Questions and Answers of Fundamentals Of Gas

Air enters a device with a Mach number of $M_{1}=2.0$ and leaves with $M_{2}=0.25$. The ratio of exit to inlet area is $A_{2} / A_{1}=3.0$.(a) Find the static pressure ratio \(p_{2} /
Oxygen, with $p_{t}=95.5 \mathrm{psia}$, enters a diverging section of area $3.0 \mathrm{ft}^{2}$. At the outlet the area is $4.5 \mathrm{ft}^{2}$, the Mach number is 0.43 , and the static
Nitrogen flows through a converging-diverging nozzle designed to operate at a Mach number of 3.0. If it is subjected to an operating pressure ratio of 0.5 :(a) Determine the Mach number at the
Consider a converging-diverging nozzle feeding air from a reservoir at $p_{1}$ and $T_{1}$. The exit area is $A_{e}=4 A_{2}$, where $A_{2}$ is the area at the throat. The back pressure
A normal shock is traveling into still air ( $14.7 \mathrm{psia}$ and $520^{\circ} \mathrm{R}$ ) at a velocity of 1800 $\mathrm{ft} / \mathrm{sec}$.(a) Determine the temperature, pressure, and
The velocity of a certain atomic explosion blast wave has been determined to be approximately $46,000 \mathrm{~m} / \mathrm{s}$ relative to the ground. Assume that it is moving into still air at
Air flows in a duct, and a valve is quickly closed. A normal shock is observed to propagate back through the duct at a speed of $1010 \mathrm{ft} / \mathrm{sec}$. The gas that has been brought to
Oxygen at $100^{\circ} \mathrm{F}$ and $20 \mathrm{psia}$ is flowing at $450 \mathrm{ft} / \mathrm{sec}$ in a duct. A valve is quickly shut, causing a normal shock to travel back through the
A closed tube contains nitrogen at $20^{\circ} \mathrm{C}$ and a pressure of $1 \times 10^{4} \mathrm{~N} / \mathrm{m}^{2}$ (Figure P7.5). A shock wave progresses through the tube at a speed of
An oblique shock forms in air at an angle of $\theta=30^{\circ}$. Before passing through the shock, the air has a temperature of $60^{\circ} \mathrm{F}$, a pressure of $10 \mathrm{psia}$, and
Conditions before a shock are $T_{1}=40^{\circ} \mathrm{C}, p_{1}=1.2 \mathrm{bar}$, and $M_{1}=3.0$. An oblique shock is observed at $45^{\circ}$ to the approaching air flow.(a) Determine the
Air at $800^{\circ} \mathrm{R}$ and 15 psia is flowing at a Mach number of $M=1.8$ and is deflected through a $15^{\circ}$ angle. The directional change is accompanied by an oblique shock.(a)
The supersonic flow of a gas $(\gamma=1.4)$ approaches a wedge with a half-angle of $24^{\circ}$ $\left(\delta=24^{\circ}\right)$.(a) What Mach number will put the shock on the verge of
A simple wedge with a total included angle of $28^{\circ}$ is used to measure the Mach number of supersonic flows. When inserted into a wind tunnel and aligned with the flow, oblique shocks are
Air approaches a sharp $15^{\circ}$ convex corner (see Figure 8.4) with a Mach number of 2.0 , temperature of $520^{\circ} \mathrm{R}$, and pressure of $14.7 \mathrm{psia}$. Determine the Mach
A Schleiren photo of the flow around a corner reveals the edges of the expansion fan to be indicated by the angles shown in Figure P8.2. Assume that $\gamma=1.4$.(a) Determine the Mach number
Nitrogen at $25 \mathrm{psia}$ and $850^{\circ} \mathrm{R}$ is flowing at a Mach number of 2.54. After expanding around a smooth convex corner, the velocity of the nitrogen is found to be \(4000
A smooth concave turn similar to that shown in Figure 8.2 turns the flow through a $30^{\circ}$ angle. The fluid is oxygen, and it approaches the turn at $M_{1}=4.0$.(a) Compute \(M_{2}, T_{2} /
The symmetrical diamond-shaped airfoil shown in Figure P8.8 is operating at a $3^{\circ}$ angle of attack. The flight speed is $M=1.8$, and the air pressure equals 8.5 psia.(a) Compute the
A biconvex airfoil (see Figure 8.14) is constructed of circular arcs. We shall approximate the curve on the upper surface by 10 straight-line segments, as shown in Figure P8.9.(a) Determine the
Properties of the flow are given at the exit plane of the two-dimensional duct shown in Figure P8.10. The receiver pressure is 12 psia.(a) Determine the Mach number and temperature just past the exit
Redraw Fig. 5.1 in P-v coordinates. 0.1 T T 2 0,1 0,1 1 M 1 0,2 S Fig. 5.1 Illustration of Flow with Friction on T-s diagram P0,2 22 22 * M=1
Air enters a $5 \mathrm{~cm} \times 5 \mathrm{~cm}$ smooth, insulated square duct with a velocity of $900 \mathrm{~m} / \mathrm{s}$, and a static temperature of $300 \mathrm{~K}$. If the duct length
Air enters a smooth, insulated circular duct at $M=3$. Determine the stagnation pressure loss in the duct for $\mathrm{L} / \mathrm{D}=20$ and 40 . Take $f=0.02$.
Air enters a smooth, insulated $3 \mathrm{~cm}$ diameter duct with stagnation pressure and temperature of $200 \mathrm{kPa}, 500 \mathrm{~K}$, and a velocity of $100 \mathrm{~m} / \mathrm{s}$.
Air enters a $3 \mathrm{~m}$ long pipe $(f=0.02)$ of diameter $0.025 \mathrm{~m}$ at a stagnation temperature of $300 \mathrm{~K}$. If the static pressure of the air at the exit of the pipe is $100
Air enters a pipe $(f=0.02)$ of diameter $0.05 \mathrm{~m}$ with stagnation pressure and temperature equal to $1 \mathrm{MPa}$ and $300 \mathrm{~K}$, respectively. The pipe exhausts into the ambient
Consider the two-tank system in Fig. 6.13. Assume, in addition, the stagnation temperature to be 300Kand the throat diameter of the nozzles to be 2.54 cm. Initially, the pressure in the small tank is
Consider again the two-tank system in Fig. 6.13. Assume that only nozzle A is present and that it is a convergent divergent nozzle of exit-to-throat area ratio 2 with the same throat diameter as
Air enters a convergent divergent nozzle of a rocket engine at a stagnation temperature of 3200 K. The nozzle exhausts into an ambient pressure of 100 kPa and the exit-to-throat area ratio is 10. The
A reservoir of volume V initially contains air at pressure Pi and temperature Ti . A hole of cross-sectional area A develops in the reservoir and the air begins to leak out. Develop an expression for
Consider a CD nozzle with exit and throat areas of 0.5 m2 and 0.25 m2, respectively.The inlet reservoir pressure is 100 kPa and the exit static pressure is 60 kPa.Determine the exit Mach number.
Air at a pressure and temperature of 400 kPa and 300Kcontained in a large vessel is discharged through an isentropic nozzle into a space at a pressure of 100 kPa. Find the mass flow rate if the
Air flows in a frictionless, adiabatic duct at M = 0.6 and P0 = 500 kPa. The cross-sectional area of the duct is 6 cm2 and the mass flow rate is 0.5 kg/s. If the area of the duct near the exit is
A student is trying to design an experimental setup to produce a correctly expanded supersonic stream at a Mach number of 2 issuing into ambient at 100 kPa. For this purpose, the student wishes to
A rocket nozzle produces 1 MN of thrust at sea level (ambient pressure and temperature 100 kPa and 300 K). The stagnation pressure and temperature are 5 MPa and 2800 K. Determine (a) the exit to
Assume that the rocket nozzle of the previous problem is designed to develop a thrust of 1MN at an altitude of 10 km. Determine the thrust developed by the nozzle at 20 km, for the same stagnation
An aircraft engine is operating at an ambient pressure and temperature of P∞ and T∞. The mass flow rate through the engine is m˙ and the air enters with a velocity of u∞. Consider the
A supersonic diffuser is designed to operate at a freestream Mach number of 1.7. Determine the ratio of mass flow rate through the diffuser when it operates at a freestream Mach number of 2 with a
Air enters the combustion chamber of a ramjet engine (Fig. ??) at T0 = 1700K and M = 0.3. How much can the stagnation temperature be increased in the combustion chamber without affecting the inlet
Air enters a constant area combustor followed by a convergent nozzle. Heat addition takes place in the combustor and the flow is isentropic in the nozzle. The inlet Mach number is 0.3, and the
Consider an arrangement consisting of a converging nozzle followed by a smooth, 1m long pipe. The diameter of the pipe is 0.04 m. The stagnation conditions upstream of the nozzle are 2.5 MPa and 500
A converging diverging frictionless nozzle is connected to a large air reservoir by means of a 20mlong pipe of diameter 0.025 m. The inlet, throat, and exit diameters of the nozzle are, respectively,
For the geometry shown in Worked Example 7.2, determine the mass flow rate through the intake and the total pressure recovery for the sub-critical mode of operation when M∞ = 2.5. Compare these
A 2D supersonic inlet (Fig. 7.9) is constructed with two ramps each of which deflects the flow through 15◦. Following the second oblique shock, a fixed throat inlet is used for internal
Consider the forebody, intake and the combustor for a conceptual scramjet engine shown in Fig. 7.11. The freestream conditions are M = 5, P∞ = 830N/m2 and T∞ = 230 K. The ramp angles are 5◦,
Sketc.h the flow field for the flow through the intake shown in Fig. 7.5 indicating oblique shocks and expansion fans clearly. Also show the external flow field around the cowl. Assume critical mode
Air at a stagnation pressure of 1 MPa flows isentropically through a CD nozzle and exhausts into ambient at 40.4 kPa. The edge of the jet, as it comes out of the nozzle is deflected by 18° (counter
A sharp throated nozzle is shown in Fig. 8.6. The flow entering the throat is sonic. The exit to throat area ratio is 3 and the throat makes an angle of 45° with the horizontal. Determine the Mach
A supersonic injector fabricated from a CD nozzle (comprising of a circular arc throat and a conical divergent portion) is shown in Fig. 8.7.3 The throat diameter is 0.55cm and the divergence angle
Dry, saturated steam enters a convergent nozzle at a static pressure of 800 kPa and is expanded to the sonic state. If the inlet and throat diameters are 0.05m and 0.025m respectively, determine the
Dry saturated steam at 1.1 MPa is expanded in a nozzle to a pressure of 15 kPa. Assuming the expansion process to be isentropic and in equilibrium throughout, determine (a) if the nozzle is
Superheated steam at 700 kPa, 220 °C in a steam chest is expanded through a nozzle to a final pressure of 20 kPa. The throat diameter is 10mm. Assuming the expansion process to be isentropic and in
Dry saturated steam at 1.2 MPa is expanded in a nozzle to 20 kPa. The throat diameter of the nozzle is 6mm. If the total mass flow rate is 0.5 kg/s, determine how many nozzles are required and the
Superheated steam at 850 kPa, 200 °C expands in a convergent nozzle until it becomes a saturated vapor. Determine the exit velocity, assuming the expansion process to be isentropic and in
Steam which is initially saturated and dry expands from 1400 kPa to 700 kPa.Assuming the expansion to be in equilibrium (n = 1.135), determine the final velocity and specific volume. If the expansion
Superheated steam at 500 kPa, 180°C is expanded in a nozzle to pressure of 170 kPa. Assuming the expansion process to be isentropic and in equilibrium determine the exit velocity. Assuming the flow
For each of the stagnation condition given below, determine the pressure, velocity and degree of supercooling just before the onset of condensation shock for a limiting value of supersaturation ratio
What is the relation between degrees Fahrenheit and degrees Rankine? And the relation between degrees Celsius and Kelvin?
State Newton's second law as you would apply it to a control mass.
Define a 1-pound force in terms of the acceleration it will give to a 1-pound mass. Give a similar definition for a newton in the SI system.
Explain the significance of $g_{c}$ in Newton's second law. What are the magnitude and units of $g_{c}$ in the English Engineering system? In the SI system?
Nitrogen gas is reversibly compressed from $70^{\circ} \mathrm{F}$ and 14.7 psia to one-fourth of its original volume by (1) a $T=$ const process or (2) a $p=$ const process followed by a
What is the relationship between density and specific volume?
Explain the difference between absolute and gage pressures.
What is the distinguishing characteristic of a fluid (as compared to a solid)? How is this related to viscosity?
In any given physical situation, why can there be a difference between the number of units and the number of dimensions? [Number of units being less or equal to number of dimensions.]
Why is the ratio of the velocity at any point downstream of the throat of a supersonic nozzle to the velocity at the throat (where it equals the speed of sound), though dimensionless, not a Mach
Describe the difference between the microscopic and macroscopic approach in the analysis of fluid behavior.
Describe the control volume approach to problem analysis and contrast it to the control mass approach. What kinds of systems are these also called?
Describe a property and give at least three examples.
Properties may be categorized as either intensive or extensive. Define what is meant by each, and list examples of each type of property.
When dealing with a unit mass of a single component substance, how many independent properties are required to fix the state?
Why do we need an equation of state? Write down one with which you are familiar.
Define point functions and path functions. Give examples of each.
What is a thermodynamic process? What is a thermodynamic cycle?
How does the zeroth law of thermodynamics relate to temperature?
State the first law of thermodynamics for a closed system that is executing a single process.
What are the sign conventions used in this book for heat and work?
State any form of the second law of thermodynamics you are familiar with.
Define a reversible process for a thermodynamic system. Is any real process ever completely reversible?
What are some phenomena that cause processes to be irreversible?
Under what conditions is an isentropic process not a reversible adiabatic process?
Give the equations that define enthalpy and entropy.
Give differential expressions that relate entropy to(a) internal energy(b) enthalpy.
Define (in the form of partial derivatives) the specific heats $c_{v}$ and $c_{p}$. Are these expressions valid for materials in any state?
State the perfect gas equation of state. Give a consistent set of units for each term in the equation.
For a perfect gas, the specific internal energy is a function of which state variables? How about the specific enthalpy?
Give expressions for $\Delta u$ and $\Delta h$ that are valid for perfect gases. Do these hold for any process?
For perfect gases, at what temperature do we arbitrarily assign $u=0$ and $h=0$ ?
State any one expression for the entropy change between two arbitrary points which is valid for a perfect gas.
If a perfect gas undergoes an isentropic process, what equation relates the pressure to the volume? Temperature to the volume? Temperature to the pressure?
Consider the general polytropic process $\left(p v^{n}=\right.$ const) for a perfect gas. In the $p-v$ and $T-s$ diagrams shown in Figure RQ1.34, label each process line with the correct value
There is three-dimensional flow of an incompressible fluid in a duct of radius $R$. The velocity distribution at any section is hemispherical, with the maximum velocity $U_{m}$ at the center and
Name the basic concepts (or equations) from which the study of gas dynamics proceeds.
A constant-density fluid flows between two flat parallel plates that are separated by a distance $\delta$ (Figure P2.2). Sketch the velocity distribution and compute the mass average velocity based
Define steady flow. Explain what is meant by one-dimensional flow.
An incompressible fluid is flowing in a rectangular duct whose dimensions are 2 units in the $Y$-direction and 1 unit in the $Z$-direction. The velocity in the $X$-direction is given by \(u=3
An incompressible fluid flows in a duct of radius $r_{0}$. At a particular location, the velocity distribution is $u=U_{m}\left[1-\left(r / r_{0}\right)^{2}\right]$ and the distribution of an
Laminar flow in circular ducts is not one-dimensional, but we may still use the equivalent mass-average velocity $V=U_{m} / 2$ from equations (2.10) and (2.11) in our onedimensional formulations.

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