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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Distinguish between flow of an ideal gas and inviscid flow of a fluid.
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
Consider the flow process in Fig. P11.3. Does the fluid flow from left to right or from right to left? Justify your answer. Assume as ideal gas with constant specific heats.Fig. P11.3 Unknown flow
As demonstrated 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
Describe briefly how a schlieren optical visualization system (Fig. 11.4) works. How else might density changes in a fluid flow be made visible to the eye?Fig. 11.4 Shock wave Flow Airfoil
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?
Air expands adiabatically through a turbine from a pressure and temperature of \(180 \mathrm{psia}, 1600{ }^{\circ} \mathrm{R}\) to a pressure of \(14.7 \mathrm{psia}\). If the actual temperature
An expression for the value of \(c_{p}\) for carbon dioxide as a function of temperature is\[ c_{p}=286-\frac{1.15 \times 10^{5}}{T}+\frac{2.49 \times 10^{6}}{T^{2}} \]where \(c_{p}\) is in
Air flows in a 15-cm-diameter horizontal pipe. At section 1, \(p=600 \mathrm{kPa}, T=70{ }^{\circ} \mathrm{C}\), and \(V=35 \mathrm{~m} / \mathrm{s}\). At section 2: \(T=42^{\circ} \mathrm{C}\) and
An air heater in a large coal-fired steam generator heats fresh air entering the steam generator by cooling flue gas leaving the steam generator. One million \(\mathrm{lbm} / \mathrm{hr}\) of air at
Determine the static pressure to stagnation pressure ratio associated with the following motion in standard air: (a) a runner moving at the rate of \(10 \mathrm{mph}\), (b) a cyclist moving at the
The air velocity in the duct in Fig. P11.12 is \(750 \mathrm{ft} / \mathrm{s}\). The air static temperature is \(100^{\circ} \mathrm{F}\). Use the mercury manometer measurement to calculate the
Air is flowing in a duct as shown in Fig. P11.13. A Pitotstatic tube and a thermocouple are inserted into the flow stream as shown. Calculate the air velocity and the air-mass flow rate.Figure P11.13
Steam \(\left(\mathrm{H}_{2} \mathrm{O}\right.\) vapor) flows in a pipeline in a power station. The steam pressure is \(150 \mathrm{psia}\), its temperature is \(500{ }^{\circ} \mathrm{F}\), and it
An ideal gas flows with velocity \(V\), pressure \(p\), temperature \(T\), and density \(ho\). Determine a set of equations for stagnation properties, including entropy, if the stagnation process is
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
Using information provided in Table C.1, develop a table of speed of sound in ft/s as a function of elevation for U.S. standard atmosphere.Table C.1 Properties of the U.S. Standard Atmosphere (BG/EE
An airplane is flying at a flight (or local) Mach number of 0.70 at \(10,000 \mathrm{~m}\) in the Standard Atmosphere. Find the ground speed(a) if the air is not moving relative to the ground (b) if
The stagnation pressure in a Mach 2 wind tunnel operating with air is \(900 \mathrm{kPa}\). A 1.0-cm-diameter sphere positioned in the wind tunnel has a drag coefficient of 0.95 . Calculate the drag
Calculate the speed of sound in air, helium, and hydrogen. The temperature is \(70^{\circ} \mathrm{F}\).
Determine the Mach number of a car moving in standard air at a speed of(a) \(25 \mathrm{mph}\),(b) \(55 \mathrm{mph}\), (c) \(100 \mathrm{mph}\).
A jet-propelled airliner flies at an altitude of \(15,000 \mathrm{~m}\) and a velocity of \(265 \mathrm{~m} / \mathrm{s}\). What is the stagnation pressure and stagnation temperature of the air
A schlieren photo of a bullet moving through air (see Video V11.10) at 14.7 psia and \(68^{\circ} \mathrm{F}\) indicates a Mach cone angle of \(28^{\circ}\). How fast was the bullet moving in: (a)
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. P11.24. Determine the
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 V11.8) travel less than,
If a new Boeing 787 Dreamliner cruises at a Mach number of 0.87 at an altitude of \(30,000 \mathrm{ft}\), how fast is this in (a) \(\mathrm{mph}\), (b) \(\mathrm{ft} / \mathrm{s}\), (c) \(\mathrm{m}
Explain how you could vary the Mach number but not the Reynolds number in airflow past a sphere. For a constant Reynolds number of 300,000, estimate how much the drag coefficient will increase as the
Air flows in a constant-area, insulated duct. The air enters the duct at \(520{ }^{\circ} \mathrm{R}, 50 \mathrm{psia}\), and \(\mathrm{Ma}=0.45\). At a downstream location, the Mach number is one.
A normal shock occurs in a stream of oxygen. The oxygen flows at \(\mathrm{Ma}=1.8\) and the upstream pressure and temperature are 15 psia and \(85^{\circ} \mathrm{F}\).(a) Calculate the following on
The Pitot tube on a supersonic aircraft (see Video V3.8) cruising at an altitude of \(30,000 \mathrm{ft}\) senses a stagnation pressure of 12 psia. If the atmosphere is considered standard, determine
An aircraft cruises at a Mach number of 2.0 at an altitude of \(15 \mathrm{~km}\). Inlet air is decelerated to a Mach number of 0.4 at the engine compressor inlet. A normal shock occurs in the inlet
At some point for air flow in a duct, \(p=20 \mathrm{psia}, T=500^{\circ} \mathrm{R}\), and \(V=500 \mathrm{ft} / \mathrm{s}\). Can a normal shock occur at this point?
A normal shock propagates at \(2000 \mathrm{ft} / \mathrm{s}\) into the still air in a tube. The temperature and pressure of the air are \(80^{\circ} \mathrm{F}\) and 14.7 psia before "hit" by the
Air at \(V_{1}=800 \mathrm{~m} / \mathrm{s}, p_{1}=100 \mathrm{kPa}\), and \(T_{1}=300 \mathrm{~K}\) passes through a normal shock. Calculate the velocity \(V_{2}\), temperature \(T_{2}\), and
A normal shock occurs in a perfect gas. Sketch a Temperature - Entropy \((T-S)\) diagram of the process and show the following: Static and stagnation pressure and temperature before and after the
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
Air flows isentropically through a duct as shown in Fig. P11.37. For the conditions shown, find the Mach number at both stations 1 and 2 and the flow rate. The diameter is not necessarily
A simplified schematic diagram of a carburetor of a gasoline engine is shown in Fig. P11.38. The throat area is \(0.5 \mathrm{in}^{2}\). The engine draws air downward through the carburetor Venturi
An engineering student wants to satisfy her curiosity about the compressibility of air in motion. She has set up a converging nozzle in which air discharges into the atmosphere. Figure P11.39 shows
A nozzle for a supersonic wind tunnel is designed to achieve a Mach number of 3.0, with a velocity of \(2000 \mathrm{~m} / \mathrm{s}\), and a density of \(1.0 \mathrm{~kg} / \mathrm{m}^{3}\) in the
Air flows isentropically through a duct to a section where \(p_{1}=25 \mathrm{kPa}, T_{1}=300 \mathrm{~K}\), and \(V_{1}=900 \mathrm{~m} / \mathrm{s}\). For these conditions:(a) Determine the
The static pressure to stagnation pressure ratio at a point in a 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}
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 converging duct is \(0.05
Helium at \(68{ }^{\circ} \mathrm{F}\) and 14.7 psia in a large tank flows steadily and isentropically through a converging nozzle to a receiver pipe. The cross-sectional area of the throat of the
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 \(80 \mathrm{psia}\) to standard atmospheric
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
At a certain point in a pipe, air flows steadily with a velocity of \(150 \mathrm{~m} / \mathrm{s}\) and has a static pressure of \(70 \mathrm{kPa}\) and a static temperature of \(4{ }^{\circ}
A tank of oxygen has a hole of area \(0.5 \mathrm{~cm}^{2}\) in its wall. The temperature of the oxygen in the tank is \(25^{\circ} \mathrm{C}\). Calculate the rate \((\mathrm{kg} / \mathrm{s})\) at
The gas entering a rocket nozzle has a stagnation pressure of \(1500 \mathrm{kPa}\) and a stagnation temperature of \(3000^{\circ} \mathrm{C}\). The rocket is traveling in the still Standard
A jet engine is to be designed for an altitude of \(12,000 \mathrm{~m}\), where the atmospheric pressure is \(19.3 \mathrm{kPa}\). The jet nozzle has a supersonic exit Mach number and is perfectly
Air is flowing in the converging-diverging nozzle shown in Fig. P11.52. Determine the three critical pressure ratios and the Mach numbers immediately upstream and immediately downstream from the
A convergent-divergent nozzle has an exit throat area ratio of 3.0. It is to be supplied with air. Find:(a) The first, second, and third critical pressure ratios;(b) The exit plane Mach number in
An ideal gas flows isentropically through a convergingdiverging nozzle. At a section in the converging portion of the nozzle, \(A_{1}=0.1 \mathrm{~m}^{2}, p_{1}=600 \mathrm{kPa}(\) abs \(),
Air is supplied to a convergent-divergent nozzle from a reservoir where the pressure is \(100 \mathrm{kPa}\). The air is then discharged through a short pipe into another reservoir where the pressure
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
Air flows adiabatically between two sections in a constant area pipe. At upstream section (1), \(p_{0,1}=100 \mathrm{psia}, T_{0,1}=600^{\circ} \mathrm{R}\), and \(\mathrm{Ma}_{1}=0.5\). At
Supersonic airflow enters an adiabatic, constant area (inside diameter \(=1 \mathrm{ft}\) ) 30-ft-long pipe with \(\mathrm{Ma}_{1}=3.0\). The pipe friction factor is estimated to be 0.02 . What ratio
Supersonic airflow enters an adiabatic, constant area pipe (inside diameter \(=0.1 \mathrm{~m}\) ) with \(\mathrm{Ma}_{1}=2.0\). The pipe friction factor is 0.02 . If a standing normal shock is
Consider the flow of air through the piping system shown in Fig. P11.60. If the system is choked, determine the location where the Mach number is 1 . Calculate the pressure ratio \(p_{B} / p_{0}\)
Estimate the maximum mass flow rate of air that can be passed by the duct shown in Fig. P11.61 for \(\mu=4 \times 10^{-7} \mathrm{lb}\). \(\mathrm{s} / \mathrm{ft}^{2}\).Figure P11.61 Po 100 psia T =
Waste gas \(\left(\mathrm{CO}_{2}\right)\) is vented to outer space from a spacecraft through a circular pipe \(0.2 \mathrm{~m}\) long. The pressure and temperature in the spacecraft are \(35
Air enters a 4-cm-square galvanized steel duct with \(p_{0}=\) \(150 \mathrm{kPa}, T_{0}=400 \mathrm{~K}\), and \(V_{1}=120 \mathrm{~m} / \mathrm{s}\). \(\mu=2.2 \times 10^{-5}\) \(\mathrm{N} \cdot
Figure P11.64 shows an insulated pipe attached to a tank of air. Estimate the maximum mass flow rate that the pipe could exhaust from the tank.Figure P11.64 p=3 MPa T= 298 K D = 10 cm f= 0.02 L = 25 m
Standard atmospheric air \(\left[T_{0}=288 \mathrm{~K}, p_{0}=101 \mathrm{kPa}(\mathrm{abs})\right]\) is drawn steadily through an isentropic converging nozzle into a frictionless diabatic \((q=500
Air 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 Btu/s is
Air enters a length of constant area pipe with \(p_{1}=200\) \(\mathrm{kPa}(\mathrm{abs}), T_{1}=500 \mathrm{~K}\), and \(V_{1}=400 \mathrm{~m} / \mathrm{s}\). If \(500 \mathrm{~kJ} / \mathrm{kg}\)
Air enters a frictionless, constant area duct with \(\mathrm{Ma}_{1}=2.0\), \(T_{0,1}=59^{\circ} \mathrm{F}\), and \(p_{0,1}=14.7 \mathrm{psia}\). The air is decelerated by heating until a normal
Air enters a frictionless, constant area duct with \(\mathrm{Ma}=2.5\), \(T_{0}=20^{\circ} \mathrm{C}\), and \(p_{0}=101 \mathrm{kPa}(\mathrm{abs})\). The gas is decelerated by heating until a normal
Air enters a \(15-\mathrm{cm}\) pipe with velocity \(120 \mathrm{~m} / \mathrm{s}, 1\) atmosphere pressure, and \(T=100^{\circ} \mathrm{C}\). How much heat must be added to bring the air to the
Show that for Rayleigh flow, the maximum amount of heat that may be added to the gas is given by:\[ \frac{q_{\max }}{c_{p} T_{1}}=\frac{\left(\mathrm{Ma}_{1}^{2}-1\right)^{2}}{2(k+1)
Air is stored in a tank where the pressure is \(40 \mathrm{psia}\) and the temperature is \(500{ }^{\circ} \mathrm{R}\). A converging-diverging nozzle with an exitto-throat area ratio of 2.5 attaches
Prove that, in Rayleigh flow, the Mach number at the point of maximum temperature is \(1 / \sqrt{k}\).
The rotor shown in Fig. P12.1 rotates clockwise. Assume that the fluid enters in the radial direction and the relative velocity is tangent to the blades and remains constant across the entire rotor.
The measured shaft torque on the turbomachine shown in Fig. P12.2 is \(-60 \mathrm{~N} \cdot \mathrm{m}\) when the absolute velocities are as indicated. Determine the mass flowrate. What is the
Uniform horizontal sheets of water of 3-mm thickness issue from the slits on the rotating manifold shown in Fig. P12.3. The velocity relative to the arm is a constant \(3 \mathrm{~m} / \mathrm{s}\)
At a given radial location, a 15-mph wind against a windmill results in the upstream (1) and downstream (2) velocity triangles shown in Fig. P12.4. Sketch an appropriate blade section at that radial
Sketch how you would arrange four 3-in.-wide by 12-in.long thin but rigid strips of sheet metal on a hub to create a windmill like the one. Discuss, with the help of velocity triangles, how you would
Sketched in Fig. P12.6 are the upstream [section (1)] and downstream [section (2)] velocity triangles at the arithmetic mean radius for flow through an axial-flow turbomachine rotor. The axial
The radial component of velocity of water leaving the centrifugal pump sketched in Fig. P12.7 is \(45 \mathrm{ft} / \mathrm{s}\). The magnitude of the absolute velocity at the pump exit is \(90
Water enters a centrifugal pump with an absolute velocity \(V_{1}=10 \mathrm{~m} / \mathrm{s}\) in the radial direction and leaves with an absolute velocity \(V_{2}\), which makes an angle of
A centrifugal pump impeller is rotating at \(1200 \mathrm{rpm}\) in the direction shown in Fig. P12.9. The flow enters parallel to the axis of rotation and leaves at an angle of \(30^{\circ}\) to the
A centrifugal radial water pump has the dimensions shown in Fig. P12.10. The volume rate of flow is \(0.25 \mathrm{ft}^{3} / \mathrm{s}\), and the absolute inlet velocity is directed radially
Water is pumped with a centrifugal pump, and measurements made on the pump indicate that for a flowrate of \(240 \mathrm{gpm}\) the required input power is \(6 \mathrm{hp}\). For a pump efficiency of
The performance characteristics of a certain centrifugal pump are determined from an experimental setup similar to that shown in Fig. 12.10. When the flowrate of a liquid \((S G=0.9)\) through the
The performance characteristics of a certain centrifugal pump having a 9-in.-diameter impeller and operating at \(1750 \mathrm{rpm}\) are determined using an experimental setup similar to that shown
Determine algebraic equations for the pump head rise, power, and efficiency as functions of flow rate based on the data from Problem 12.18. Analytically determine the Best Efficiency Point and the
In Example 12.3, how will the maximum height, \(z_{1}\), that the pump can be located above the water surface change if the water temperature is decreased to \(40^{\circ} \mathrm{F}\)?Example 12.3A
A centrifugal pump with a 7-in.-diameter impeller has the performance characteristics shown in Fig. 12.12. The pump is used to pump water at \(100{ }^{\circ} \mathrm{F}\), and the pump inlet is
Water at \(40{ }^{\circ} \mathrm{C}\) is pumped from an open tank through \(200 \mathrm{~m}\) of 50-mm-diameter smooth horizontal pipe as shown in Fig. P12.17 and discharges into the atmosphere with
The centrifugal pump shown in Fig. P12.18 is not selfpriming. That is, if the water is drained from the pump and pipe as shown in Fig. P12.18(a), the pump will not draw the water into the pump and
A centrifugal pump having a head-capacity relationship given by the equation \(h_{a}=180-6.10 \times 10^{-4} Q^{2}\), with \(h_{a}\) in feet when \(Q\) is in gpm, is to be used with a system similar
A centrifugal pump having a 6-in.-diameter impeller and the characteristics shown in Fig. 12.7 is to be used to pump gasoline through \(4000 \mathrm{ft}\) of commercial steel 3-in.-diameter pipe. The
A centrifugal pump having the characteristics shown in Example 12.4 is used to pump water between two large open tanks through \(100 \mathrm{ft}\) of 8-in.-diameter pipe. The pipeline contains four
Both the suction and discharge piping for the pump shown in Fig. P12.22 consist of 4-in. I.D. 40-ft-long plastic pipe. Find the volume flow rate of \(60{ }^{\circ} \mathrm{F}\) water through the
In a chemical processing plant a liquid is pumped from an open tank, through a \(0.1-\mathrm{m}\)-diameter vertical pipe, and into another open tank as shown in Fig. P12.23(a). A valve is located in
Two of the pumps in Fig. P12.24 are operated in series to supply water through the piping system. Determine the flow rate through the piping system for \(10^{\circ} \mathrm{C}\) water and screwed
Water is pumped between the two tanks described in Example 12.4 once a day, 365 days a year, with each pumping period lasting two hours. The water levels in the two tanks remain essentially constant.
A centrifugal pump having an impeller diameter of \(1 \mathrm{~m}\) is to be constructed so that it will supply a head rise of \(200 \mathrm{~m}\) at a flowrate of \(4.1 \mathrm{~m}^{3} /
Do the head-flowrate data shown in Fig. 12.7 appear to follow the similarity laws as expressed by Eqs. 12.39 and 12.40? Explain.Eq. 12.39Eq. 12.40 (a) (b) Figure 12.7 (a) Open impeller, (b) enclosed
A centrifugal fan operating in a duct has the dimensionless parameters\[ C_{Q}=\frac{Q}{\omega D^{3}} \quad \text { and } \quad C_{H}=\frac{\Delta p}{ho \omega^{2} D^{2}} \]where \(C_{Q}\) is a

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