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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Water flows around the vertical two-dimensional bend with circular streamlines and constant velocity as shown in Fig. P3.12. If the pressure is \(40 \mathrm{kPa}\) at point (1), determine the
Air flows along a horizontal, curved streamline with a \(20 \mathrm{ft}\) radius with a speed of \(100 \mathrm{ft} / \mathrm{s}\). Determine the pressure gradient normal to the streamline.
Water flows around the vertical two-dimensional bend with circular streamlines as is shown in Fig. P3.13. The pressure at point (1) is measured to be \(p_{1}=25 \mathrm{psi}\) and the velocity across
Water in a container and air in a tornado flow in horizontal circular streamlines of radius \(r\) and speed \(V\) as shown in Video V3.6 and Fig. P3.14. Determine the radial pressure gradient,
Air flows smoothly over the hood of your car and up past the windshield. However, a bug in the air does not follow the same path; it becomes splattered against the windshield. Explain why this is so.
At a given point on a horizontal streamline in flowing air, the static pressure is \(-2.0 \mathrm{psi}\) (i.e., a vacuum) and the velocity is \(150 \mathrm{ft} / \mathrm{s}\). Determine the pressure
A drop of water in a zero-g environment (as in the International Space Station) will assume a spherical shape as shown in Fig. P3.18a. A raindrop in the cartoons is typically drawn as in Fig. P3.18b.
When an airplane is flying \(200 \mathrm{mph}\) at \(5000-\mathrm{ft}\) altitude in a standard atmosphere, the air velocity at a certain point on the wing is \(273 \mathrm{mph}\) relative to the
Air flows over the airfoil shown in Fig. P3.20. Sensors give the pressures shown at points \(A, B, C\), and \(D\). Find the air velocities just above points \(A, B, C\), and \(D\). The air density is
Some animals have learned to take advantage of the Bernoulli effect without having read a fluid mechanics book. For example, a typical prairie dog burrow contains two entrances-a flat front door and
Estimate the pressure on your hand when you hold it in the stream of air coming from the air hose at a filling station. List all assumptions and show calculations. Warning: Do not try this
What is the minimum height for an oil \((S G=0.75)\) manometer to measure airplane speeds up to \(30 \mathrm{~m} / \mathrm{s}\) at altitudes up to \(1500 \mathrm{~m}\) ? The manometer is connected to
A Pitot-static tube is used to measure the velocity of helium in a pipe. The temperature and pressure are \(40^{\circ} \mathrm{F}\) and 25 psia. A water manometer connected to the Pitot-static tube
A Bourdon-type pressure gage is used to measure the pressure from a Pitot tube attached to the leading edge of an airplane wing. The gage is calibrated to read in miles per hour at standard sea level
Estimate the force of a hurricane strength wind against the side of your house. List any assumptions and show all calculations.
A 40-mph wind blowing past your house speeds up as it flows up and over the roof. If elevation effects are negligible, determine(a) the pressure at the point on the roof where the speed is \(60
The Wide World of Fluids article titled "Pressurized eyes,". Determine the air velocity needed to produce a stagnation pressure equal to \(10 \mathrm{~mm}\) of mercury.
Water flows through a hole in the bottom of a large, open tank with a speed of \(8 \mathrm{~m} / \mathrm{s}\). Determine the depth of water in the tank. Viscous effects are negligible.
Estimate the pressure needed at the pumper truck in order to shoot water from the street level onto a fire on the roof of a five-story building. List all assumptions and show all calculations.
The tank shown in Fig. P3.32 contains air at atmospheric pressure above the water surface. The velocity of the water flowing from the tank is \(22.5 \mathrm{ft} / \mathrm{sec}\). Determine the water
Water flows from the faucet on the first floor of the building shown in Fig. P3. 33 with a maximum velocity of \(20 \mathrm{ft} / \mathrm{s}\). For steady inviscid flow, determine the maximum water
Laboratories containing dangerous materials are often kept at a pressure slightly less than ambient pressure so that contaminants can be filtered through an exhaust system rather than leaked through
The "supersoaker" water gun shown in Fig. P3. 35 can shoot more than \(30 \mathrm{ft}\) in the horizontal direction. Estimate the minimum pressure, \(p_{1}\), needed in the chamber in order to
Streams of water from two tanks impinge upon each other as shown in Fig. P3.36. If viscous effects are negligible and point \(A\) is a stagnation point, determine the height \(h\).Figure P3.36 Free
Several holes are punched into a tin can as shown in Fig. P3.37. Which of the figures represents the variation of the water velocity as it leaves the holes? Justify your choice.Figure P3.37 (2) (9)
Water flows from a pressurized tank, through a 6 -in.-diameter pipe, exits from a 2-in.-diameter nozzle, and rises \(20 \mathrm{ft}\) above the nozzle as shown in Fig. P3.38. Determine the pressure
The piston shown in Fig. P3.39 is forcing \(70{ }^{\circ} \mathrm{F}\) water out the exit at \(12 \mathrm{ft} / \mathrm{sec}\). The exit pressure has been measured as \(p_{e}=40 \mathrm{psig}\).
Air flows steadily through a horizontal 4-in.-diameter pipe and exits into the atmosphere through a 3-in.-diameter nozzle. The velocity at the nozzle exit is \(150 \mathrm{ft} / \mathrm{s}\).
Figure P3.42 shows a tube for siphoning water from an aquarium. Determine the rate at which the water leaves the aquarium for the conditions shown. Is there an advantage to having the large-diameter
For the pipe enlargement shown in Fig. P3.43, the pressures at sections (1) and (2) are 56.3 and 58.2 psi, respectively. Determine the weight flowrate ( \(\mathrm{lb} / \mathrm{s})\) of the gasoline
A fire hose nozzle has a diameter of \(1 \frac{1}{8} \mathrm{in}\). According to some fire codes, the nozzle must be capable of delivering at least 250 \(\mathrm{gal} / \mathrm{min}\). If the nozzle
Water flowing from the 0.75-in.-diameter outlet shown in Video V8.15 and Fig. P3.45 rises 2.8 in. above the outlet. Determine the flowrate.Figure P3.45 2.8 in. C 0.75 in.
At what rate does oil \((S G=0.85)\) flow from the tank shown in Fig. P3.47?Figure P3.47 D= 14 cm 13.5 cm 10.5 cm d=3.0 cm Oil d = 3.0 cm
A fire hose has a nozzle outlet velocity of \(30 \mathrm{mph}\). What is the maximum height the water can reach?
Find the water height \(h_{B}\) in tank \(B\) shown in Fig. P3.48 for steady-state conditions.Figure P3.48 h = 10.0 cm Tank A 4 = 0.01 m Tank B hs d = 0.02 m
The pressure and average velocity at point \(A\) in the pipe shown in Fig. P3.49 are 16.0 psia and \(4.0 \mathrm{ft} / \mathrm{sec}\), respectively. Find the height \(h\) and the pressure and average
Water (assumed inviscid and incompressible) flows steadily in the vertical variable-area pipe shown in Fig. P3.50. Determine the flowrate if the pressure in each of the gages reads \(50
Air is drawn into a wind tunnel used for testing automobiles as shown in Fig. P3.51.(a) Determine the manometer reading, \(h\), when the velocity in the test section is \(60 \mathrm{mph}\). Note that
Figure P3.52 shows a duct for testing a centrifugal fan. Air is drawn from the atmosphere ( \(p_{\text {atm }}=14.7 \mathrm{psia}, T_{\mathrm{atm}}=70^{\circ} \mathrm{F}\) ). The inlet box is \(4
Air flows radially outward between the two parallel circular plates shown in Fig. P3.54. The pressure at the outer radius \(R_{o}=\) \(5.0 \mathrm{~cm}\) is atmospheric. Find the pressure at the
Repeat Problem 3.54 for air flowing radially inward.Problem 3.54Air flows radially outward between the two parallel circular plates shown in Fig. P3.54. The pressure at the outer radius \(R_{o}=\)
Find the water mass flow rate at the nozzle outlet \(O\) shown in Fig. P3.56, and calculate the maximum height to which the water stream will rise. The water density is 1.9 slugs \(/
Water (assumed frictionless and incompressible) flows steadily from a large tank and exits through a vertical, constant diameter pipe as shown in Fig. P3.57. The air in the tank is pressurized to
Water (assumed inviscid and incompressible) flows steadily with a speed of \(10 \mathrm{ft} / \mathrm{s}\) from the large tank shown in Fig. P3.58. Determine the depth, \(H\), of the layer of light
Water flows through the pipe contraction shown in Fig. P3.59. For the given \(0.2-\mathrm{m}\) difference in the manometer level, determine the flowrate as a function of the diameter of the small
Carbon tetrachloride flows in a pipe of variable diameter with negligible viscous effects. At point \(A\) in the pipe the pressure and velocity are \(20 \mathrm{psi}\) and \(30 \mathrm{ft} /
A liquid stream directed vertically upward leaves a nozzle with a steady velocity \(V_{0}\) and cross-sectional area \(A_{0}\). Find the velocity \(V\) and cross-sectional area \(A\) as a function of
Water flows from a 20-mm-diameter pipe with a flowrate QQ as shown in Fig. P3.61. Plot the diameter of the water stream, dd, as a function of distance below the faucet, hh, for values of
The U-tube in Fig. P2.160 rotates at \(2.0 \mathrm{rev} / \mathrm{sec}\). Find the absolute pressures at points \(C\) and \(B\) if the atmospheric pressure is 14.696 psia. Recall that \(70{ }^{\circ}
Water flows steadily from a large, closed tank as shown in Fig. P3.72. The deflection in the mercury manometer is \(1 \mathrm{in}\). and viscous effects are negligible.(a) Determine the volume
Oil of specific gravity 0.83 flows in the pipe shown in Fig. P3.74. If viscous effects are neglected, what is the flowrate?Figure P3.74 Water. 4 in. 3 in. SG= 0.83 4 in.
Carbon dioxide flows at a rate of \(1.5 \mathrm{ft}^{3} / \mathrm{s}\) from a 3-in. pipe in which the pressure and temperature are \(20 \mathrm{psi}\) (gage) and \(120^{\circ} \mathrm{F}\) into a
Water flows steadily through the variable area pipe shown in Fig. P3.75 with negligible viscous effects. Determine the manometer reading, \(H\), if the flowrate is \(0.4 \mathrm{~m}^{3} /
The specific gravity of the manometer fluid shown in Fig. P3.76 is 1.07. Determine the volume flowrate, \(Q\), if the flow is inviscid and incompressible and the flowing fluid is(a) water,(b)
Water flows steadily with negligible viscous effects through the pipe shown in Fig. P3.77. It is known that the 4-in.-diameter section of thin-walled tubing will collapse if the pressure within it
Helium flows through a \(0.30-\mathrm{m}\)-diameter horizontal pipe with a temperature of \(20^{\circ} \mathrm{C}\) and a pressure of \(200 \mathrm{kPa}\) (abs) at a rate of \(0.30 \mathrm{~kg} /
Water is pumped from a lake through an 8-in. pipe at a rate of \(10 \mathrm{ft}^{3} / \mathrm{s}\). If viscous effects are negligible, what is the pressure in the suction pipe (the pipe between the
Air is drawn into a small open-circuit wing tunnel as shown in Fig. P3.80. Atmospheric pressure is \(98.7 \mathrm{kPa}\) (abs) and the temperature is \(27^{\circ} \mathrm{C}\). If viscous effects are
Water leaves a pump at \(200 \mathrm{kPa}\) and a velocity of \(12 \mathrm{~m} / \mathrm{s}\). It then enters a diffuser to increase its pressure to \(250 \mathrm{kPa}\). What must be the ratio of
Water flows upward through a variable area pipe with a constant flowrate, \(Q\), as shown in Fig. P3.64. If viscous effects are negligible, determine the diameter, \(D(z)\), in terms of \(D_{1}\) if
Water is siphoned from the tank shown in Fig. P3.66. The water barometer indicates a reading of \(30.2 \mathrm{ft}\). Determine the maximum value of \(h\) allowed without cavitation occurring. Note
Water is siphoned from a tank as shown in Fig. P3.67. Determine the flowrate and the pressure at point \(A\), a stagnation point.Figure P3.67 0.04-m diameter A 3 m 1
The circular stream of water from a faucet is observed to taper from a diameter of \(20 \mathrm{~mm}\) to \(10 \mathrm{~mm}\) in a distance of \(50 \mathrm{~cm}\). Determine the flowrate.
Water is siphoned from the tank shown in Fig. P3.69. Determine the flowrate from the tank and the pressure at points (1), (2), and (3) if viscous effects are negligible.Figure P3.69 2-in.-diameter
Redo Problem 3.69 if a 1-in.-diameter nozzle is placed at the end of the tube.Problem 3.69Water is siphoned from the tank shown in Fig. P3.69. Determine the flowrate from the tank and the pressure at
Water exits a pipe as a free jet and flows to a height \(h\) above the exit plane as shown in Fig. P3.71. The flow is steady, incompressible, and frictionless.(a) Determine the height \(h\).(b)
Air flows through the device shown in Fig. P3.81. If the flowrate is large enough, the pressure within the constriction will be low enough to draw the water up into the tube. Determine the flowrate,
Water flows steadily from the large open tank shown in Fig. 3.82. If viscous effects are negligible, determine(a) the flowrate, \(Q\), (b) the manometer reading, \(h\).Figure P3.82 2 m h 4 m 0.08 m
The nozzle shown in Fig. P3.84 has two water manometers to indicate the static pressures at sections 1 and 2 . The diameters \(D_{1}\) and \(D_{2}\) are 8 in. and 2 in., respectively. Air flows
Water from a faucet fills a \(16-\mathrm{oz}\) glass (volume \(=28.9 \mathrm{in.}^{3}\) ) in \(20 \mathrm{~s}\). If the diameter of the jet leaving the faucet is \(0.60 \mathrm{in}\)., what is the
Air flows steadily through a converging-diverging rectangular channel of constant width as shown in Fig. 3.85 and Video V3.10. The height of the channel at the exit and the exit velocity are
Water flows from a large tank and through a pipe of variable area as shown in Fig. 3.86. The area of the pipe is given by \(A=A_{0}[1-x(1-x / \ell) / 2 \ell]\), where \(A_{0}\) is the area at the
If viscous effects are neglected and the tank is large, determine the flowrate from the tank shown in Fig. P3.87.Figure P3.87 50-mm diameter 2 m 0.7 m Oil. SG=0.81 Water
Water flows steadily downward in the pipe shown in Fig. P.3.88 with negligible losses. Determine the flowrate.Figure P3.88 Open Oil SG = 0.7 -1.2 m 1 m- 1.5 m. 2 m
The force, \(F\), of the wind blowing against a building is given by \(F=C_{D} ho V^{2} A / 2\), where \(V\) is the wind speed, \(ho\) the density of the air, \(A\) the cross-sectional area of the
The Mach number is a dimensionless ratio of the velocity of an object in a fluid to the speed of sound in the fluid. For an airplane flying at velocity \(V\) in air at absolute temperature \(T\), the
If \(u\) is a velocity, \(x\) a length, and \(t\) a time, what are the dimensions (in the MLT system) of (a) \(\partial u / \partial t\), (b) \(\partial^{2} u / \partial x \partial t\), and (c)
The momentum flux is given by the product \(\dot{m} V\), where \(\dot{m}\) is mass flow rate and \(V\) is velocity. If mass flow rate is given in units of mass per unit time, show that the momentum
An equation for the frictional pressure loss \(\Delta p\) (inches \(\mathrm{H}_{2} \mathrm{O}\) ) in a circular duct of inside diameter \(d\) (in.) and length \(L\) (ft) for air flowing with velocity
Show that each term in the following equation has units of \(\mathrm{lb} / \mathrm{ft}^{3}\). Consider \(u\) a velocity, \(y\) a length, \(x\) a length, \(p\) a pressure, and \(\mu\) an absolute
A formula to estimate the volume rate of flow, \(Q\), flowing over a dam of length, \(B\), is given by the equation\[ Q=3.09 B H^{3 / 2} \]where \(H\) is the depth of the water above the top of the
A commercial advertisement shows a pearl falling in a bottle of shampoo. If the diameter \(D\) of the pearl is quite small and the shampoo sufficiently viscous, the drag \(\mathscr{D}\) on the pearl
Cite an example of a restricted homogeneous equation contained in a technical article found in an engineering journal in your field of interest. Define all terms in the equation, explain why it is a
The universal gas constant \(R_{0}\) is equal to \(49,700 \mathrm{ft}^{2} /\left(\mathrm{s}^{2} \cdot{ }^{\circ} \mathrm{R}\right)\), or \(8310 \mathrm{~m}^{2} /\left(\mathrm{s}^{2} \cdot
Dimensionless combinations of quantities (commonly called dimensionless parameters) play an important role in fluid mechanics. Make up five possible dimensionless parameters by using combinations of
Obtain a photograph/image of a situation in which the density or specific weight of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved.
A tank contains \(500 \mathrm{~kg}\) of a liquid whose specific gravity is 2. Determine the volume of the liquid in the tank.
A stick of butter at \(35^{\circ} \mathrm{F}\) measures 1.25 in. \(\times 1.25\) in. \(\times\) 4.65 in. and weighs 4 ounces. Find its specific weight.
The density of a certain type of jet fuel is \(775 \mathrm{~kg} / \mathrm{m}^{3}\). Determine its specific gravity and specific weight.
At \(4{ }^{\circ} \mathrm{C}\) a mixture of automobile antifreeze \((50 \%\) water and \(50 \%\) ethylene glycol by volume) has a density of \(1064 \mathrm{~kg} / \mathrm{m}^{3}\). If the water
Estimate the number of pounds of mercury it would take to fill your bathtub. List all assumptions and show all calculations.
A mountain climber's oxygen tank contains \(1 \mathrm{lb}\) of oxygen when he begins his trip at sea level where the acceleration of gravity is \(32.174 \mathrm{ft} / \mathrm{s}^{2}\). What is the
With the exception of the 410 bore, the gauge of a shotgun barrel indicates the number of round lead balls, each having the bore diameter of the barrel, that together weigh \(1 \mathrm{lb}\). For
The presence of raindrops in the air during a heavy rainstorm increases the average density of the air-water mixture. Estimate by what percent the average air-water density is greater than that of
A regulation basketball is initially flat and is then inflated to a pressure of approximately \(24 \mathrm{lb} / \mathrm{in}^{2}\) absolute. Consider the air temperature to be constant at
Nitrogen is compressed to a density of \(4 \mathrm{~kg} / \mathrm{m}^{3}\) under an absolute pressure of \(400 \mathrm{kPa}\). Determine the temperature in degrees Celsius.
Assume that the air volume in a small automobile tire is constant and equal to the volume between two concentric cylinders \(13 \mathrm{~cm}\) high with diameters of \(33 \mathrm{~cm}\) and \(52
A compressed air tank contains \(5 \mathrm{~kg}\) of air at a temperature of \(80^{\circ} \mathrm{C}\). A gage on the tank reads \(300 \mathrm{kPa}\). Determine the volume of the tank.
The helium-filled blimp shown in Fig. P1.52 is used at various athletic events. Determine the number of pounds of helium within it if its volume is \(68,000 \mathrm{ft}^{3}\) and the temperature and
Develop a computer program for calculating the density of an ideal gas when the gas pressure in pascals (abs), the temperature in degrees Celsius, and the gas constant in \(\mathrm{J} / \mathrm{kg}

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