Questions and Answers of Fundamentals Of Gas

A supersonic flow of air has a pressure of \(1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) and a temperature of \(350 \mathrm{~K}\). After expanding through a \(35^{\circ}\) turn, the Mach number is
In a problem similar to Problem 8.2, \(\theta_{1}\) is unknown, but \(\theta_{2}=15.90^{\circ}\) and \(\theta_{3}=82.25^{\circ}\). Can you determine the initial Mach number?Data in Problem 8.2,A
Conditions at the entrance to a duct are \(M_{1}=3.0\) and \(p_{1}=8 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}\). After a certain length the flow has reached \(M_{2}=1.5\). Determine \(p_{2}\) and
A flow of nitrogen is discharged from a duct with \(M_{2}=0.85, T_{2}=500^{\circ} \mathrm{R}\), and \(p_{2}=28\) psia. The temperature at the inlet is \(560^{\circ} \mathrm{R}\). Compute the pressure
Air enters a circular duct with a Mach number of 3.0.The friction factor is 0.01 .(a) How long a duct (measured in diameters) is required to reduce the Mach number to 2.0 ?(b) What is the percentage
Oxygen enters a 6-in.-diameter duct with \(T_{1},=600^{\circ} \mathrm{R}, p_{1}=50 \mathrm{psia}\), and \(V_{1}=600 \mathrm{ft} /\) sec. The friction factor is \(f=0.02\).(a) What is the maximum
Air flows in an 8-cm-inside diameter pipe that is \(4 \mathrm{~m}\) long. The air enters with a Mach number of 0.45 and a temperature of \(300 \mathrm{~K}\).(a) What friction factor would cause sonic
At one section in a constant-area duct the stagnation pressure is \(66.8 \mathrm{psia}\) and the Mach number is 0.80 . At another section the pressure is \(60 \mathrm{psia}\) and the temperature is
A \(50 \times 50 \mathrm{~cm}\) duct is \(10 \mathrm{~m}\) in length. Nitrogen enters at \(M_{1}=3.0\) and leaves at \(M_{2}=1.7\), with \(T_{2}=280 \mathrm{~K}\) and \(p_{2}=7 \times 10^{4}
Air enters a duct with a mass flow rate of \(35 \mathrm{lbm} / \mathrm{sec}\) at \(T_{1}=520^{\circ} \mathrm{R}\) and \(p_{1}=20 \mathrm{psia}\). The duct is square and has an area of \(0.64
Consider the flow of a perfect gas along a Fanno line. Show that the pressure at the * reference state is given by the relation 1/2 m 2RT, P Ayge(y+1)
Air enters a constant-area duct with \(M_{1}=2.95\) and \(T_{1}=500^{\circ} \mathrm{R}\). Heat transfer decreases the outlet Mach number to \(M_{2}=1.60\).(a) Compute the exit static and stagnation
At the beginning of a duct the nitrogen pressure is \(1.5 \mathrm{bar}\), the stagnation temperature is \(280 \mathrm{~K}\), and the Mach number is 0.80 . After some heat transfer the static pressure
Air flows at the rate of \(39.0 \mathrm{lbm} / \mathrm{sec}\) with a Mach number of 0.30 , a pressure of 50 psia, and a temperature of \(650^{\circ} \mathrm{R}\). The duct has a
In a flow of air \(ho_{1}=1.35 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}, T_{1}=500 \mathrm{~K}\), and \(V_{1}=540 \mathrm{~m} / \mathrm{s}\). Heat transfer occurs in a constant-area duct until the
At some point in a flow system of oxygen \(M_{1}=3.0, T_{t 1}=800^{\circ} \mathrm{R}\), and \(p_{1}=35\) psia. At a section farther along in the duct, the Mach number has been reduced to
Show that for a constant-area, frictionless, steady, one-dimensional flow of a perfect gas, the maximum amount of heat that can be added to such system is given by the expression Imax (M-1) CpT 2M(+1)
Air enters a \(15-\mathrm{cm}\)-diameter duct with a velocity of \(120 \mathrm{~m} / \mathrm{s}\). The pressure is \(1 \mathrm{~atm}\) and the temperature is \(100^{\circ} \mathrm{C}\).(a) How much
Conditions just prior to a standing normal shock in air are \(M_{1}=3.53\), with a temperature of \(650^{\circ} \mathrm{R}\) and a pressure of 12 psia.(a) Compute the conditions that exist just after
Air at \(1000^{\circ} \mathrm{R}\) and \(100 \mathrm{psia}\) undergoes a heat addition process to \(1500^{\circ} \mathrm{R}\) and 80 psia. Compute the entropy change. If no work is done, also compute
Conditions entering the compressor of an ideal Brayton cycle are \(520^{\circ} \mathrm{R}\) and 5 psia. The compressor pressure ratio is 12 and the maximum allowable cycle temperature is
A stationary power plant produces \(1 \times 10^{7} \mathrm{~W}\) output when operating under the following conditions: Compressor inlet is \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{bar}\) abs,
An airplane is traveling at \(550 \mathrm{mph}\) at an altitude where the ambient pressure is \(6.5 \mathrm{psia}\). The exit area of the jet engine is \(1.65 \mathrm{ft}^{2}\) and the exit jet has a
The air flow through a jet engine is \(30 \mathrm{~kg} / \mathrm{s}\), and the fuel flow is \(1 \mathrm{~kg} / \mathrm{s}\). The exhaust gases leave with a relative velocity of \(610 \mathrm{~m} /
A twin-engine jet aircraft requires a total net propulsive thrust of \(6000 \mathrm{lbf}\). Each engine consumes air at the rate of \(120 \mathrm{lbm} / \mathrm{sec}\) when traveling at \(650
A boat is propelled by an hydraulic jet. The inlet scoop has an area of \(0.5 \mathrm{ft}^{2}\), and the area of the exit duct is \(0.20 \mathrm{ft}^{2}\). Since the exit velocity will always be
It is proposed to power a monorail car by a pulsejet. A net propulsive thrust of \(5350 \mathrm{~N}\) is required when traveling at a speed of \(210 \mathrm{~km} / \mathrm{h}\). The gases leave the
Consider steady one-dimensional flow of a perfect gas in a horizontal insulated frictionless duct. Start with the pressure-energy equation and show that V2 7 P + = const 28c (y-1)p
It is proposed to determine the flow rate through a pipeline from pressure measurements at two points of different cross-sectional areas. No energy transfers are involved \(\left(q=w_{s}=0\right)\)
Pressure taps in a low-speed wind tunnel reveal the difference between stagnation and static pressure to be 0.5 psi. Calculate the test section air velocity under the assumption that the air density
Water flows through a duct of varying area. The difference in stagnation pressures between two sections is \(4.5 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\).(a) If the water remains at a constant
The following information is known about the steady flow of methane through a horizontal insulated duct:(a) Determine the outlet velocity.(b) What is the stagnation temperature at the outlet?(c)
Under what conditions would it be possible to have an adiabatic flow process with a real fluid (with friction) and have the stagnation pressures at inlet and outlet to the system be the same?
An incompressible fluid \(\left(ho=55 \mathrm{lbm} / \mathrm{ft}^{3}\right)\) leaves the pipe shown in Figure \(\mathrm{P} 3.9\) with a velocity of \(15 \mathrm{ft} / \mathrm{sec}\).(a) Calculate the
For the flow depicted in Figure P3.10, what \(\Delta z\) value is required to produce a jet velocity \(\left(V_{j}\right)\) of \(30 \mathrm{~m} / \mathrm{s}\) if the flow losses are \(h_{\ell}=15
Water flows in a 2 -ft-diameter duct under the following conditions: \(p_{1}=55 \mathrm{psia}\) and \(V_{1}=20 \mathrm{ft} / \mathrm{sec}\). At another section \(12 \mathrm{ft}\) below the first the
For Figure P3.12, find the pipe diameter required to produce a flow rate of \(50 \mathrm{~kg} / \mathrm{s}\) if the flow losses are \(h_{\ell}=6 V^{2} / 2 g_{c}\). Water h = 6 V/28 V - Figure P3.12 3
A pump at the surface of a lake expels a vertical jet of water (the water falls back into the lake).(a) Discuss briefly (but clearly) all possible sources of irreversibilities in this situation.(b)
Which of the two pumping arrangements shown in Figure P3.14 is more desirable (i.e., less demanding of pump work)? You may neglect the minor loss at the elbow in arrangement (A). PB B Figure P3.14
For a given mass, we can relate the moment of the applied force to the angular momentum by the following:(a) What is the angular momentum per unit mass?(b) What form does the equation above take for
An incompressible fluid flows through a \(10 \mathrm{in}\). diameter horizontal constant-area pipe. At one section the pressure is \(150 \mathrm{psia}\) and \(1000 \mathrm{ft}\) downstream the
Methane gas flows through a horizontal constant-area pipe of \(15 \mathrm{~cm}\) diameter. At section \(1, p_{1}=6\) bar abs., \(T_{1}=66^{\circ} \mathrm{C}\), and \(V_{1}=30 \mathrm{~m} /
Seawater \(\left(ho=64 \mathrm{lbm} / \mathrm{ft}^{3}\right)\) flows through the reducer shown in Figure \(\mathrm{P} 3.18\) with \(p_{1}=50 \mathrm{psig}\). The flow losses between the two sections
(a) Neglect all losses and compute the exit velocity from the tank shown in Figure P3.19.(b) If the opening is 4 in. in diameter, determine the mass flow rate.(c) Compute the force tending to push
A jet of water with a velocity of \(5 \mathrm{~m} / \mathrm{s}\) has an area of \(0.05 \mathrm{~m}^{2}\). It strikes a \(1 \mathrm{~m}\) thick concrete block at a point \(2 \mathrm{~m}\) above the
It is proposed to brake a racing car by opening an air scoop to deflect the air as shown in Figure P3.21. You may assume that the density of the air remains approximately constant at the inlet
A fluid jet strikes a vane and is deflected through angle \(\theta\) (Figure P3.22). For a given jet (fluid, area, and velocity are fixed), what deflection angle will cause the greatest
Entropy changes can be divided into two categories. Define these categories in words and where possible with equations. Comment on the sign of each part.
Given the differential form of the energy equation, derive the pressure-energy equation.
(a) Define the stagnation process. Be careful to state all conditions.(b) Give a general equation for stagnation enthalpy that is valid for all substances.(c) Under what conditions can you use the
One can use either person \(A\) (who is standing still) or person \(B\) (who is running) as a frame of reference (Figure CT3.4). Check the statement below that is correct.(a) The stagnation pressure
Consider the case of steady one-dimensional flow with one stream in and one stream out of the control volume.(a) Under what conditions can we say that the stagnation enthalpy remains constant? (Can
Under certain circumstances, the momentum equation is sometimes written in the following form when used to analyze a control volume:(a) Which of the sections ( \(r\) or \(s\) ) represents the
Compute and compare sonic speeds in air, water, and steel. Assume normal room temperature and pressure. For steel, use Table 4.1 and take \(ho=0.284 \mathrm{lbm} / \mathrm{in}^{3}\). What do your
At what temperature and pressure would carbon monoxide, water vapor, and helium have the same speed of sound as standard air ( \(288 \mathrm{~K}\) and \(1 \mathrm{~atm}\) )?
Start with the relation for stagnation pressure that is valid for a perfect gas:Expand the right side in a binomial series and evaluate the result for small (but not zero) Mach numbers. Show that
Measurement of airflow shows the static and stagnation pressures to be 30 and 32 psig, respectively. (Note that these are gage pressures.) Assume that \(p_{\mathrm{amb}}=14.7\) psia and the
If \(\gamma=1.2\) and the fluid is a perfect gas, what Mach number will give a temperature ratio of \(T / T_{t}=0.909\) ? What will the ratio of \(p / p_{t}\) be for this flow?
Carbon dioxide with a temperature of \(335 \mathrm{~K}\) and a pressure of \(1.4 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) is flowing with a velocity of \(200 \mathrm{~m} / \mathrm{s}\).(a)
The temperature of argon is \(100^{\circ} \mathrm{F}\), the pressure \(42 \mathrm{psia}\), and the velocity \(2264 \mathrm{ft} /\) sec. Calculate the Mach number and stagnation pressure.
Helium flows in a duct with a temperature of \(50^{\circ} \mathrm{C}\), a pressure of 2.0 bar abs., and a total pressure of 5.3 bar abs. Determine the helium velocity in the duct.
An airplane flies \(600 \mathrm{mph}\) at an altitude of \(16,500 \mathrm{ft}\), where the temperature is \(0^{\circ} \mathrm{F}\) and the pressure is \(1124 \mathrm{psfa}\). What temperature and
Air flows at \(M=1.35\) and has a stagnation enthalpy of \(4.5 \times 10^{5} \mathrm{~J} / \mathrm{kg}\). The stagnation pressure is \(3.8 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\). Determine the
A large chamber contains a perfect gas under conditions \(p_{1}, T_{1}, h_{1}\), and so on. The gas is allowed to flow from the chamber (with \(q=w_{s}=0\) ). Show that because the initial energy is
Air flows steadily in an adiabatic duct where no shaft work is involved. At one section, the total pressure is \(50 \mathrm{psia}\), and at another section, it is \(67.3 \mathrm{psia}\). In which
Methane gas flows in an adiabatic, no-work system with negligible change in potential. At one section \(p_{1}=14\) bar abs., \(T_{1}=500 \mathrm{~K}\), and \(V_{1}=125 \mathrm{~m} / \mathrm{s}\). At
Air flows through a constant-area, insulated passage. Entering conditions are \(T_{1}=\) \(520^{\circ} \mathrm{R}, p_{1}=50 \mathrm{psia}\), and \(M_{1}=0.45\). At a point downstream, the Mach number
Carbon dioxide flows in a horizontal adiabatic, no-work system. Pressure and temperature at section 1 are \(7 \mathrm{~atm}\) and \(600 \mathrm{~K}\). At a downstream section, \(p_{2}=4
Oxygen with \(T_{t 1}=1000^{\circ} \mathrm{R}, p_{t 1}=100 \mathrm{psia}\), and \(M_{1}=0.2\) enters a device with a cross-sectional area \(A_{1}=1 \mathrm{ft}^{2}\). There is no heat transfer, work
Consider steady, one-dimensional, constant-area, horizontal, isothermal flow of a perfect gas with no shaft work (Figure P4.17). The duct has a cross-sectional area \(A\) and perimeter \(P\). Let
(a) Define Mach number and Mach angle.(b) Give an expression that represents sonic speed in an arbitrary fluid.(c) Give the relation used to compute sonic speed in a perfect gas.
Consider the steady, one-dimensional flow of a perfect gas with heat transfer. The \(T-\) \(s\) diagram (Figure CT4.2) shows both static and stagnation points at two locations in the system. It is
State whether each of the following statements is true or false.(a) Changing the frame of reference (or superposition of a velocity onto an existing flow) does not change the static enthalpy.(b)
Cite the conditions that are necessary for the stagnation temperature to remain constant in a flow system.
For steady flow of a perfect gas, the continuity equation can be written asDetermine the precise function. m=f(p,M,T,Y,A,R,ge) = const
The following information is common to both parts (a) and (b). Nitrogen flows through a diverging section with \(A_{1}=1.5 \mathrm{ft}^{2}\) and \(A_{2}=4.5 \mathrm{ft}^{2}\). You may assume steady,
Air enters a converging section where \(A_{1}=0.50 \mathrm{~m}^{2}\). At a downstream section, \(A_{2}=\) \(0.25 \mathrm{~m}^{2}, M_{2}=1.0\), and \(\Delta s_{1-2}=0\). It is known that
Oxygen flows into an insulated device with initial conditions as follows: \(p_{1}=30\) psia, \(T_{1}=750^{\circ} \mathrm{R}\), and \(V_{1}=639 \mathrm{ft} / \mathrm{sec}\). The area changes from
Air flows with \(T_{1}=250 \mathrm{~K}, p_{1}=3\) bar abs., \(p_{t 1}=3.4\) bar abs., and the cross-sectional area \(A_{1}=0.40 \mathrm{~m}^{2}\). The flow is isentropic to a point where \(A_{2}=0.30
The following information is known about the steady flow of air through an adiabatic system:At section \(1, T_{1}=556^{\circ} \mathrm{R}, p_{1},=28.0 \mathrm{psia}\)At section \(2, T_{2}=70^{\circ}
Assuming the flow of a perfect gas in an adiabatic, no-work system, show that the sonic speed corresponding to the stagnation conditions \(\left(a_{t}\right)\) is related to the sonic speed where the
Carbon monoxide flows through an adiabatic system. \(M_{1}=4.0\) and \(p_{t 1}=45\) psia. At a point downstream, \(M_{2}=1.8\) and \(p_{2}=7.0\) psia.(a) Are there losses in this system? If so,
Two venturi meters are installed in a \(30-\mathrm{cm}\)-diameter duct that is insulated (Figure P5.8). The conditions are such that sonic flow exists at each throat (i.e., \(M_{1}=M_{4}=1.0\) ).
Starting with the mass flow rate form given as equation (2.30), derive the following relation [equation \((5.44 a)\) ]: m A | = M (1+ [(y1)/2]M)(r+1)/2(r1) (78c)' 1/2 Pt T,
A smooth 3-in.-diameter hole is punched into the side of a large chamber where oxygen is stored at \(500^{\circ} \mathrm{R}\) and 150 psia. Assume frictionless flow.(a) Compute the initial mass flow
Nitrogen is stored in a large chamber under conditions of \(450 \mathrm{~K}\) and \(1.5 \times 10^{5} \mathrm{~N} /\) \(\mathrm{m}^{2}\). The gas leaves the chamber through a convergent-only nozzle
A converging-only nozzle has an efficiency of \(96 \%\). Air enters with negligible velocity at a pressure of \(150 \mathrm{psia}\) and a temperature of \(750^{\circ} \mathrm{R}\). The receiver
A large chamber contains air at \(80 \mathrm{psia}\) and \(600^{\circ} \mathrm{R}\). The air enters a convergingdiverging nozzle which has an area ratio (exit to throat) of 3.0.(a) What pressure must
Air enters a convergent-divergent nozzle at \(20 \mathrm{bar}\) abs. and \(40^{\circ} \mathrm{C}\). At the end of the nozzle the pressure is 2.0 bar abs. Assume a frictionless adiabatic process. The
A converging-diverging nozzle is designed to operate with an exit Mach number of \(M=2.25\). It is fed by a large chamber of oxygen at \(15.0 \mathrm{psia}\) and \(600^{\circ} \mathrm{R}\) and
A converging-diverging nozzle (Figure P5.16) discharges air into a receiver where the static pressure is \(15 \mathrm{psia}\). A \(1-\mathrm{ft}^{2}\) duct feeds the nozzle with air at \(100
Ten kilograms per second of air is flowing in an adiabatic system. At one section, the pressure is \(2.0 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\), the temperature is \(650^{\circ} \mathrm{C}\),
A standing normal shock occurs in air that is flowing at a Mach number of 1.8.(a) What are the pressure, temperature, and density ratios across the shock?(b) Compute the entropy change for the air as
It is known that sonic speed exists in each throat of the system shown in Figure P6.4. The entropy change for the air is \(0.062 \mathrm{Btu} / \mathrm{lbm}-{ }^{\circ} \mathrm{R}\). Negligible
Air flows in the system shown in Figure P6.5. It is known that the Mach number after the shock is \(M_{3}=0.52\). Considering \(p_{1}\) and \(p_{2}\), it is also known that one of these pressures is
A shock stands at the inlet to the system shown in Figure P6.6. The free-stream Mach number is \(M_{1}=2.90\), the fluid is nitrogen, \(A_{2}=0.25 \mathrm{~m}^{2}\), and \(A_{3}=0.20
A converging-diverging nozzle is designed to produce a Mach number of 2.5 with air.(a) What operating pressure ratio ( \(p_{\text {red }} / p_{t}\) inlet) will cause this nozzle to operate at the
Air enters a convergent-divergent nozzle at \(20 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) and \(40^{\circ} \mathrm{C}\). The receiver pressure is \(2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\)
The diverging section of a supersonic nozzle is formed from the frustum of a cone. When operating at its third critical point with nitrogen, the exit Mach number is 2.6 . Compute the operating
A converging-diverging nozzle receives air from a tank at \(100 \mathrm{psia}\) and \(600^{\circ} \mathrm{R}\). The pressure is 28.0 psia immediately preceding a plane shock that is located in the

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