Fluid Mechanics in SI Units

R. C. Hibbeler, Kai Beng Yap

Chapter 13

Compressible Flow - all with Video Answers

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Chapter Questions

Problem 1

Oxygen is decompressed from an absolute pressure of $600 \mathrm{kPa}$ to $100 \mathrm{kPa}$, with no change in temperature. Determine the changes in the entropy and enthalpy.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 2

Helium is contained in a closed vessel under an absolute pressure of $400 \mathrm{kPa}$. If the temperature increases from $20^{\circ} \mathrm{C}$ to $85^{\circ} \mathrm{C},$ determine the changes in pressure and entropy.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 3

If a pipe contains helium at a gage pressure of $100 \mathrm{kPa}$ and a temperature of $20^{\circ} \mathrm{C}$, determine the density of the helium. Also, determine the temperature if the helium is compressed isentropically to a gage pressure of $250 \mathrm{kPa}$. The atmospheric pressure is $101.3 \mathrm{kPa}$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 4

The closed tank contains helium at $200^{\circ} \mathrm{C}$ and under an absolute pressure of $530 \mathrm{kPa}$. If the temperature is increased to $250^{\circ} \mathrm{C}$, determine the changes in density and pressure, and the change per unit mass in the internal energy and enthalpy of the helium.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 5

A gas has a specific heat that varies with the absolute temperature, such that $c_{p}=\left(1256+36728 / T^{2}\right) \mathrm{J} / \mathrm{kg} \cdot \mathrm{K} .$ If
the temperature rises from $300 \mathrm{~K}$ to $400 \mathrm{~K}$, determine the change in enthalpy per unit mass.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 6

Air flows in a horizontal duct at $20^{\circ} \mathrm{C}$ with a velocity of $180 \mathrm{~m} / \mathrm{s}$. If the velocity increases to $250 \mathrm{~m} / \mathrm{s}$, determine the corresponding temperature of the air. Hint: Use the energy equation to find $\Delta h$.

Narayan Hari

Numerade Educator

Problem 7

The half-angle $\alpha$ on the Mach cone of a rocket is $20^{\circ} .$ If the air temperature is $15^{\circ} \mathrm{C}$, determine the speed of the rocket.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 8

A ship is located where the depth of the ocean is $3 \mathrm{~km} .$ Determine the time needed for a sonar signal to bounce off the bottom and return to the ship. Assume the water temperature is $10^{\circ} \mathrm{C}$. Take $\rho=1030 \mathrm{~kg} / \mathrm{m}^{3}$ and $E_{\gamma}=2.11\left(10^{9}\right)$ Pa for sea water.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 9

Determine how fast a race car must travel in $20^{\circ} \mathrm{C}$ weather in order for $\mathrm{M}=0.3$.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 10

Compare the speed of sound in water and air at a temperature of $20^{\circ} \mathrm{C}$. The bulk modulus of water at $T=20^{\circ} \mathrm{C}$ is $E_{V}=2.2 \mathrm{GPa}$

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 11

A jet plane is flying at Mach 2.2. Determine its speed in kilometers per hour. The air is at $10^{\circ} \mathrm{C}$.

Zack A

Numerade Educator

Problem 12

A jet plane has a speed of $600 \mathrm{~m} / \mathrm{s}$. If the air has a temperature of $10^{\circ} \mathrm{C},$ determine the Mach number and the half-angle $\alpha$ of the Mach cone.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 13

Determine the half-angle $\alpha$ of the Mach cone at the nose of a jet if it is flying at $1125 \mathrm{~m} / \mathrm{s}$ in air at $5^{\circ} \mathrm{C}$.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 14

A jet plane passes $5 \mathrm{~km}$ directly overhead. If the sound of the plane is heard 6 s later, determine the speed of the plane. The average air temperature is $10^{\circ} \mathrm{C}$.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 15

The Mach number of the airflow in the wind tunnel at $B$ is to be $\mathrm{M}=2.0$ with an air temperature of $10^{\circ} \mathrm{C}$ and absolute pressure of $25 \mathrm{kPa}$. Determine the required absolute pressure and temperature within the large reservoir at $A$.

James Kiss

Numerade Educator

Problem 16

Determine the pressure of air if it is flowing at $1600 \mathrm{~km} / \mathrm{h}$. When the air is still, the temperature is $20^{\circ} \mathrm{C}$ and the absolute pressure is $101.3 \mathrm{kPa}$.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 17

What are the ratios of the critical pressure, temperature, and density to the stagnation pressure, temperature, and density for methane?

James Kiss

Numerade Educator

Problem 18

The temperature and absolute pressure of air within the circular duct are $40^{\circ} \mathrm{C}$ and $800 \mathrm{kPa}$, respectively. If the mass flow is $30 \mathrm{~kg} / \mathrm{s}$, determine the Mach number.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 19

The flow at a point in a wind tunnel has a speed of $\mathrm{M}=2.5$ when the absolute pressure of the air is $16 \mathrm{kPa}$ and the temperature is $200 \mathrm{~K}$. Determine the speed of the air at the point, and also find the temperature and pressure of the air in the supply reservoir.

James Kiss

Numerade Educator

Problem 20

The absolute stagnation pressure for air is $875 \mathrm{kPa}$ when the stagnation temperature is $25^{\circ} \mathrm{C}$. If the absolute pressure for the flow is $630 \mathrm{kPa}$, determine the velocity of the flow.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 21

Nitrogen in the reservoir is at a temperature of $20^{\circ} \mathrm{C}$ and an absolute pressure of $300 \mathrm{kPa}$. Determine the mass flow through the nozzle. The atmospheric pressure is $100 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 22

Nitrogen, at an absolute pressure of $600 \mathrm{kPa}$ and temperature of $800 \mathrm{~K},$ is contained in the large tank. Determine the backpressure in the hose to choke the nozzle and yet maintain isentropic supersonic flow through the divergent portion of the nozzle. The nozzle has an outer diameter of $40 \mathrm{~mm}$, and the throat has a diameter of $20 \mathrm{~mm}$.

James Kiss

Numerade Educator

Problem 23

Nitrogen, at an absolute pressure of $600 \mathrm{kPa}$ and temperature of $800 \mathrm{~K},$ is contained in the large tank. Determine the backpressure in the hose to choke the nozzle and maintain isentropic subsonic flow through the divergent portion of the nozzle. The nozzle has an outer diameter of $40 \mathrm{~mm}$, and the throat has a diameter of $20 \mathrm{~mm}$.

James Kiss

Numerade Educator

Problem 24

The large tank contains air at an absolute pressure of $150 \mathrm{kPa}$ and temperature of $20^{\circ} \mathrm{C}$. The 5 -mm-diameter nozzle at $A$ is opened to let air out of the tank. Determine the mass flow and the horizontal force that must be applied to the tank to prevent it from moving. The atmospheric pressure is $100 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 25

The large tank contains air at an absolute pressure of $600 \mathrm{kPa}$ and temperature of $70^{\circ} \mathrm{C}$. The Laval nozzle has a throat diameter of $20 \mathrm{~mm}$ and an exit diameter of $50 \mathrm{~mm}$. Determine the absolute pressure within the connected pipe so that the nozzle chokes but also maintains isentropic subsonic flow within the divergent portion of the nozzle. Also, what is the mass flow from the tank if the absolute pressure within the pipe is $150 \mathrm{kPa}$ ?

James Kiss

Numerade Educator

Problem 26

The large tank contains air at an absolute pressure of $600 \mathrm{kPa}$ and temperature of $70^{\circ} \mathrm{C}$. The nozzle has a throat diameter of $20 \mathrm{~mm}$ and an exit diameter of $50 \mathrm{~mm}$. Determine the absolute pressure within the connected pipe, and the corresponding mass flow through the pipe, when the nozzle chokes and maintains isentropic supersonic flow within the divergent portion of the nozzle.

James Kiss

Numerade Educator

Problem 27

The large tank contains air at an absolute pressure of $700 \mathrm{kPa}$ and temperature of $400 \mathrm{~K}$. Determine the mass flow from the tank into the pipe if the converging nozzle has an exit diameter of $40 \mathrm{~mm}$ and the absolute pressure in the pipe is $150 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 28

The large tank contains air at an absolute pressure of $700 \mathrm{kPa}$ and temperature of $400 \mathrm{~K}$. Determine the mass flow from the tank into the pipe if the converging nozzle has an exit diameter of $40 \mathrm{~mm}$ and the absolute pressure in the pipe is $400 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 29

Air exits a large tank through a converging nozzle having an exit diameter of $20 \mathrm{~mm}$. If the temperature of the air in the tank is $35^{\circ} \mathrm{C}$ and the absolute pressure in the tank is $600 \mathrm{kPa}$, determine the velocity of the air as it exits the nozzle. The absolute pressure outside the tank is $101.3 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 30

Air exits a large tank through a converging nozzle having an exit diameter of $20 \mathrm{~mm}$. If the temperature of the air in the tank is $35^{\circ} \mathrm{C}$ and the absolute pressure in the tank is $150 \mathrm{kPa}$, determine the mass flow of the air as it exits the nozzle. The absolute pressure outside the tank is $101.3 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 31

The absolute pressure is $400 \mathrm{kPa}$ and the temperature is $20^{\circ} \mathrm{C}$ in the large tank. If the pressure at the entrance $A$ of the nozzle is $300 \mathrm{kPa}$, determine the mass flow out of the tank through the exit of the nozzle.

James Kiss

Numerade Educator

Problem 32

Atmospheric air at an absolute pressure of $103 \mathrm{kPa}$ and temperature of $20^{\circ} \mathrm{C}$ flows through the converging nozzle into the tank where the absolute pressure at $A$ is $30 \mathrm{kPa}$. Determine the mass flow into the tank.

James Kiss

Numerade Educator

Problem 33

The diameter of the exit of a converging nozzle is $50 \mathrm{~mm}$. If its entrance is connected to a large tank containing air at an absolute pressure of $500 \mathrm{kPa}$ and temperature of $125^{\circ} \mathrm{C}$, determine the mass flow through the nozzle. The ambient air is at an absolute pressure of $101.3 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 34

Air flows at $V_{A}=100 \mathrm{~m} / \mathrm{s}$ at $1200 \mathrm{~K}$ and has an absolute pressure of $p_{A}=6.25 \mathrm{MPa}$. Determine the diameter $d$ of the pipe at $B$ so that $\mathrm{M}=1$ at $B$.

James Kiss

Numerade Educator

Problem 35

Air flows at $V_{A}=100 \mathrm{~m} / \mathrm{s}$ at $1200 \mathrm{~K}$ and has an absolute pressure of $p_{A}=6.25$ MPa. Determine the diameter $d$ of the pipe at $B$ so that $\underline{M}=0.8$ at $B$.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 36

If the fuel mixture within the chamber of the rocket is under an absolute pressure of $1.30 \mathrm{MPa}$, determine the Mach number of the exhaust if the area ratio of the exit to the throat is 2.5 . Assume that fully expanded supersonic flow occurs. Take $k=1.40$ for the fuel mixture. The atmosphere has a pressure of $101.3 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 37

The diameter of the exit of a converging nozzle is $50 \mathrm{~mm}$. If its entrance is connected to a large tank containing air at an absolute pressure of $180 \mathrm{kPa}$ and temperature of $125^{\circ} \mathrm{C}$, determine the mass flow from the tank. The ambient air is at an absolute pressure of $101.3 \mathrm{kPa}$.

James Kiss

Numerade Educator

Problem 38

The converging-diverging nozzle at the end of a supersonic jet engine is to be designed to operate efficiently when the absolute outside air pressure is $25 \mathrm{kPa}$. If the absolute stagnation pressure within the engine is $400 \mathrm{kPa}$ and the stagnation temperature is $1200 \mathrm{~K},$ determine the exit plane diameter and the throat diameter for the nozzle if the mass flow is $15 \mathrm{~kg} / \mathrm{s}$. Take $k=1.40$ and $R=256 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$.

James Kiss

Numerade Educator

Problem 39

Air flows at $200 \mathrm{~m} / \mathrm{s}$ through the pipe. Determine the Mach number of the flow and the mass flow if the temperature is $500 \mathrm{~K}$ and the absolute stagnation pressure is $200 \mathrm{kPa}$. Assume isentropic flow.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 40

Air flows at $200 \mathrm{~m} / \mathrm{s}$ through the pipe. Determine the pressure within the flow if the temperature is $400 \mathrm{~K}$ and the absolute stagnation pressure is $280 \mathrm{kPa}$. Assume isentropic flow.

Prabhakar Kumar

Prabhakar Kumar

Numerade Educator

Problem 41

Natural gas (methane) has an absolute pressure of $400 \mathrm{kPa}$ and flows through the pipe at $A$ at $M=0.1$. Determine the diameter of the throat of the nozzle so that $\mathrm{M}=1$ at the throat. Also, what are the stagnation pressure, the pressure at the throat, and the subsonic and supersonic Mach numbers of the flow through pipe $B$ ?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 42

Air has an absolute pressure of $400 \mathrm{kPa}$ and flows through the pipe at $A$ at $M=0.5 .$ Determine the Mach number at the throat of the nozzle where $d_{t}=110 \mathrm{~mm},$ and the Mach number in the pipe at $B$. Also, what are the stagnation pressure and the pressure in the pipe at $B ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 43

The tank contains oxygen at a temperature of $70^{\circ} \mathrm{C}$ and absolute pressure of $800 \mathrm{kPa}$. If the converging nozzle at the exit has a diameter of $6 \mathrm{~mm}$, determine the initial mass flow out of the tank if the outside absolute pressure is $100 \mathrm{kPa}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 44

The tank contains helium at a temperature of $80^{\circ} \mathrm{C}$ and absolute pressure of $175 \mathrm{kPa}$. If the converging nozzle at the exit has a diameter of $6 \mathrm{~mm}$, determine the initial mass flow out of the tank if the outside absolute pressure is $98 \mathrm{kPa}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 45

The large tank contains air at $250 \mathrm{~K}$ under an absolute pressure of $1.20 \mathrm{MPa}$. When the valve is opened, the nozzle chokes. The outside atmospheric pressure is $101.3 \mathrm{kPa}$. Determine the mass flow from the tank. The nozzle has an exit diameter of $40 \mathrm{~mm}$ and a throat diameter of $20 \mathrm{~mm}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 46

The large tank contains air at $250 \mathrm{~K}$ under an absolute pressure of $150 \mathrm{kPa}$. When the valve is opened, determine if the nozzle is choked. The outside atmospheric pressure is $90 \mathrm{kPa}$. Determine the mass flow from the tank. Assume the flow is isentropic. The nozzle has an exit diameter of $40 \mathrm{~mm}$ and a throat diameter of $20 \mathrm{~mm}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 47

Air at $A$ flows into the nozzle at $\mathrm{M}=0.4$. Determine the Mach number at $C$ and at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 48

Air flows isentropically into the nozzle at $\mathrm{M}_{A}=0.2$ and out at $\mathrm{M}_{B}=2$. If the diameter of the nozzle at $A$ is $30 \mathrm{~mm},$ determine the diameter of the throat and the diameter at $B$. Also, if the absolute pressure at $A$ is $300 \mathrm{kPa}$, determine the stagnation pressure and the pressure at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 49

Air flows isentropically into the nozzle at $\mathrm{M}_{A}=0.2$ and out at $\mathrm{M}_{B}=2$. If the diameter of the nozzle at $A$ is 30 $\mathrm{mm},$ determine the diameter of the throat and the diameter at $B$. Also, if the temperature at $A$ is $300 \mathrm{~K},$ determine the stagnation temperature and the temperature at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 50

Air flows through a pipe having a diameter of $50 \mathrm{~mm}$. Determine the mass flow if the stagnation temperature of the air is $20^{\circ} \mathrm{C},$ the absolute pressure is $300 \mathrm{kPa}$, and the stagnation pressure is $375 \mathrm{kPa}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 51

Air at $A$ flows into the nozzle at $M=0.4$. If $p_{A}=$ $125 \mathrm{kPa}$ and $T_{A}=300 \mathrm{~K},$ determine the pressure at $B$ and the velocity at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 52

Air at a temperature of $25^{\circ} \mathrm{C}$ and standard atmospheric pressure of $101.3 \mathrm{kPa}$ flows through the nozzle into the pipe where the absolute internal pressure is $80 \mathrm{kPa}$. Determine the mass flow into the pipe. The nozzle has a throat diameter of $10 \mathrm{~mm}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 53

Air at a temperature of $25^{\circ} \mathrm{C}$ and standard atmospheric pressure of $101.3 \mathrm{kPa}$ flows through the nozzle into the pipe where the absolute internal pressure is $30 \mathrm{kPa}$. Determine the mass flow into the pipe. The nozzle has a throat diameter of $10 \mathrm{~mm}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 54

The duct has a diameter of $200 \mathrm{~mm}$. If the average friction factor is $f=0.003$, and air is drawn into the duct with an inlet velocity of $200 \mathrm{~m} / \mathrm{s}$, temperature of $300 \mathrm{~K},$ and absolute pressure of $180 \mathrm{kPa}$, determine these properties at the exit.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 55

The duct has a diameter of $200 \mathrm{~mm}$. If the average friction factor is $f=0.003$, and air is drawn into the duct with an inlet velocity of $200 \mathrm{~m} / \mathrm{s}$, temperature of $300 \mathrm{~K},$ and absolute pressure of $180 \mathrm{kPa}$, determine the mass flow through the duct and the resultant friction force acting on the $30-\mathrm{m}$ length of duct.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 56

Air in a large room has a temperature of $24^{\circ} \mathrm{C}$ and absolute pressure of $101 \mathrm{kPa}$. If it is drawn into the 200-mm-diameter duct isentropically such that the absolute pressure at section 1 is $90 \mathrm{kPa}$, determine the critical length of duct $L_{\max }$ where the flow becomes choked, and the Mach number, temperature, and pressure at section $2 .$ Take the average friction factor to be $f=0.002$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 57

Air in a large room has a temperature of $24^{\circ} \mathrm{C}$ and absolute pressure of $101 \mathrm{kPa}$. If it is drawn into the 200 -mm-diameter duct isentropically such that the absolute pressure at section 1 is $90 \mathrm{kPa}$, determine the mass flow through the duct and calculate the resultant friction acting on the duct. Also, what is the required length $L_{\max }$ to choke the flow? Take the average friction factor to be $f=0.002$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 58

A large reservoir contains air at a temperature of $T=20^{\circ} \mathrm{C}$ and absolute pressure of $p=300 \mathrm{kPa}$. The air flows isentropically through the nozzle and then through the 1.5 -m-long, 50 -mm-diameter pipe having an average friction factor of $0.03 .$ Determine the mass flow through the pipe and the corresponding velocity, pressure, and temperature at the inlet 1 and outlet 2 if the flow is choked at section $2 .$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 59

A large reservoir contains air at a temperature of $T=20^{\circ} \mathrm{C}$ and absolute pressure of $p=300 \mathrm{kPa}$. The air flows isentropically through the nozzle and then through the 1.5 -m-long, 50 -mm-diameter pipe having an average friction factor of 0.03 . Determine the stagnation temperature and pressure at outlet 2 and the change in entropy between the inlet 1 and outlet 2 if the pipe is choked at section $2 .$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 60

The $40-\mathrm{mm}$ -diameter pipe has a friction factor of $f=0.015 .$ A nozzle on the large tank $A$ delivers nitrogen isentropically to the pipe at section 1 with a velocity of $1200 \mathrm{~m} / \mathrm{s}$, temperature of $460 \mathrm{~K},$ and absolute pressure of $750 \mathrm{kPa}$. Determine the mass flow. Show that a normal shock forms within the pipe. Take $L^{\prime}=1.35 \mathrm{~m}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 61

The 40 -mm-diameter pipe has a friction factor of $f=0.015 .$ A nozale on the large tank $A$ delivers nitrogen isentropically to the pipe at section 1 with a velocity of $200 \mathrm{~m} / \mathrm{s}$ and temperature of $460 \mathrm{~K}$. Determine the velocity and temperature of the nitrogen at $L=2 \mathrm{~m}$ if $L^{\prime}=3 \mathrm{~m}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 62

The 100 -mm-diameter pipe is connected by a nozzle to a large reservoir of air that is at a temperature of $40^{\circ} \mathrm{C}$ and absolute pressure of $450 \mathrm{kPa}$. If the absolute pressure at section 1 is $30 \mathrm{kPa}$, determine the mass flow through the pipe and the length $L$ of the pipe so that a backpressure of $90 \mathrm{kPa}$ in the tank maintains supersonic flow through the pipe. Assume a constant friction factor of 0.0085 throughout the pipe.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 63

The $100-\mathrm{mm}$ -diameter pipe is connected by a nozzle to a large reservoir of air that is at a temperature of $40^{\circ} \mathrm{C}$ and absolute pressure of $450 \mathrm{kPa}$. If the absolute pressure at section 1 is $30 \mathrm{kPa}$, determine the mass flow through the pipe and the length $L$ of the pipe so that sonic flow occurs into the tank. What is the required backpressure in the tank for this to occur? Assume a constant friction factor of 0.0085 throughout the pipe.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 64

The 100 -mm-diameter pipe is connected by a nozzle to a large reservoir of air that is at a temperature of $40^{\circ} \mathrm{C}$ and absolute pressure of $450 \mathrm{kPa}$. If the backpressure causes $\mathrm{M}_{1}>1$, and the flow is choked at the exit, section 2 , when $L=5 \mathrm{~m},$ determine the mass flow through the pipe. Assume a constant friction factor of 0.0085 throughout the pipe.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 65

The 100-mm-diameter pipe is connected by a nozle to a large reservoir of air that is at a temperature of $40^{\circ} \mathrm{C}$ and absolute pressure of $450 \mathrm{kPa}$. If the backpressure causes $\mathrm{M}_{1}<1$, and the flow is choked at the exit, section 2 , when $L=5 \mathrm{~m}$, determine the mass flow through the pipe. Assume a constant friction factor of 0.0085 throughout the pipe.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 66

Air from a large reservoir is at a temperature of $275 \mathrm{~K}$ and absolute pressure of $101 \mathrm{kPa}$. It isentropically enters the duct at section 1 . If $80 \mathrm{~kJ} / \mathrm{kg}$ of heat is added to the flow, determine the greatest possible velocity it can have at section 1 . The backpressure at 2 causes $\mathrm{M}_{1}<1$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 67

Air from a large reservoir is at a temperature of $275 \mathrm{~K}$ and absolute pressure of $101 \mathrm{kPa}$. It isentropically enters the duct at section 1 . If $80 \mathrm{~kJ} / \mathrm{kg}$ of heat is added to the flow, determine the temperature and pressure at the entrance of the duct. The backpressure at 2 causes $\mathrm{M}_{1}=1$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 68

Nitrogen having a temperature of $T_{1}=270 \mathrm{~K}$ and absolute pressure of $p_{1}=330 \mathrm{kPa}$ flows into the smooth pipe at $\mathrm{M}_{1}=0.3$. If it is heated at $100 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{m},$ determine the velocity and pressure of the nitrogen when it exits the pipe at section 2 .

Anand Jangid

Numerade Educator

Problem 69

Nitrogen having a temperature of $T_{1}=270 \mathrm{~K}$ and absolute pressure of $p_{1}=330 \mathrm{kPa}$ flows into the smooth pipe at $\mathrm{M}_{1}=0.3 .$ If it is heated at $100 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{m}$, determine the stagnation temperatures at sections 1 and 2 , and the change in entropy per unit mass between these two sections

James Kiss

Numerade Educator

Problem 70

Nitrogen having a temperature of $300 \mathrm{~K}$ and absolute pressure of $450 \mathrm{kPa}$ flows from a large reservoir into a $100-\mathrm{mm}$ -diameter duct. As it flows, $100 \mathrm{~kJ} / \mathrm{kg}$ of heat is added. Determine the temperature, pressure, and density at section 1 if the backpressure causes $\mathrm{M}_{1}>1$ and the flow becomes choked at section 2 .

James Kiss

Numerade Educator

Problem 71

Nitrogen having a temperature of $300 \mathrm{~K}$ and absolute pressure of $450 \mathrm{kPa}$ flows from a large reservoir into a $100-\mathrm{mm}$ -diameter duct. As it flows, $100 \mathrm{~kJ} / \mathrm{kg}$ of heat is added. Determine the mass flow if the backpressure causes $\mathrm{M}_{1}<1$ and the flow becomes choked at section $2 .$

James Kiss

Numerade Educator

Problem 72

Air is drawn isentropically into the pipe $\underline{\text { at }}$ $V_{1}=640 \mathrm{~m} / \mathrm{s}, \quad T_{1}=80^{\circ} \mathrm{C},$ and absolute pressure of
$p_{1}=250 \mathrm{kPa}$. If it exits the pipe having a speed of $470 \mathrm{~m} / \mathrm{s}$ determine the amount of heat per unit mass that the pipe supplies to the air.

James Kiss

Numerade Educator

Problem 73

Air is drawn into the 100-mm-diameter pipe at $V_{1}=640 \mathrm{~m} / \mathrm{s}, \quad T_{1}=80^{\circ} \mathrm{C},$ and absolute pressure of
$p_{1}=250 \mathrm{kPa}$. If it exits the pipe having a speed of $470 \mathrm{~m} / \mathrm{s}$ determine the stagnation temperatures at sections 1 and 2 and the change in entropy per unit mass between these sections.

James Kiss

Numerade Educator

Problem 74

The converging nozzle has an exit diameter of $0.25 \mathrm{~m}$. If the fuel-oxidizer mixture within the large tank has an absolute pressure of $4 \mathrm{MPa}$ and temperature of $1800 \mathrm{~K}$, determine the mass flow from the nozzle when the backpressure is a vacuum. The mixture has $k=1.38$ and $R=296 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 75

The converging nozzle has an exit diameter of $0.25 \mathrm{~m}$. If the fuel-oxidizer mixture within the large tank has an absolute pressure of $4 \mathrm{MPa}$ and temperature of $1800 \mathrm{~K}$, determine the mass flow from the nozzle if the atmospheric pressure is $100 \mathrm{kPa}$. The mixture has $k=1.38$ and $R=296 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 76

The nozzle is attached onto the end of the pipe. The air supplied from the pipe is at a stagnation temperature of $120^{\circ} \mathrm{C}$ and an absolute stagnation pressure of $800 \mathrm{kPa}$. Determine the mass flow from the nozzle if the backpressure is $60 \mathrm{kPa}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 77

The nozzle is attached onto the end of the pipe. The air in the pipe is at a stagnation temperature of $120^{\circ} \mathrm{C}$ and an absolute stagnation pressure of $800 \mathrm{kPa}$. Determine the two values of the backpressure that will choke the nozzle yet produce isentropic flow. Also, what is the maximum velocity of the isentropic flow?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 78

A standing shock occurs in the pipe when the upstream conditions for air have an absolute pressure of $p_{1}=80 \mathrm{kPa}$, temperature $T_{1}=75^{\circ} \mathrm{C},$ and velocity $V_{1}=700 \mathrm{~m} / \mathrm{s}$. Determine the downstream pressure, temperature, and velocity of the air. Also, what are the upstream and downstream Mach numbers?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 79

The jet plane creates a shock that forms in air having a temperature of $20^{\circ} \mathrm{C}$ and absolute pressure of $80 \mathrm{kPa}$. If it travels at $1200 \mathrm{~m} / \mathrm{s}$, determine the pressure and temperature just behind the shock wave.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 80

Air at a temperature of $20^{\circ} \mathrm{C}$ and an absolute pressure of $180 \mathrm{kPa}$ flows from a large tank through the nozzle. Determine the backpressure at the exit that causes a shock wave to form at the location where the nozzle diameter is $50 \mathrm{~mm}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 81

The large tank supplies air at a temperature of $350 \mathrm{~K}$ and an absolute pressure of $600 \mathrm{kPa}$ to the nozzle. If the throat diameter is $0.3 \mathrm{~m}$ and the exit diameter is $0.5 \mathrm{~m}$, determine the range of backpressures that will cause expansion shock waves to form at the exit.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 82

The jet engine is tested on the ground at standard atmospheric pressure of $101.3 \mathrm{kPa}$. If the fuel-air mixture enters the inlet of the 300 -mm-diameter nozzle at $250 \mathrm{~m} / \mathrm{s}$, with an absolute pressure of $300 \mathrm{kPa}$ and temperature of $800 \mathrm{~K}$, and exits with supersonic flow, determine the velocity of the exhaust developed by the engine. Take $k=1.4$ and $R=249 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$. Assume isentropic flow.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 83

The jet engine is tested on the ground at standard atmospheric pressure of $101.3 \mathrm{kPa}$. If the fuel-air mixture enters the inlet of the 300 -mm-diameter nozzle at $250 \mathrm{~m} / \mathrm{s}$, with an absolute pressure of $300 \mathrm{kPa}$ and temperature of $800 \mathrm{~K}$, determine the required diameter of the throat $d_{r}$, and the exit diameter $d_{e}$ so that the flow exits with isentropic supersonic flow. Take $k=1.4$ and $R=249 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 84

The large tank supplies air at a temperature of $350 \mathrm{~K}$ and an absolute pressure of $600 \mathrm{kPa}$ to the nozzle. If the throat diameter is $0.3 \mathrm{~m}$ and the exit diameter is $0.5 \mathrm{~m}$, determine the range of backpressures that will cause oblique shock waves to form at the exit.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 85

A $200-\mathrm{mm}$ -diameter pipe contains air at a temperature of $10^{\circ} \mathrm{C}$ and an absolute pressure of $100 \mathrm{kPa}$. If a shock is formed in the pipe and the speed of the air in front of the shock is $1000 \mathrm{~m} / \mathrm{s}$, determine the speed of the air behind the shock.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 86

The bottle tank contains $0.13 \mathrm{~m}^{3}$ of oxygen at an absolute pressure of $900 \mathrm{kPa}$ and temperature of $20^{\circ} \mathrm{C}$. If the nozzle has an exit diameter of $15 \mathrm{~mm}$, determine the time needed to drop the absolute pressure in the tank to $300 \mathrm{kPa}$ once the valve is opened. Assume the temperature remains constant in the tank during the flow and the ambient air is at an absolute pressure of $101.3 \mathrm{kPa}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 87

The large tank supplies air at a temperature of $350 \mathrm{~K}$ and an absolute pressure of $600 \mathrm{kPa}$ to the nozzle. If the throat diameter is $30 \mathrm{~mm}$ and the exit diameter is $60 \mathrm{~mm},$ determine the range of backpressures that will cause a standing shock to form within the nozzle.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 88

The jet is flying at $M=1.3$, where the absolute air pressure is $50 \mathrm{kPa}$. If a shock is formed at the inlet of the engine, determine the Mach number of the air flow just within the engine where the diameter is $0.6 \mathrm{~m}$. Also, what are the pressure and the stagnation pressure in this region? Assume isentropic flow within the engine.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 89

The large tank supplies air at a temperature of $350 \mathrm{~K}$ and an absolute pressure of $600 \mathrm{kPa}$ to the nozzle. If the throat diameter is $30 \mathrm{~mm}$ and the exit diameter is $60 \mathrm{~mm},$ determine the range of backpressures that will cause oblique shock waves to form at the exit.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 90

A shock is formed in the nozzle at $C,$ where the diameter is $100 \mathrm{~mm}$. If the air flows through the pipe at $A$ at $\mathrm{M}_{A}=3.0$ and the absolute pressure is $p_{A}=15 \mathrm{kPa}$, determine the pressure in the pipe at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 91

The cylindrical plug is fired with a speed of $150 \mathrm{~m} / \mathrm{s}$ in the pipe that contains still air at $20^{\circ} \mathrm{C}$ and an absolute pressure of $100 \mathrm{kPa}$. This causes a shock wave to move down the pipe as shown. Determine its speed and the pressure acting on the plug.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 92

Air flows at $800 \mathrm{~m} / \mathrm{s}$ through a long duct in a wind tunnel, where the temperature is $20^{\circ} \mathrm{C}$ and the absolute pressure is $90 \mathrm{kPa}$. The leading edge of a wing in the tunnel is represented by the $7^{\circ}$ wedge. Determine the pressure created on its top surface if the angle of attack is set at $\alpha=2^{\circ}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 93

Air flows at $800 \mathrm{~m} / \mathrm{s}$ through a long duct in a wind tunnel, where the temperature is $20^{\circ} \mathrm{C}$ and the pressure is $90 \mathrm{kPa}$. The leading edge of a wing in the tunnel is represented by the $7^{\circ}$ wedge. Determine the pressure created on its bottom surface if the angle of attack is set at $\alpha=2^{\circ}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 94

A jet plane is flying in air that has a temperature of $8^{\circ} \mathrm{C}$ and absolute pressure of $90 \mathrm{kPa}$. The leading edge of the wing has the wedge shape shown. If the plane has a speed of $800 \mathrm{~m} / \mathrm{s}$ and the angle of attack is $2^{\circ},$ determine the pressure and temperature of the air at the upper surface $A$ just in front or to the right of the oblique shock wave that forms at the leading edge.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 95

A jet plane is flying in air that has a temperature of $8^{\circ} \mathrm{C}$ and absolute pressure of $90 \mathrm{kPa}$. The leading edge of the wing has the wedge shape shown. If the plane has a speed of $800 \mathrm{~m} / \mathrm{s}$ and the angle of attack is $2^{\circ},$ determine the pressure and temperature of the air at the lower surface $B$ just in front or to the right of the oblique shock wave that forms at the leading edge.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 96

Air flows at $800 \mathrm{~m} / \mathrm{s}$ through a long duct in a wind tunnel, where the temperature is $20^{\circ} \mathrm{C}$ and the absolute pressure is $90 \mathrm{kPa}$. The leading edge of a wing in the tunnel can be represented by the $7^{\circ}$ wedge. Determine the pressure created on its top surface if the angle of attack is set at $\alpha=5^{\circ}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 97

Air flows at $800 \mathrm{~m} / \mathrm{s}$ through a long duct in a wind tunnel, where the temperature is $20^{\circ} \mathrm{C}$ and the absolute pressure is $90 \mathrm{kPa}$. The leading edge of a wing in the tunnel can be represented by the $7^{\circ}$ wedge. Determine the pressure created on its bottom surface if the angle of attack is set at $\alpha=5^{\circ}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 98

The jet plane is flying upward such that its wings make an angle of attack of $15^{\circ}$ with the horizontal. The plane is traveling at $700 \mathrm{~m} / \mathrm{s}$, in air having a temperature of $8^{\circ} \mathrm{C}$ and absolute pressure of $90 \mathrm{kPa}$. If the leading edge of the wing has an angle of $8^{\circ},$ determine the pressure and temperature of the air just in front or to the right of the expansion waves.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 99

Nitrogen gas at a temperature of $30^{\circ} \mathrm{C}$ and an absolute pressure of $150 \mathrm{kPa}$ flows through the large rectangular duct at $1200 \mathrm{~m} / \mathrm{s}$. When it comes to the transition, it is redirected as shown. Determine the angle $\beta$ of the oblique shock that forms at $A$, and the temperature and pressure of the nitrogen just in front or to the right of the wave.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 100

Nitrogen gas at a temperature of $30^{\circ} \mathrm{C}$ and an absolute pressure of $150 \mathrm{kPa}$ flows in the large rectangular duct at $1200 \mathrm{~m} / \mathrm{s}$. When it comes to the transition, it is redirected as shown. Determine the temperature and pressure just in front or to the right of the expansion waves that form in the duct at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 101

The wing of a jet plane is assumed to have the profile shown. It is traveling horizontally at $900 \mathrm{~m} / \mathrm{s}$, in air having a temperature of $8^{\circ} \mathrm{C}$ and absolute pressure of $85 \mathrm{kPa}$. Determine the pressure that acts on the top surface in front or to the right of the oblique shock at $A$ and in front or to the right of the expansion waves at $B$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator