datum at $B$. Take $\rho_{o}=900 \mathrm{~kg} / \mathrm{m}^{3}$.

James Kiss

Numerade Educator

Problem 59

The pump discharges water at $B$ at $0.05 \mathrm{~m}^{3} / \mathrm{s}$. If the friction head loss between the intake at $A$ and the outlet at $B$ is $0.9 \mathrm{~m},$ and the power input to the pump is $8 \mathrm{~kW}$ determine the difference in pressure between $A$ and $B$. The efficiency of the pump is $e=0.7$.

James Kiss

Numerade Educator

Problem 60

The power input of the pump is $10 \mathrm{~kW}$ and the friction head loss between $A$ and $B$ is $1.25 \mathrm{~m}$. If the pump has an efficiency of $e=0.8,$ and the increase in pressure from $A$ to $B$ is $100 \mathrm{kPa}$, determine the volumetric flow of water through the pump.

Penny Riley

Numerade Educator

Problem 61

There is an open tank on a roof. Water is siphoned from the open tank. Determine the volumetric discharge from the 12 -mm-diameter hose. Draw the energy and hydraulic grade lines for the hose using a datum at $B$.

James Kiss

Numerade Educator

Problem 62

A water reservoir is connected to a turbine using a pipe of diameter $0.24 \mathrm{~m}$. If the discharge at $B$ is $0.6 \mathrm{~m}^{3} / \mathrm{s}$, determine the power output of the turbine. Assume the turbine runs with an efficiency of $85 \%$. Neglect frictional losses in the pipe.

Penny Riley

Numerade Educator

Problem 63

A water reservoir is connected to a turbine using a pipe of diameter $0.24 \mathrm{~m}$. If the discharge at $B$ is $0.6 \mathrm{~m}^{3} / \mathrm{s}$, determine the power output of the turbine. Assume the turbine runs with an efficiency of $85 \%$. There is a lead loss of $0.3 \mathrm{~m}$ in the pipe.

Penny Riley

Numerade Educator

Problem 64

Two oil reservoirs at the same levels are connected by a pipeline of diameter $240 \mathrm{~mm}$ and length $10 \mathrm{~km}$. If the friction loss in the pipe is $1.2 \mathrm{~m}$ for every $100 \mathrm{~m}$ of pipe length, determine the power that must be supplied by a pump to produce a flow of $5 \mathrm{~m}^{3} / \mathrm{min}$ through the pipe. The ends of the pipe are submerged in the reservoirs. Take $\rho_{o}=880 \mathrm{~kg} / \mathrm{m} 3$.

Penny Riley

Numerade Educator

Problem 65

Water is delivered from one reservoir to another at a height of $18 \mathrm{~m}$. If the friction head loss in the connection pipe is $3 \mathrm{~m}$ per kilometer of the pipe. The diameter and the length of the connection pipe are $180 \mathrm{~mm}$ and $3 \mathrm{~km}$ long, respectively. Determine the required power output of a pump to maintain the flow of $0.6 \mathrm{~m}^{3} / \mathrm{s}$. The ends of the pipe are submerged in the reservoir.

Penny Riley

Numerade Educator

Problem 66

The pump draws water from the large reservoir $A$ and discharges it at $0.2 \mathrm{~m}^{3} / \mathrm{s}$ at $C$. If the diameter of the pipe is $200 \mathrm{~mm}$, determine the power the pump delivers to the water. Neglect friction losses. Construct the energy and hydraulic grade lines for the pipe using a datum at $B$.

James Kiss

Numerade Educator

Problem 67

Solve Prob. $5-66,$ but include a friction head loss in the pump of $0.5 \mathrm{~m}$, and a friction loss of $1 \mathrm{~m}$ for every $5 \mathrm{~m}$ length of pipe. The pipe extends $3 \mathrm{~m}$ from the reservoir to $B$, then $12 \mathrm{~m}$ from $B$ to $C$.

James Kiss

Numerade Educator

Problem 68

The pressure drop of air in a duct is observed from $210 \mathrm{kPa}$ to $209.99 \mathrm{kPa}$. If the temperature remains constant at $T=50^{\circ} \mathrm{C}$, determine the head loss between these points. Assume the air is incompressible.

Penny Riley

Numerade Educator

Problem 69

Determine the power required to run the pump to draw the water from inlet $A$ at pressure $-30 \mathrm{kPa}$ and discharge at the outlet $B$ with pressure $100 \mathrm{kPa}$. The discharge at $B$ is $0.06 \mathrm{~m}^{3} / \mathrm{s}$. Neglect friction losses. The pipe has a constant diameter of $120 \mathrm{~mm}$. Take $h=2.5 \mathrm{~m}$.

James Kiss

Numerade Educator

Problem 70

Draw the energy and hydraulic grade lines for the pipe of $100-\mathrm{mm}$ -diameter $A C B$ in Prob. $5-69$ using a datum at $A$.

James Kiss

Numerade Educator

Problem 71

The turbine $C$ removes $300 \mathrm{~kW}$ of power from the water that passes through it. If the pressure at the intake $A$ is $p_{A}=300 \mathrm{kPa}$ and the velocity is $8 \mathrm{~m} / \mathrm{s}$, determine the pressure and velocity of the water at the exit $B$. Neglect the frictional losses between $A$ and $B$.

Supratim Pal

Numerade Educator

Problem 72

The vertical pipe is filled with oil. When the valve at $A$ is closed, the pressure at $A$ is $150 \mathrm{kPa},$ and at $B$ it is $80 \mathrm{kPa}$. When the valve is open, the oil flows at $2.5 \mathrm{~m} / \mathrm{s}$, and the pressure at $A$ is $140 \mathrm{kPa}$ and at $B$ it is $60 \mathrm{kPa}$. Determine the head loss in the pipe between $A$ and $B$. Take $\rho_{o}=900 \mathrm{~kg} / \mathrm{m}^{3}$.

James Kiss

Numerade Educator

Problem 73

The flow of air through a 200-mm-diameter duct has an absolute inlet pressure of $180 \mathrm{kPa}$, a temperature of $15^{\circ} \mathrm{C}$, and a velocity of $10 \mathrm{~m} / \mathrm{s}$. Farther downstream a $2-\mathrm{kW}$ exhaust system increases the outlet velocity to $25 \mathrm{~m} / \mathrm{s}$. Determine the density of the air at the outlet, and the change in enthalpy of the air. Neglect heat transfer through the pipe.

James Kiss

Numerade Educator

Problem 74

Nitrogen gas having an enthalpy of $250 \mathrm{~J} / \mathrm{kg}$ is flowing at $6 \mathrm{~m} / \mathrm{s}$ into the 10 -m-long pipe at $A$. If the heat loss from the walls of the duct is $60 \mathrm{~W}$, determine the enthalpy of the gas at the exit $B$. Assume that the gas is incompressible with a density of $\rho=1.36 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 75

If the pressure at $A$ is $60 \mathrm{kPa}$, and the pressure at $B$ is $180 \mathrm{kPa}$, determine the power output supplied by the pump if the water flows at $0.02 \mathrm{~m}^{3} / \mathrm{s}$. Neglect friction losses.

Penny Riley

Numerade Educator

Problem 76

The pump supplies a power of $1.5 \mathrm{~kW}$ to the water producing a volumetric flow of $0.015 \mathrm{~m}^{3} / \mathrm{s}$. If the total frictional head loss within the system is $1.35 \mathrm{~m}$, determine the pressure difference between the inlet $A$ and outlet $B$ of the pipes.

Penny Riley

Numerade Educator

Problem 77

The wave overtopping device consists of a floating reservoir that is continuously filled by waves, so that the water level in the reservoir is always higher than that of the surrounding ocean. As the water drains out at $A,$ the energy is drawn by the low-head hydroturbine, which then generates electricity. Determine the power that can be produced by this system if the water level in the reservoir is always $1.5 \mathrm{~m}$ above that of the ocean, The waves add $0.3 \mathrm{~m}^{3} / \mathrm{s}$ to the reservoir, and the diameter of the tunnel containing the turbine is $600 \mathrm{~mm}$. The head loss through the turbine is $0.2 \mathrm{~m}$. Take $\rho_{w}=1050 \mathrm{~kg} / \mathrm{m}^{3}$.

Penny Riley

Numerade Educator

Problem 78

Air and fuel enter a turbojet engine (turbine) having an enthalpy of $800 \mathrm{~kJ} / \mathrm{kg}$ and a relative velocity of $15 \mathrm{~m} / \mathrm{s}$. The mixture exits with a relative velocity of $60 \mathrm{~m} / \mathrm{s}$ and an enthalpy of $650 \mathrm{~kJ} / \mathrm{kg} .$ If the mass flow is $30 \mathrm{~kg} / \mathrm{s}$, determine the power output of the jet. Assume no heat transfer occurs.

Penny Riley

Numerade Educator

Problem 79

The measured water pressure at the inlet and exit portions of the pipe are indicated for the pump. If the flow is $0.1 \mathrm{~m}^{3} / \mathrm{s}$, determine the power that the pump supplies to the water. Neglect friction losses.

Penny Riley

Numerade Educator

Problem 80

The circular hovercraft draws in air through the $\operatorname{fan} A$ and discharges it through the bottom $B$ near the ground, where it produces a pressure of $1.50 \mathrm{kPa}$ on the ground. Determine the average velocity of the air entering at $A$ that is needed to lift the hovercraft $100 \mathrm{~mm}$ off the ground. The open area at $A$ is $0.75 \mathrm{~m}^{2}$. Neglect friction losses. Take $\rho_{a}=1.22 \mathrm{~kg} / \mathrm{m}^{3}$.

James Kiss

Numerade Educator

Problem 81

The pump at $C$ produces a discharge of water at $B$ of $0.035 \mathrm{~m}^{3} / \mathrm{s}$. If the pipe at $B$ has a diameter of $50 \mathrm{~mm}$ and the hose at $A$ has a diameter of $30 \mathrm{~mm},$ determine the power output supplied by the pump. Assume frictional head losses within the pipe system are determined from $3 V_{B}^{2} / 2 g$.

James Kiss

Numerade Educator

Problem 82

The pump is used to transfer carbon tetrachloride in a processing plant from a storage tank $A$ to the mixing tank $C$. If the total head loss due to friction and the pipe fittings in the system is $1.8 \mathrm{~m}$, and the diameter of the pipe is $50 \mathrm{~mm}$, determine the power developed by the pump when $h=3 \mathrm{~m}$. The velocity at the pipe exit is $10 \mathrm{~m} / \mathrm{s}$, and the storage tank is opened to the atmosphere. Take $\rho_{c t}=1590 \mathrm{~kg} / \mathrm{m}^{3}$.

James Kiss

Numerade Educator