Fox And McDonald's Introduction To Fluid Mechanics 9th Edition Philip J. Pritchard, John W. Mitchell - Solutions

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Air is expanded in a steady flow process through a turbine. Initial conditions are \(1300^{\circ} \mathrm{C}\) and \(2.0 \mathrm{MPa}\) absolute. Final conditions are \(500^{\circ} \mathrm{C}\) and atmospheric pressure. Show this process on a Ts diagram. Evaluate the changes in internal energy,
Five kilograms of air is cooled in a closed tank from 250 to \(50^{\circ} \mathrm{C}\). The initial absolute pressure is \(3 \mathrm{MPa}\). Compute the changes in entropy, internal energy, and enthalpy. Show the process state points on a \(T s\) diagram.
Air is contained in a piston-cylinder device. The temperature of the air is \(100^{\circ} \mathrm{C}\). Using the fact that for a reversible process the heat transfer \(q=\int T d s\), compare the amount of heat \((\mathrm{J} / \mathrm{kg})\) required to raise the temperature of the air to
Calculate the power delivered by the turbine per unit mass of airflow when the heat transfer in the heat exchanger is zero. Then, how does the power depend on the heat transfer through the exchanger if all other conditions remain the same? Assume air is a perfect gas. Large reservoir p=1013 kPa T =
If hydrogen flows as a perfect gas without friction between stations (1) and (2) while \(q_{H}=7.5 \times 10^{5} \mathrm{~J} / \mathrm{kg}\), find \(V_{2}\). 75 m/s T = 50C T = 100C P12.5
A \(1-\mathrm{m}^{3}\) tank contains air at \(0.1 \mathrm{MPa}\) absolute and \(20^{\circ} \mathrm{C}\). The tank is pressurized to \(2 \mathrm{MPa}\). Assuming that the tank is filled adiabatically and reversibly, calculate the final temperature of the air in the tank. Now assuming that the tank
Air enters a turbine in steady flow at \(0.5 \mathrm{~kg} / \mathrm{s}\) with negligible velocity. Inlet conditions are \(1300^{\circ} \mathrm{C}\) and \(2.0 \mathrm{MPa}\) absolute. The air is expanded through the turbine to atmospheric pressure. If the actual temperature and velocity at the
Natural gas, with the thermodynamic properties of methane, flows in an underground pipeline of \(0.6 \mathrm{~m}\) diameter. The gage pressure at the inlet to a compressor station is \(0.5 \mathrm{MPa}\); outlet pressure is 8.0 MPa gage. The gas temperature and speed at inlet are \(13^{\circ}
Carbon dioxide flows at a speed of \(10 \mathrm{~m} / \mathrm{s}\) in a pipe and then through a nozzle where the velocity is \(50 \mathrm{~m} / \mathrm{s}\), What is the change in gas temperature between pipe and nozzle? Assume this is an adiabatic flow of a perfect gas.
In an isothermal process, 0.1 cubic feet of standard air per minute (SCFM) is pumped into a balloon. Tension in the rubber skin of the balloon is given by \(\sigma=k A\), where \(k=200 \mathrm{lbf} / \mathrm{ft}^{3}\), and \(A\) is the surface area of the balloon in \(\mathrm{ft}^{2}\). Compute the
Calculate the speed of sound at \(20^{\circ} \mathrm{C}\) for(a) hydrogen,(b) helium,(c) methane,(d) nitrogen, (e) carbon dioxide.
An airplane flies at \(550 \mathrm{~km} / \mathrm{hr}\) at \(1500 \mathrm{~m}\) altitude on a standard day. The plane climbs to \(15,000 \mathrm{~m}\) and flies at \(1200 \mathrm{~km} / \mathrm{h}\). Calculate the Mach number of flight in both cases.
Actual performance characteristics of the Lockheed SR-71 "Blackbird" reconnaissance aircraft never were released. However, it was thought to cruise at \(M=3.3\) at \(85,000 \mathrm{ft}\) altitude. Evaluate the speed of sound and flight speed for these conditions. Compare to the muzzle speed of a
For a speed of sound in steel of \(4300 \mathrm{~m} / \mathrm{s}\), determine the bulk modulus of elasticity. Compare the modulus of elasticity of steel to that of water. Determine the speed of sound in steel, water, and air at atmospheric conditions. Comment on the differences.
Determine and plot the Mach number of an automobile as a function of speed from \(25 \mathrm{mph}\) to \(100 \mathrm{mph}\) for winter \(\left(T=0^{\circ} \mathrm{F}\right)\) and summer \(\left(T=100^{\circ} \mathrm{F}\right)\) conditions.
Investigate the effect of altitude on Mach number by plotting the Mach number of a \(500 \mathrm{mph}\) airplane as it flies at altitudes ranging from sea level to \(10 \mathrm{~km}\).
The grandstand at the Kennedy Space Center is located \(3.5 \mathrm{mi}\) away from the Space Shuttle Launch Pad. On a day when the air temperature is \(80^{\circ} \mathrm{F}\), how long does it take the sound from a blastoff to reach the spectators? If the launch was early on a winter morning, the
Use data for specific volume to calculate and plot the speed of sound in saturated liquid water over the temperature range from 0 to \(200^{\circ} \mathrm{C}\)
An object traveling in atmospheric air emits two pressure waves at different times. At an instant in time, the waves appear as in the figure. Determine the velocity and Mach number of the object and its current location. (+) 0.01 m 1.5 m P12.19 0.1 m
An object traveling in atmospheric air emits two pressure waves at different times. At an instant in time, the waves appear as in the figure. Determine the velocity and Mach number of the object and its current location. + 0.2 m 0.5 m P12.20 1 m
While at the seashore, you observe an airplane that is flying at \(10,000 \mathrm{ft}\). You hear the airplane 8 seconds after it passes directly overhead. Estimate the airplane speed and Mach number. If the airplane had been flying at 30,000 ft, how many seconds would have passed before you heard
The temperature varies linearly from sea level to approximately \(11 \mathrm{~km}\) altitude in the standard atmosphere. Evaluate the lapse rate- the rate of decrease of temperature with altitude-in the standard atmosphere. Derive an expression for the rate of change of sonic speed with altitude in
A projectile is fired into a gas (ratio of specific heats \(k=1.625\) ) in which the pressure is \(450 \mathrm{kPa}\) absolute and the density is \(4.5 \mathrm{~kg} / \mathrm{m}^{3}\). It is observed experimentally that a Mach cone emanates from the projectile with \(25^{\circ}\) total angle. What
A photograph of a bullet shows a Mach angle of \(32^{\circ}\). Determine the speed of the bullet for standard air.
An F-4 aircraft makes a high-speed pass over an airfield on a day when \(T=35^{\circ} \mathrm{C}\). The aircraft flies at \(M=1.4\) and \(200 \mathrm{~m}\) altitude. Calculate the speed of the aircraft. How long after it passes directly over point A on the ground does its Mach cone pass over point
An aircraft passes overhead at \(3 \mathrm{~km}\) altitude. The aircraft flies at \(M=1.5\). Assume the air temperature is constant at \(20^{\circ} \mathrm{C}\). Find the air speed of the aircraft. A headwind blows at \(30 \mathrm{~m} / \mathrm{s}\). How long after the aircraft passes directly
A supersonic aircraft flies at \(3 \mathrm{~km}\) altitude at a speed of \(1000 \mathrm{~m} / \mathrm{s}\) on a standard day. How long after passing directly above a ground observer is the sound of the aircraft heard by the ground observer?
For the conditions of Problem 12.27, find the location at which the sound wave that first reaches the ground observer was emitted.Data From Problem 12.27 12.27 A supersonic aircraft flies at 3 km altitude at a speed of 1000 m/s on a standard day. How long after passing directly above a ground
The Concorde supersonic transport cruised at \(M=2.2\) at \(17 \mathrm{~km}\) altitude on a standard day. How long after the aircraft passed directly above a ground observer was the sound of the aircraft heard?
Plot the percentage discrepancy between the density at the stagnation point and the density at a location where the Mach number is \(M\), of a compressible flow, for Mach numbers ranging from 0.05 to 0.95 . Find the Mach numbers at which the discrepancy is 1 percent, 5 percent, and 10 percent.
Compute the air density in the undisturbed air and at the stagnation point of an aircraft flying at \(250 \mathrm{~m} / \mathrm{s}\) in air at \(28 \mathrm{kPa}\) and \(250^{\circ} \mathrm{C}\). What is the percentage increase in density? Can we approximate this as an incompressible flow?
Carbon dioxide flows in a duct at a velocity of \(90 \mathrm{~m} / \mathrm{s}\), absolute pressure \(140 \mathrm{kPa}\), and temperature \(90^{\circ} \mathrm{C}\). Calculate pressure and temperature on the nose of a small object placed in this flow.
If nitrogen at \(15^{\circ} \mathrm{C}\) is flowing and the stagnation temperature on the nose of a small object in the flow is measured as \(38^{\circ} \mathrm{C}\), what is the velocity in the pipe?
An aircraft cruises at \(M=0.65\) at \(10 \mathrm{~km}\) altitude on a standard day. The aircraft speed is deduced from measurement of the difference between the stagnation and static pressures. What is the value of this difference? Compute the air speed from this actual difference assuming(a)
High-speed aircraft use "air data computers" to compute air speed from measurement of the difference between the stagnation and static pressures. Plot, as a function of actual Mach number \(M\), for \(M=0.1\) to \(M=0.9\), the percentage error in computing the Mach number assuming incompressibility
A supersonic wind tunnel test section is designed to have \(M=2.5\) at \(15^{\circ} \mathrm{C}\) and \(35 \mathrm{kPa}\) absolute. The fluid is air. Determine the required inlet stagnation conditions, \(T_{0}\) and \(p_{0}\). Calculate the required mass flow rate for a test section area of \(0.175
Oxygen flows in a passage at a pressure of 25 psia. The pressure and temperature on the nose of a small object in the flow are 28 psia and \(150^{\circ} \mathrm{F}\), respectively. What is the velocity in the passage?
What is the pressure on the nose of a bullet moving through standard sea ievel air at \(300 \mathrm{~m} / \mathrm{s}\) assuming that(a) the flow is incompressible (b) the flow is compressible? Compare results.
Air flows steadily through an insulated constant area duct, where (1) denotes the inlet and (2) the outlet. Properties change along the duct as a result of friction.(a) Beginning with the control volume form of the first law of thermodynamics, show that the equation can be reduced
Air flows in an insulated duct. At point (1) the conditions are \(M_{1}=0.1, T_{1}=-20^{\circ} \mathrm{C}\) and \(p_{1}=1.0 \mathrm{MPa}\) absolute. Downstream, at point (2), because of friction the conditions are \(M_{2}=0.7\), \(T_{2}=-5.62^{\circ} \mathrm{C}\), and \(p_{2}=136.5 \mathrm{kPa}\)
Consider steady, adiabatic flow of air through a long straight pipe with \(A=0.05 \mathrm{~m}^{2}\). At the inlet section (1) the air is at \(200 \mathrm{kPa}\) absolute, \(60^{\circ} \mathrm{C}\), and \(146 \mathrm{~m} / \mathrm{s}\). Downstream at section (2), the air is at \(95.6 \mathrm{kPa}\)
Air passes through a normal shock in a supersonic wind tunnel. Upstream conditions are \(M_{1}=1.8, T_{1}=270 \mathrm{~K}\), and \(p_{1}=\)\(10.0 \mathrm{kPa}\) absolute. Downstream conditions are \(M_{2}=0.6165, T_{2}=\) \(413.6 \mathrm{~K}\), and \(p_{2}=36.13 \mathrm{kPa}\) absolute. (Four
A Boeing 747 cruises at \(M=0.87\) at an altitude of \(13 \mathrm{~km}\) on a standard day. A window in the cockpit is located where the external flow Mach number is 0.2 relative to the plane surface. The cabin is pressurized to an equivalent altitude of \(2500 \mathrm{~m}\) in a standard
Space debris impact is a real concern for spacecraft. If a piece of space debris were to create a hole of \(0.001 \mathrm{in} .^{2}\) area in the hull of the International Space Station (ISS), at what rate would air leak from the ISS? Assume that the atmosphere in the International Space Station
\(\mathrm{A} \mathrm{CO}_{2}\) cartridge is used to propel a toy rocket. Gas in the cartridge is pressurized to \(45 \mathrm{MPa}\) gage and is at \(25^{\circ} \mathrm{C}\). Calculate the critical conditions (temperature, pressure, and flow speed) that correspond to these stagnation conditions.
Nitrogen flows from a large tank, through a convergent nozzle of 2-in. tip diameter, into the atmosphere. The temperature in the tank is \(200^{\circ} \mathrm{F}\). Calculate pressure, velocity, temperature, and sonic velocity in the jet, and calculate the flow rate when the tank pressure is(a) 30
Air flows from the atmosphere into an evacuated tank through a convergent nozzle of \(38-\mathrm{mm}\) tip diameter. If atmospheric pressure and temperature are \(101.3 \mathrm{kPa}\) and \(15^{\circ} \mathrm{C}\), respectively, what vacuum must be maintained in the tank to produce sonic velocity
Oxygen discharges from a tank through a convergent nozzle. The temperature and velocity in the jet are \(-20^{\circ} \mathrm{C}\) and \(270 \mathrm{~m} / \mathrm{s}\), respectively. What is the temperature in the tank? What is the temperature on the nose of a small object in the jet?
The hot gas stream at the turbine inlet of a JT9-D jet engine is at \(1500^{\circ} \mathrm{C}, 140 \mathrm{kPa}\) absolute, and \(M=0.32\). Calculate the critical conditions (temperature, pressure, and flow speed) that correspond to these conditions. Assume the fluid properties of pure air.
Carbon dioxide discharges from a tank through a convergent nozzle into the atmosphere. If the tank temperature and gage pressure are \(38^{\circ} \mathrm{C}\) and \(140 \mathrm{kPa}\), respectively, what jet temperature, pressure, and velocity can be expected? Barometric pressure is \(101.3
Air at \(100^{\circ} \mathrm{F}\) and 100 psia in a large tank flows into a 6 -in.diameter pipe, from which it discharges to the atmosphere at 15.0 psia through a convergent nozzle of 4-in. tip-diameter. Calculate pressure, temperature, and velocity in the pipe.
Calculate the required diameter of a convergent nozzle to discharge \(5.0 \mathrm{lb} / \mathrm{s}\) of air from a iarge tank in which the temperatures is \(100^{\circ} \mathrm{F}\) to the atmosphere at \(14.7 \mathrm{psia}\) if the pressure in the tank is(a) 25.0 psia(b) 30.0 psia.
Steam flows steadily and isentropically through a nozzle. At an upstream section where the speed is negligible, the temperature and pressure are \(450^{\circ} \mathrm{C}\) and \(6 \mathrm{MPa}\) absolute. At a section where the nozzle diameter is \(2 \mathrm{~cm}\), the steam pressure is \(2
Nitrogen flows through a diverging section of duct with \(A_{1}=0.15 \mathrm{~m}^{2}\) and \(A_{2}=0.45 \mathrm{~m}^{2}\). If \(M_{1}=0.7\) and \(p_{1}=450 \mathrm{kPa}\), find \(M_{2}\) and \(p_{2}\).
At a section in a passage, the pressure is \(30 \mathrm{psia}\), the temperature is \(100^{\circ} \mathrm{F}\), and the speed is \(1750 \mathrm{ft} / \mathrm{s}\). At a section downstream the Mach number is 2.5. Determine the pressure at this downstream location for isentropic flow of air. Sketch
In a given duct flow \(\mathrm{M}=2.0\); the velocity undergoes a 20 percent decrease. What percent change in area was needed to accomplish this? What would be the answer if \(\mathrm{M}=0.5\) ?
Air flows isentropically through a converging nozzle into a receiver in which the absolute pressure is 35 psia. The air enters the nozzle with negligible speed at a pressure of \(60 \mathrm{psia}\) and a temperature of \(200^{\circ} \mathrm{F}\). Determine the mass flow rate through the nozzle for
Five pounds of air per second discharge from a tank through a convergent-divergent nozzle into another tank where a vacuum of 10 in. of mercury is maintained. If the pressure and temperature in the upstream tank are \(100 \mathrm{in}\). of mercury absolute and \(100^{\circ} \mathrm{F}\),
Air flows isentropically through a converging-diverging nozzle from a large tank containing air at \(250^{\circ} \mathrm{C}\). At two locations where the area is \(1 \mathrm{~cm}^{2}\), the static pressures are \(200 \mathrm{kPa}\) and \(50 \mathrm{kPa}\). Find the mass flow rate, the throat area,
Air, at an absolute pressure of \(60.0 \mathrm{kPa}\) and \(27^{\circ} \mathrm{C}\), enters a passage at \(486 \mathrm{~m} / \mathrm{s}\), where \(A=0.02 \mathrm{~m}^{2}\). At section (1) downstream, \(p=78.8 \mathrm{kPa}\) absolute. Assuming isentropic flow, calculate the Mach number at section
Carbon dioxide flows from a tank through a convergentdivergent nozzle of \(25-\mathrm{mm}\) throat and \(50-\mathrm{mm}\) exit diameter. The absolute pressure and temperature in the tank are \(241.5 \mathrm{kPa}\) and \(37.8^{\circ} \mathrm{C}\), respectively. Calculate the mass flow rate when the
A convergent-divergent nozzle of \(50-\mathrm{mm}\) tip diameter discharges to the atmosphere \((103.2 \mathrm{kPa})\) from a tank in which air is maintained at an absolute pressure and temperature of \(690 \mathrm{kPa}\) and \(37.8^{\circ} \mathrm{C}\), respectively. What is the maximum mass flow
Air flows adiabatically through a duct. At the entrance, the static temperature and pressure are \(310 \mathrm{~K}\) and \(200 \mathrm{kPa}\), respectively. At the exit, the static and stagnation temperatures are \(294 \mathrm{~K}\) and \(316 \mathrm{~K}\), respectively, and the static pressure is
Air flows isentropically through a converging nozzle into a receiver where the pressure is \(250 \mathrm{kPa}\) absolute. If the pressure is \(350 \mathrm{kPa}\) absolute and the speed is \(150 \mathrm{~m} / \mathrm{s}\) at the nozzle location where the Mach number is 0.5 , determine the pressure,
Air flows isentropically through a converging nozzle into a receiver in which the absolute pressure is 35 psia. The air enters the nozzle with negligible speed at a pressure of \(60 \mathrm{psia}\) and a temperature of \(200^{\circ} \mathrm{F}\). Determine the mass flow rate through the nozzle for
Atmospheric air at \(98.5 \mathrm{kPa}\) and \(20^{\circ} \mathrm{C}\) is drawn into a vacuum tank through a convergent-divergent nozzle of \(50-\mathrm{mm}\) throat diameter and \(75-\mathrm{mm}\) exit diameter. Caiculate the largest mass flow rate that can be drawn through this nozzle under these
The exit section of a convergent-divergent nozzle is to be used for the test section of a supersonic wind tunnel. If the absolute pressure in the test section is to be \(140 \mathrm{kPa}\), what pressure is required in the reservoir to produce a Mach number of 5 in the test section? For the air
Air flowing isentropically through a converging nozzle discharges to the atmosphere. At the section where the absolute pressure is \(250 \mathrm{kPa}\), the temperature is \(20^{\circ} \mathrm{C}\) and the air speed is \(200 \mathrm{~m} / \mathrm{s}\). Determine the nozzle throat pressure.
Air flows from a large tank at \(p=650 \mathrm{kPa}\) absolute, \(T=550^{\circ} \mathrm{C}\) through a converging nozzle, with a throat area of \(600 \mathrm{~mm}^{2}\), and discharges to the atmosphere. Determine the mass rate of flow for isentropic flow through the nozzle.
A converging nozzle is connected to a large tank that contains compressed air at \(15^{\circ} \mathrm{C}\). The nozzle exit area is \(0.001 \mathrm{~m}^{2}\). The exhaust is discharged to the atmosphere. To obtain a satisfactory shadow photograph of the flow pattern leaving the nozzle exit, the
Air at \(0^{\circ} \mathrm{C}\) is contained in a large tank on the space shuttle. A converging section with exit area \(1 \times 10^{-3} \mathrm{~m}^{2}\) is attached to the tank, through which the air exits to space at a rate of \(2 \mathrm{~kg} / \mathrm{s}\). What are the pressure in the tank,
A large tank initially is evacuated to \(-10 \mathrm{kPa}\) gage. Ambient conditions are \(101 \mathrm{kPa}\) at \(20^{\circ} \mathrm{C}\). At \(t=0\), an orifice of \(5 \mathrm{~mm}\) diameter is opened in the tank wall; the vena contracta area is 65 percent of the geometric area. Calculate the
Air flows isentropically through a converging nozzle attached to a large tank, where the absolute pressure is \(171 \mathrm{kPa}\) and the temperature is \(27^{\circ} \mathrm{C}\). At the inlet section the Mach number is 0.2 . The nozzle discharges to the atmosphere; the discharge area is \(0.015
Air enters a converging-diverging nozzle at \(2 \mathrm{MPa}\) absolute and \(313 \mathrm{~K}\). At the exit of the nozzle, the pressure is \(200 \mathrm{kPa}\) absolute.Assume adiabatic, frictionless flow through the nozzle. The throat area is \(20 \mathrm{~cm}^{2}\). What is the area at the
A converging nozzle is bolted to the side of a large tank. Air inside the tank is maintained at a constant \(50 \mathrm{psia}\) and \(100^{\circ} \mathrm{F}\). The inlet area of the nozzle is \(10 \mathrm{in} .{ }^{2}\) and the exit area is \(1 \mathrm{in.}^{2}\) The nozzle discharges to the
A jet transport aircraft, with pressurized cabin, cruises at \(11 \mathrm{~km}\) altitude. The cabin temperature and pressure initially are at \(25^{\circ} \mathrm{C}\) and equivalent to \(2.5 \mathrm{~km}\) altitude. The interior volume of the cabin is \(25 \mathrm{~m}^{3}\). Air escapes through a
A converging-diverging nozzle, with a throat area of \(2 \mathrm{in.}^{2}\), is connected to a large tank in which air is kept at a pressure of \(80 \mathrm{psia}\) and a temperature of \(60^{\circ} \mathrm{F}\). If the nozzle is to operate at design conditions and the ambient pressure outside the
Air, at a stagnation pressure of 7.20 MPa absolute and a stagnation temperature of \(1100 \mathrm{~K}\), flows isentropically through a converging-diverging nozzle having a throat area of \(0.01 \mathrm{~m}^{2}\). Determine the speed and the mass flow rate at the downstream section where the Mach
A small rocket motor, fueled with hydrogen and oxygen, is tested on a thrust stand at a simulated altitude of \(10 \mathrm{~km}\). The motor is operated at chamber stagnation conditions of \(1500 \mathrm{~K}\) and \(8.0 \mathrm{MPa}\) gage. The combustion product is water vapor, which may be
Testing of a demolition explosion is to be evaluated. Sensors indicate that the shock wave generated at the instant of explosion is \(30 \mathrm{MPa}\) absolute. If the explosion occurs in air at \(20^{\circ} \mathrm{C}\) and \(101 \mathrm{kPa}\), find the speed of the shock wave, and the
A total-pressure probe is placed in a supersonic wind tunnel where \(T=530^{\circ} \mathrm{R}\) and \(M=2.0\). A normal shock stands in front of the probe. Behind the shock, \(M_{2}=0.577\) and \(p_{2}=5.76\) psia. Find (a) the downstream stagnation pressure and stagnation temperature and (b) all
Air flows steadily through a long, insulated constant-area pipe. At section (1), \(M_{1}=2.0, T_{1}=140^{\circ} \mathrm{F}\), and \(p_{1}=35.9 \mathrm{psia}\). At section (2), downstream from a normal shock, \(V_{2}=1080 \mathrm{ft} / \mathrm{s}\). Determine the density and Mach number at section
Air discharges through a convergent-divergent nozzle which is attached to a large reservoir. At a point in the nozzle a normal shock wave is detected across which the absolute pressure jumps from 69 to \(207 \mathrm{kPa}\). Calculate the pressures in the throat of the nozzle and in the reservoir.
A normal shock wave exists in an airflow. The absolute pressure, velocity, and temperature just upstream from the wave are \(207 \mathrm{kPa}, 610 \mathrm{~m} / \mathrm{s}\), and \(-17.8^{\circ} \mathrm{C}\), respectively. Calculate the pressure, velocity, temperature, and sonic velocity just
Air approaches a normal shock at \(V_{1}=900 \mathrm{~m} / \mathrm{s}, p_{1}=50 \mathrm{kPa}\) absolute, and \(T_{1}=220 \mathrm{~K}\). What are the velocity and pressure after the shock? What would the velocity and pressure be if the flow were decelerated isentropically to the same Mach number?
Air approaches a normal shock at \(M_{1}=2.5\), with \(T_{0_{1}}=1250^{\circ} \mathrm{R}\) and \(p_{1}=20\) psia. Determine the speed and temperature of the air leaving the shock and the entropy change across the shock.
Air undergoes a normal shock. Upstream, \(T_{1}=35^{\circ} \mathrm{C}\), \(p_{1}=229 \mathrm{kPa}\) absolute, and \(V_{1}=704 \mathrm{~m} / \mathrm{s}\). Determine the temperature and stagnation pressure of the air stream leaving the shock.
If, through a normal shock wave in air, the absolute pressure rises from 275 to \(410 \mathrm{kPa}\) and the velocity diminishes from 460 to \(346 \mathrm{~m} / \mathrm{s}\), what temperatures are to be expected upstream and downstream from the wave?
The stagnation temperature in an airflow is \(149^{\circ} \mathrm{C}\) upstream and downstream from a normal shock wave. The absolute stagnation pressure downstream from the shock wave is \(229.5 \mathrm{kPa}\). Through the wave the absolute pressure rises from 103.4 to \(138 \mathrm{kPa}\).
A supersonic aircraft cruises at \(M=2.2\) at \(12 \mathrm{~km}\) altitude. A pitot tube is used to sense pressure for calculating air speed. A normal shock stands in front of the tube. Evaluate the local isentropic stagnation conditions in front of the shock. Estimate the stagnation pressure
The Concorde supersonic transport flew at \(M=2.2\) at \(20 \mathrm{~km}\) altitude. Air is decelerated isentropically by the engine inlet system to a local Mach number of 1.3. The air passed through a normal shock and was decelerated further to \(M=0.4\) at the engine compressor section. Assume,
Verify the equation given in Table 11.1 for the hydraulic radius of a circular channel. Evaluate and plot the ratio \(R / D\), for liquid depths between 0 and \(D\).Data From Table 11.1 Geometric Properties of Common Open-Channel Shapes Shape Section Flow Area, A Wetted Perimeter, P Hydraulic
A pebble is dropped into a stream of water that flows in a rectangular channel at \(2 \mathrm{~m}\) depth. In one second, a ripple caused by the stone is carried \(7 \mathrm{~m}\) downstream. What is the speed of the flowing water?
Solution of the complete differential equations for wave motion without surface tension shows that wave speed is given by\[c=\sqrt{\frac{g \lambda}{2 \pi} \tanh \left(\frac{2 \pi y}{\lambda}\right)}\]where \(\lambda\) is the wave wavelength and \(y\) is the liquid depth. Show that when \(\lambda /
A water flow rate of \(250 \mathrm{cfs}\) flows at a depth of \(5 \mathrm{ft}\) in a rectangular channel that is \(9 \mathrm{ft}\) wide. Determine whether the flow is sub- or supercritical. For this flow rate, determine the depth for critical flow.
Determine and plot the relation between water velocity and depth over the range of \(V=0.1 \mathrm{~m} / \mathrm{s}\) to \(10 \mathrm{~m} / \mathrm{s}\) for Froude numbers of 0.5 (subcritical), 1.0 (critical), and 2 (supercritical). Explain how the flow can be subcritical, critical, or
Capillary waves (ripples) are small amplitude and wavelength waves, commonly seen, for example, when an insect or small particle hits the water surface. They are waves generated due to the interaction of the inertia force of the fluid \(ho\) and the fluid surface tension \(\sigma\). The wavelength
The Froude number characterizes flow with a free surface. Plot on a \(\log\)-log scale the speed versus depth for \(0.1 \mathrm{~m} / \mathrm{s}
Consider waves on the surface of a tank of water that travel at \(5 \mathrm{ft} / \mathrm{s}\). How fast would the waves travel if the tank were(a) on the moon,(b) on Jupiter, (c) on an orbiting space station? Explain your results.
A submerged body traveling horizontally beneath a liquid surface at a Froude number (based on body length) about 0.5 produces a strong surface wave pattern if submerged less than half its length. (The wave pattern of a surface ship also is pronounced at this Froude number.) On a log-log plot of

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Fox And McDonald's Introduction To Fluid Mechanics 9th Edition Philip J. Pritchard, John W. Mitchell - Solutions

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