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Fundamentals of Fluid Mechanics

Bruce R. Munson, Donald F. Young, Theodore H. Okiishi

Chapter 11

Compressible Flow - all with Video Answers

Educators

Chapter Questions

01:17

Problem 1

As demonstrated in Video VII.A, fluid density differences in a flow may be seen with the help of a schlieren optical system. Discuss what variables affect fluid density and the different ways in which a variable density flow can be achieved.

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 2

Describe briefly how a schlieren optical visualization system (Videos V11.1 and V11.2 , also Fig.11.4) works. How else might density changes in a fluid flow be made visible to the eye?

Chai Santi
Chai Santi
Numerade Educator
01:01

Problem 3

Are the flows shown in Videos V 11.1 and V 11.2 com pressible? Do they involve high-speed flow velocities? Discuss.

Narayan Hari
Narayan Hari
Numerade Educator
01:18

Problem 4

Explain why the Bernoulli equation (Eq. 3.7) cannot be accurately used for compressible flows.

Ajay Singhal
Ajay Singhal
Numerade Educator
04:40

Problem 5

Air flows steadily between two sections in a duct. At section $(1),$ the temperature and pressure are $T_{1}=80^{\circ} \mathrm{C}$ $p_{1}=301 \mathrm{kPa}(\mathrm{abs}),$ and at section $(2),$ the temperature and pressure are $T_{2}=180^{\circ} \mathrm{C}, p_{2}=181 \mathrm{kPa}(\mathrm{abs}) .$ Calculate the (a) change in internal energy between sections (1) and (2), (b) change in enthalpy between sections (1) and (2), (c) change in density between sections (1) and $(2),(d)$ change in entropy between sections (1) and $(2) .$ How would you estimate the loss of available energy between the two sections of this flow?

Narayan Hari
Narayan Hari
Numerade Educator
02:01

Problem 6

Helium is compressed isothermally from 121 kPa(abs) to $301 \mathrm{kPa}(\mathrm{abs}) .$ Determine the entropy change associated with this process.

Anjali Tiwari
Anjali Tiwari
Numerade Educator
03:39

Problem 7

Air at 14.7 psia and $70^{\circ} \mathrm{F}$ is compressed adiabatically by a centrifugal compressor to a pressure of 100 psia. What is the minimum temperature rise possible? Explain.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
01:01

Problem 8

Methane is compressed adiabatically from $100 \mathrm{kPa}(\mathrm{abs})$ and $25^{\circ} \mathrm{C}$ to $200 \mathrm{kPa}$ (abs). What is the minimum compressor exit temperature possible? Explain.

Narayan Hari
Narayan Hari
Numerade Educator
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Problem 9

Air expands adiabatically through a turbine from a pressure and temperature of 180 psia, $1600^{\circ} \mathrm{R}$ to a pressure of 14.7 psia. If the actual temperature change is $85 \%$ of the ideal tem perature change, determine the actual temperature of the expanded air and the actual enthalpy and entropy differences across the turbine.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 10

An expression for the value of $c_{p}$ for carbon dioxide as a function of temperature is
$$c_{\rho}=286-\frac{1.15 \times 10^{5}}{T}+\frac{2.49 \times 10^{6}}{T^{2}}$$where $c_{p}$ is in $(\mathrm{ft} \cdot \mathrm{lb}) /\left(\mathrm{lbm} \cdot^{\circ} \mathrm{R}\right)$ and $T$ is in $^{\circ} \mathrm{R}$. Compare the change in enthalpy of carbon dioxide using the constant value of $c_{p}$ (see Table 1.7 ) with the change in enthalpy of carbon dioxide using the expression above, for $T_{2}-T_{1}$ equal to (a) $10^{\circ} \mathrm{R}$.
(b) $1000^{\circ} \mathrm{R},(\mathrm{c}) 3000^{\circ} \mathrm{R} .$ Set $T_{1}=540^{\circ} \mathrm{R}$

Victor Salazar
Victor Salazar
Numerade Educator
00:12

Problem 11

Does sound travel faster in the winter or summer? Why?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
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Problem 12

Using information provided in Table $C .1$, develop a table of speed of sound in $\mathrm{ft} / \mathrm{s}$ as a function of elevation for U.S. standard atmosphere.

Victor Salazar
Victor Salazar
Numerade Educator
01:07

Problem 13

Determine the Mach number of a car moving in standard air at a speed of (a) $25 \mathrm{mph},(\mathrm{b}) 55 \mathrm{mph}$, and (c) $100 \mathrm{mph}$

Narayan Hari
Narayan Hari
Numerade Educator
01:32

Problem 14

Estimate the Mach Numbers levels associated with space shuttle main engine nozzle exit flows at launch (see Video V11.3)

James Kiss
James Kiss
Numerade Educator
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Problem 15

How would you estimate the distance between you and an approaching storm front involving lightning and thunder?

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 16

11.16 If a high-performance aircraft is able to cruise at a Mach number of 3.0 at an altitude of $80,000 \mathrm{ft}$, how fast is this in (a) mph,(b) $\mathrm{ft} / \mathrm{s},(\mathrm{c}) \mathrm{m} / \mathrm{s} ?$

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 17

Compare values of the speed of sound in $\mathrm{ft} / \mathrm{s}$ at $68^{\circ} \mathrm{F}$ the following gases: (a) air, (b) carbon dioxide, (c) helium,
(d) hydrogen, (e) methane. Give one example of why knowing this may be important.

Victor Salazar
Victor Salazar
Numerade Educator
00:16

Problem 18

If a person inhales helium and then talks, his or her voice sounds like "Donald Duck." Explain why this happens.

Shoukat Ali
Shoukat Ali
Other Schools
01:00

Problem 19

Explain how you could vary the Mach number but not the Reynolds number in air flow past a sphere. For a constant Reynolds number of 300,000 , estimate how much the drag $\mathrm{co}$. efficient will increase as the Mach number is increased from 0.3 to 1.0.

Chai Santi
Chai Santi
Numerade Educator
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Problem 20

If the observed speed of sound in steel is $5300 \mathrm{m} / \mathrm{s}$, determine the bulk modulus of elasticity of steel in $\mathrm{N} / \mathrm{m}^{3}$. The density of steel is nominally $7790 \mathrm{kg} / \mathrm{m}^{3}$. How does your value of $E_{v}$ for steel compare with $E_{v}$ for water at $15.6^{\circ} \mathrm{C}$ ? Compare the speed of sound in steel and in water and comment on what you observe.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 21

At the seashore, you observe a high-speed aircraft moving overhead at an elevation of $10,000 \mathrm{ft}$. You hear the plane $8 \mathrm{s}$ after it passes directly overhead. Using a nominal air temperature of $40^{\circ} \mathrm{F}$, estimate the Mach number and speed of the aircraft.

Victor Salazar
Victor Salazar
Numerade Educator
00:39

Problem 22

For the situation described in Example 11.4 , show that as the Mach number of the aircraft becomes much larger, the time delay between seeing the airplane overhead and hearing it approaches z/c.

Erika Bustos
Erika Bustos
Numerade Educator
15:41

Problem 23

At a given instant of time, two pressure waves, each moving at the speed of sound, emitted by a point source moving with constant velocity in a fluid at rest are shown in Fig. P11.23. Determine the Mach number involved and indicate with a sketch the instantaneous location of the point source.

Paul A.
Paul A.
California State Polytechnic University, Pomona
15:41

Problem 24

At a given instant of time, two pressure waves, each moving at the speed of sound, emitted by a point source moving with constant velocity in a fluid at rest, are shown in Fig. P1 $1.24 .$ Determine the Mach number involyed and indicate with a sketch the instantaneous location of the point source.

Paul A.
Paul A.
California State Polytechnic University, Pomona
01:01

Problem 25

How much time in seconds will it take for the "bang" of a firecracker exploding to be heard after the blast from 200 yards away on a standard day (see Video V11.5)?

Amy Jiang
Amy Jiang
Numerade Educator
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Problem 26

Sound waves are very small amplitude pressure pulses that travel at the "speed of sound." Do very large amplitude waves such as a blast wave caused by an explosion (see Video V11.5) travel less than, equal to, or greater than the speed of sound? Explain.

Victor Salazar
Victor Salazar
Numerade Educator
06:44

Problem 27

Starting with the enthalpy form of the energy equation (Eq. $5.69),$ show that for isentropic flows, the stagnation temperature remains constant.

Robert Zaballa
Robert Zaballa
Numerade Educator
01:42

Problem 28

Explain how fluid pressure varies with cross-sectional area change for the isentropic flow of an ideal gas when the flow is (a) subsonic, (b) supersonic.

Dading Chen
Dading Chen
Numerade Educator
05:00

Problem 29

For any ideal gas, prove that the slope of constant pressure lines on a temperature-entropy diagram is positive and that higher pressure lines are above lower pressure lines. Why is this important?

Mahnoor Amin
Mahnoor Amin
Numerade Educator
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Problem 30

Determine the critical pressure and temperature ratios for (a) air, (b) carbon dioxide, (c) helium, (d) hydrogen,
(e) methane, (f) nitrogen, (g) oxygen. What is the critical state?

Victor Salazar
Victor Salazar
Numerade Educator
01:45

Problem 31

Air flows steadily and isentropically from standard atmospheric conditions to a receiver pipe through a converging duct. The cross-sectional area of the throat of the con verging duct is $0.05 \mathrm{ft}^{2}$. Determine the mass flowrate through the duct if the receiver pressure is (a) 10 psia, (b) 5 psia. Sketch temperature - entropy diagrams for situations (a) and (b). Verify results obtained with values from the appropriate graph in Appendix D with calculations involving ideal gas equations.

Dominador Tan
Dominador Tan
Numerade Educator
13:01

Problem 32

Helium at $68^{\circ} \mathrm{F}$ and 14.7 psia in a large tank flows steadify and isentropically through a converging nozzle to a receiver pipe. The cross-sectional area of the throat of the converging passage is $0.05 \mathrm{ft}^{2}$. Determine the mass flowrate through the duct if the receiver pressure is (a) 10 psia, (b) 5 psia. Sketch temperature - entropy diagrams for situations (a) and (b).

Susan Hallstrom
Susan Hallstrom
Numerade Educator
04:45

Problem 33

Determine the static pressure to stagnation pressure ratio associated with the following motion in standard air: (a) a runner moving at the rate of 10 mph, (b) a cyclist moving at the rate of $40 \mathrm{mph},(\mathrm{c})$ a car moving at the rate of $65 \mathrm{mph}$ (d) an airplane moving at the rate of 500 mph.

Narayan Hari
Narayan Hari
Numerade Educator
05:37

Problem 34

The static pressure to stagnation pressure ratio at a point in an ideal gas flow field is measured with a Pitot-static probe as being equal to $0.6 .$ The stagnation temperature of the gas is $20^{\circ} \mathrm{C}$. Determine the flow speed in $\mathrm{m} / \mathrm{s}$ and the Mach number if the gas is (a) air, (b) carbon dioxide, (c) hydrogen.

Narayan Hari
Narayan Hari
Numerade Educator
02:11

Problem 35

The stagnation pressure and temperature of air flowing past a probe are $120 \mathrm{kPa}(\mathrm{abs})$ and $100^{\circ} \mathrm{C},$ respectively. The air pressure is $80 \mathrm{kPa}(\text { abs })$. Determine the air speed and the Mach number considering the flow to be (a) incompress¿ble, (b) compressible.

Chai Santi
Chai Santi
Numerade Educator
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Problem 36

The stagnation pressure indicated by a Pitot tube mounted on an airplane in flight is $45 \mathrm{kPa}(\mathrm{abs})$. If the aircraft is cruising in standard atmosphere at an altitude of $10,000 \mathrm{m}$ determine the speed and Mach number involved.

Victor Salazar
Victor Salazar
Numerade Educator
01:48

Problem 37

Estimate the stagnation pressure level necessary at the entrance of a space shuttle main engine nozzle to achieve the over expansion condition shown in Video V11.3

Chai Santi
Chai Santi
Numerade Educator
02:57

Problem 38

An ideal gas enters subsonically and flows isentropi. cally through a choked converging - diverging duct having a circular cross-sectional area $A$ that varies with axial distance from the throat, $x,$ according to the formula $$A=0.1+x^{2}$$ where $A$ is in square feet and $x$ is in feet. For this flow situar tion, sketch the side view of the duct and graph the variation of Mach number, static temperature to stagnation temperature ratio, $T / T_{0},$ and static pressure to stagnation pressure ratio, $p / p_{0}$ through the duct from $x=-0.6 \mathrm{ft}$ to $x=+0.6 \mathrm{ft}$, Also show the possible fluid states at $x=-0.6 \mathrm{ft}, 0 \mathrm{ft},$ and $+0.6 \mathrm{ft}$ using temperature-entropy coordinates. Consider the gas as being helium (use $0.051 \leq \mathrm{Ma} \leq 5.193$ ). Sketch on your pressure variation graph the nonisentropic paths that would occur with over-and under expanded duct exit flows (see Video $V 11.4$ ) and explain when they will occur. When will isentropic supersonic duct exit flow occur?

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 39

An ideal gas enters supersonically and flows isentropically through the choked converging- diverging duct described in Problem $11.38 .$ Graph the variation of $\mathrm{Ma}, T / T_{0},$ and $\mathrm{p} / \mathrm{p}_{0}$ from the entrance to the exit sections of the duct for helium (use $0.051 \leq \mathrm{Ma} \leq 5.193$ ). Show the possible - fluid states at $x=-0.6 \mathrm{ft}, 0 \mathrm{ft},$ and $+0.6 \mathrm{ft}$ using temperature-entropy coordiates. Sketch on your pressure yariation graph the nonisentropic paths that would occur with over- and underexpanded duct exit flows (see Video V1 1.4 ) and explain when they will occur. When will isentropic supersonic duct exit flow occur?

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 40

Helium enters supersonically and flows isentropically through the choked converging-diverging duct described in Ex. ample $11.8 .$ Compare the variation of $\mathrm{Ma}, T / T_{0},$ and $p / p_{0}$ for helium with the variation of these parameters for air throughout the duct. Use $0.163 \leq \mathrm{Ma} \leq 3.221 .$ Sketch on your pressure variation graph the nonisentropic paths that would occur with over- and underexpanded duct exit flows (see Video V 11.4 ) and explain when they will occur. When will isentropic supersonic ?uct exit flow occur?

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 41

Helium enters subsonically and flows isentropically through the converging - diverging duct of Example $11.8 . \mathrm{Com}$ pare the values of $\mathrm{Ma}, T / T_{0},$ and $p / p_{0}$ for helium with those for air at several locations in the duct. Use $0.163 \leq \mathrm{Ma} \leq 3.221$ Sketch on your pressure variation graph the nonisentropic paths that would occur with over- and underexpanded duct exit flows (see Video 11.4 ) and explain when they will occur. When will isentropic supersonic duct exit flow occur?

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 42

Helium flows subsonically and isentropically through the converging-diverging duct of Example $11.8 .$ Graph the variation of $\mathrm{Ma}, T / T_{0},$ and $p / p_{0}$ through the duct from $x=-0.5 \mathrm{m}$ to $x=+0.5 \mathrm{m}$ for $p / p_{0}=0.99$ at $x=-0.5 \mathrm{m} .$ Sketch the cor responding $T-s$ diagram. Use $0.110 \leq \mathrm{M}_{2} \leq 0.430$

Dominador Tan
Dominador Tan
Numerade Educator
01:36

Problem 43

An ideal gas flows subsonically and isentropically through the converging - diverging duct described in Problem $11.38 .$ Graph the variation of $\mathrm{Ma}, T / T_{0},$ and $p / p_{0}$ from the entrance to the exit sections of the duct for (a) air, (b) helium $(\text { use } 0.047 \leq \mathrm{Ma} \leq 0.722)$ The value of $p / p_{0}$ is 0.6708 at $x=0$ ft. Sketch important states on a $T-s$ diagram.

Dominador Tan
Dominador Tan
Numerade Educator
01:19

Problem 44

Graph, for the isentropic flow of an ideal gas having a constant specific heat ratio, $k,$ of $1.4,$ the variation of critical area ratio, $A / A^{*},$ as a function of Mach number for $0.1 \leq$ $\mathrm{Ma} \leq 3.0$.

Manik Pulyani
Manik Pulyani
Numerade Educator
02:46

Problem 45

An ideal gas is to flow isentropically from a large tank where the air is maintained at a temperature and pressure of $59^{\circ} \mathrm{F}$ and 80 psia to standard atmospheric discharge conditions. Describe in general terms the kind of duct involved and deter". mine the duct exit Mach number and velocity in $\mathrm{ft} / \mathrm{s}$ if the gas is (a) air, (b) methane, (c) helium.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:34

Problem 46

An ideal gas flows isentropically through a converging-diverging nozzle. At a section in the converging portion of the nozzle, $A_{1}=0.1 \mathrm{m}^{2}, p_{1}=600 \mathrm{kPa}(\mathrm{abs}), T_{1}=20^{\circ} \mathrm{C},$ and
$\mathrm{Ma}_{1}=0.6 .$ For section (2) in the diverging part of the $\mathrm{nozzle}$ determine $A_{2}, p_{2},$ and $T_{2}$ if $\mathrm{Ma}_{2}=3.0$ and the gas is (a) air, (b) helium.

Chai Santi
Chai Santi
Numerade Educator
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Problem 47

Upstream of the throat of an isentropic converging diverging nozzle at section $(1), V_{1}=150 \mathrm{m} / \mathrm{s}, p_{1}=100 \mathrm{kP}_{2}(\mathrm{abs})$ and $T_{1}=20^{\circ} \mathrm{C}$. If the discharge flow is supersonic and the throat area is $0.1 \mathrm{m}^{2}$, determine the mass flowrate in $\mathrm{kg} / \mathrm{s}$ for the flow of (a) aix, (b) methane, (c) helium.

Victor Salazar
Victor Salazar
Numerade Educator
01:26

Problem 48

The flow blockage associated with the use of an intrusive probe can be important. Determine the percentage increase in section velocity corresponding to a $0.5 \%$ reduction in flow area due to probe blockage for air flow if the section area is $1.0 \mathrm{m}^{2}, T_{0}=20^{\circ} \mathrm{C},$ and the unblocked flow Mach numbers are (a) $\mathrm{Ma}=0.2,(b) \mathrm{Ma}=0.8,(\mathrm{c}) \mathrm{Ma}=1.5,(\mathrm{d}) \mathrm{Ma}=30$

Chai Santi
Chai Santi
Numerade Educator
02:00

Problem 49

An ideal gas enters [section ( 1 )] an insulated, constant cross sectional area duct with the following properties:
$$\begin{aligned}
T_{0} &=293 \mathrm{K} \\
p_{0} &=101 \mathrm{kPa}(\mathrm{abs}) \\
\mathrm{Ma}_{1} &=0.2
\end{aligned}$$
For Fanno flow, determine corresponding values of fluid temperature and entropy change for various levels of pressure and plot the Fanno line if the gas is helium.

Dominador Tan
Dominador Tan
Numerade Educator
03:49

Problem 50

For Fanno flow, prove that
$$\frac{d V}{V}=\frac{f K\left(M a^{3} / 2\right)(d x / D)}{1-M a^{2}}$$
and in so doing show that when the flow is subsonic, friction accelerates the fluid, and when the flow is supersonic, friction decelerates the fluid.

Netra Sharma
Netra Sharma
University of Wisconsin - Milwaukee
01:17

Problem 51

Standard atmospheric air $\left(T_{0}=59^{\circ} \mathrm{F}, p_{0}=14.7 \mathrm{psia}\right)$ is drawn steadily through a frictionless and adiabatic converging nozzle into an adiabatic, constant cross-sectional area duct. The duct is 10 ft long and has an inside diameter of 0.5 ft. The average friction factor for the duct may be estimated as being equal to $0.03 .$ What is the maximum mass flowrate in slugs/s through the duct? For this maximum flowrate, determine the values of static temperature, static pressure, stagnation temperature, stagnation pressure, and velocity at the inlet [section ( 1 )] and exit [section (2)] of the constant area duct. Sketch a temperature - entropy diagram for this flow.

Dominador Tan
Dominador Tan
Numerade Educator
01:01

Problem 52

The upstream pressure of a Fanno flow venting to the atmosphere is increased until the flow chokes, What will happen to the flowrate when the upstream pressure is further increased?

Narayan Hari
Narayan Hari
Numerade Educator
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Problem 53

The duct in Problem 11.51 is shortened by $50 \%$. The duct discharge pressure is maintained at the choked flow value deter mined in Problem 11.51 . Determine the change in mass flowrate through the duct associated with the $50 \%$ reduction in length. The average friction factor remains constant at a value of 0.03

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 54

If the same mass flowrate of air obtained in Problem 11.51 is desired through the shortened duct of Problem 11.53 determine the back pressure, $p_{2},$ required. Assume $f$ remains constant at a value of 0.03

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 55

If the average friction factor of the duct of Example 11.12 is changed to (a) 0.01 or (b) $0.03,$ determine the maximum mass flowrate of air through the duct associated with each new friction factor; compare with the maximum mass flowrate value of Example 11.12

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 56

If the length of the constant area duct of Example 11.12 is changed to (a) I $\mathrm{m}$ or (b) $3 \mathrm{m}$, and all other specifications in the problem statement remain the same, determine the maximum mass flowrate of air through the duct associated with each new length; compare with the maximum mass flowrate of Example 11.12

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 57

The duct of Example 11.12 is lengthened by $50 \%$. If the duct discharge pressure is set at a value of $p_{d}=46.2 \mathrm{kPa}(\mathrm{abs})$ ?etermine the mass flowrate of air through the lengthened duct. The average friction factor for the duct remains constant at a value of 0.02

Victor Salazar
Victor Salazar
Numerade Educator
01:34

Problem 58

An ideal gas flows adiabatically with friction through a long, constant area pipe. At upstream section ( 1 ), $p_{1}=60$ $\mathrm{kPa}(\mathrm{abs}), \mathrm{T}_{1}=60^{\circ} \mathrm{C},$ and $V_{3}=200 \mathrm{m} / \mathrm{s}$. At downstream section $\tan (2), T_{2}=30^{\circ} \mathrm{C} .$ Determine $p_{2}, V_{2},$ and the stagnation pressure ratio $p_{0.2} / p_{0.1}$ if the gas is (a) air, (b) helium.

Chai Santi
Chai Santi
Numerade Educator
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Problem 59

For the air flow of Problem $11.58,$ determine $T, p,$ and V for the section halfway between sections (1) and (2).

Victor Salazar
Victor Salazar
Numerade Educator
02:54

Problem 60

An ideal gas flows adiabatically between two sections in a constant area pipe. At upstream section $(1), p_{0.4}=100$ psia, $T_{0,1}=600^{\circ} \mathrm{R},$ and $\mathrm{Ma}_{1}=0.5 .$ At downstream section $(2),$ the flow is choked. Determine the magnitude of the force per unit cross-sectional area exerted by the inside wall of the pipe on the thuid between sections (l) and (2) if the gas is (a) air, (b) helium.

Narayan Hari
Narayan Hari
Numerade Educator
02:00

Problem 61

An ideal gas enters \{section (1)] a frictionless, constant area duct with the following properties:
$$\begin{aligned}
T_{0} &=293 \mathrm{K} \\
p_{0} &=101 \mathrm{kPa}(\mathrm{abs}) \\
\mathrm{Ma}_{\mathrm{j}} &=0.2
\end{aligned}$$
For Rayleigh flow, determine corresponding values of fluid temperature and entropy change for various levels of pressure and plot the Rayleigh line if the gas is helium.

Dominador Tan
Dominador Tan
Numerade Educator
01:34

Problem 62

Standard atmospheric air $\left[T_{0}=288 \mathrm{K}, \quad p_{0}=101\right.$$\mathrm{kPa}(\mathrm{abs})]$ is drawn steadily through an isentropic converging nozzle into a frictionless diabatic $(q=500 \mathrm{kJ} / \mathrm{kg})$ constant area duct. For maximum flow, determine the values of static temperature, static pressure, stagnation temperature, stagnation pressure, and flow velocity at the inlet [section (1)] and exit [section $(2)]$ of the constant area duct. Sketch a temperature entropy diagram for this flow.

Dominador Tan
Dominador Tan
Numerade Educator
03:19

Problem 63

An ideal gas enters a 0.5 -ft inside diameter duct with $p_{1}=20$ psia $, T_{1}=80^{\circ} \mathrm{F},$ and $V_{1}=200 \mathrm{ft} / \mathrm{s} .$ What frictionless heat addition rate in $\mathrm{Btu} / \mathrm{s}$ is necessary for an exit gas temperature $T_{2}=1500^{\circ} \mathrm{F} ?$ Determine $p_{2}, V_{2},$ and $\mathrm{Ma}_{2}$ also. The gas is (a) air, (b) helium.

Narayan Hari
Narayan Hari
Numerade Educator
10:16

Problem 64

Air enters a length of constant area pipe with $p_{1}=$ $200 \mathrm{kPa}(\mathrm{abs}), T_{4}=500 \mathrm{K},$ and $V_{1}=400 \mathrm{m} / \mathrm{s} .$ If $500 \mathrm{kJ} / \mathrm{kg}$ of energy is removed from the air by frictionless heat transfer between sections (1) and (2), determine $p_{3}, T_{2},$ and $V_{2} .$ Sketch a temperature-entropy diagram for the flow between sections (I) and (2)

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:10

Problem 65

Describe what happens to a Fanno flow when heat trans fer is allowed to occur. Is this the same as a Rayleigh flow with friction considered?

Dominador Tan
Dominador Tan
Numerade Educator
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Problem 66

The Mach number and stagnation pressure of an ideal gas are 2.0 and $200 \mathrm{kPa}(\text { abs })$ just upstream of a normal shock. Determine the stagnation pressure loss across the shock for the following gases: (a) air, (b) helium. Comment on the effect of specific heat ratio, $k,$ on shock loss.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 67

The stagnation pressure ratio across a normal shock in an ideal gas flow is $0.6 .$ Determine the Mach number of the flow entering the shock if the gas is air.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 68

Just upstream of a normal shock in an ideal gas flow, $\mathrm{Ma}=3.0, T=600^{\circ} \mathrm{R},$ and $p=30$ psia. Determine values of Ma, $T_{0}, T, p_{6}, p,$ and $V$ downstream of the shock if the gas is (a) air, (b) helium.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 69

A total pressure probe like the one shown in Video V3.4 is inserted into a supersonic air flow. A shock wave forms just upstream of the impact hole. The probe measures a total pressure of $500 \mathrm{kPa}(\text { abs })$. The stagnation temperature at the probe head is $500 \mathrm{K}$. The static pressure upstream of the shock is measured with a wall tap to be $100 \mathrm{kpa}$ (abs). From these data, determine the Mach number and velocity of the flow.

Victor Salazar
Victor Salazar
Numerade Educator
01:35

Problem 70

The Pitot tube on a supersonic aircraft (see Video V3.4 ) cruising at an altitude of $30,000 \mathrm{ft}$ senses a stagnation pressure of 12 psia. If the atmosphere is considered standard, determine the airspeed and Mach number of the aircraft. A shock wave is present just upstream of the probe impact hole.

Narayan Hari
Narayan Hari
Numerade Educator
02:10

Problem 71

An aircraft cruises at a Mach number of 2.0 at an altitude of $15 \mathrm{km}$. Infet air is decelerated to a Mach number of 0.4 at the engine compressor inlet. A normal shock occurs in the inlet diffuser upstream of the compressor inlet at a section where the Mach number is $1.2 .$ For isentropic diffusion, except across the shock, and for standard atmosphere, determine the stagnation temperature and pressure of the air entering the engine compressor.

Chai Santi
Chai Santi
Numerade Educator
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Problem 72

Determine, for the air flow through the frictionless and adiabatic converging-diverging duct of Example 11.8 , the ratio of duct exit pressure to duct inlet stagnation pressure that will result in a standing normal shock at: (a) $x=+0.1 \mathrm{m}$ (b) $x=+0.2 \mathrm{m},$ (c) $x=+0.4 \mathrm{m}$. How large is the stagnation pressure loss in each case?

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 73

A normal shock is positioned in the diverging portion of a frictionless, adiabatic, converging-diverging air flow duct where the cross-sectional area is $0.1 \mathrm{ft}^{2}$ and the local Mach number is 2.0. Upstream of the shock, $p_{0}=200$ psia and $T_{0}=1200^{\circ} \mathrm{R}$ If the duct exit area is $0.15 \mathrm{ft}^{2}$, determine the exit area temperature and pressure and the duct mass flowrate.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 74

Supersonic air flow enters an adiabatic, constant area (inside diameter $=\{f t) 30$ -ft-long pipe with $M a_{1}=3,0 .$ The pipe friction factor is estimated to be $0.02 .$ What ratio of pipe exit pressure to pipe inlet stagnation pressure would result in a normal shock wave standing at (a) $x=5 \mathrm{ft},$ or (b) $x=10 \mathrm{ft}$ where $x$ is the distance downstream from the pipe entrance? Determine also the duct exit Mach number and sketch the temperature-entropy diagram for each situation.

Victor Salazar
Victor Salazar
Numerade Educator
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Problem 75

Supersonic ideal gas flow enters an adiabatic, constant area pipe (inside diameter $=0.1 \mathrm{m}$ ) with $\mathrm{Ma}_{\mathrm{f}}=2.0 .$ The pipe friction factor is $0.02 .$ If a standing normal shock is located right at the pipe exit, and the Mach number just upstream of the shock is $1.2,$ determine the length of the pipe if the gas is (a) air,
(b) helium.

Victor Salazar
Victor Salazar
Numerade Educator
02:52

Problem 76

Air enters a frictionless, constant area duct with $\mathrm{Ma}_{1}=2.0, T_{0.1}=59^{\circ} \mathrm{F},$ and $p_{0,4}=14.7$ psia. The air is decelerated by heating until a normal shock wave occurs where the local Mach number is $1.5 .$ Downstream of the normal shock, the subsonic flow is accelerated with heating until it chokes at the duct exit. Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit. Sketch the temperature-entropy diagram for this flow.

Dominador Tan
Dominador Tan
Numerade Educator
01:42

Problem 77

An ideal gas enters a frictionless, constant area duct with $\mathrm{Ma}=2.5, T_{0}=20^{\circ} \mathrm{C},$ and $p_{0}=101 \mathrm{kPa}$ (abs). The gas is decelerated by heating until a normal shock occurs where the local Mach number is $1.3 .$ Downstream of the shock, the subsonic flow is accelerated with heating until it exits with a Mach number of $0.9 .$ Determine the static temperature and pressure, the stagnation temperature and pressure, and the fluid velocity at the duct entrance, just upstream and downstream of the normal shock, and at the duct exit if the gas is (a) air or (b) helium. Sketch the temperature-entropy diagram for each flow.

Dominador Tan
Dominador Tan
Numerade Educator
03:37

Problem 78

Discuss the similarities between hydraulic jumps in open-channel flow and shock waves in compressible flow

Ren Jie Tuieng
Ren Jie Tuieng
Numerade Educator
01:40

Problem 79

Estimate the surface temperature associated with the re-entry of the Space Shuttle into the earth's atmosphere. List all assumptions and show calculations.

Supratim Pal
Supratim Pal
Numerade Educator
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Problem 80

Estimate the maximum temperature developed on the leading edge of the wings of a stealth fighter airplane. List all assumptions and show calculations.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
00:59

Problem 81

Prove that the linear momentum parallel to a Mach wave is conserved across the Mach wave.

Monica Miller
Monica Miller
Numerade Educator
01:19

Problem 82

[See "Hilsch tube( Rangue vortex tube)," Section 11.1.] Explain why a Hilch tube works and cite some high and low gas temperatures actually achieved.

David Collins
David Collins
Numerade Educator
01:19

Problem 83

[See "Hilsch tube (Ranque vortex )." Section 11.1] What is the most important limitation of a Hilsch tube?

David Collins
David Collins
Numerade Educator
00:42

Problem 84

( See "Sonification," Section 11.2.) Give one specific example of how a data set that was made "visible" could also be made "audible."

Nick Johnson
Nick Johnson
Numerade Educator
03:35

Problem 85

(See "Supersonic and compressible flows in gas turbine rotors, prove that supersonic fluid velocities relative to blade surfaces are possible.

Nathan Nowack
Nathan Nowack
Numerade Educator
01:46

Problem 86

(See "Super Rocket nozzles." Section $11.4 .2 .)$ Comment on the practical limits of area ratio for the diverging portion of a converging-diverging nozzle designed to achieve supersonic exit flow.

Dominador Tan
Dominador Tan
Numerade Educator