Questions and Answers of Introduction To Fluid Mechanics

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
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
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
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 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
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
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
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
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} /
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 \(1200 \mathrm{~km} / \mathrm{h}\).
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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, \(60^{\circ} \mathrm{C}\),
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
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
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
\(\mathrm{A} \mathrm{CO}_{2}\) 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
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,
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
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
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,
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,
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.
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
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 \(6 \mathrm{MPa}\)
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
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
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 \(60 \mathrm{psia}\)
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
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
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,
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
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
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
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
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 \(60 \mathrm{psia}\)
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 \(75-\mathrm{mm}\)
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
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 \(20^{\circ} \mathrm{C}\)
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
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
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
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
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
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,
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
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
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}
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
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
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
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
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
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
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}
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.

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