Air is drawn into a wind tunnel used for testing automobilesas shown in Fig. P3.51. (a)

Obtain a photograph/image of a situation that involves a confined flow for which the Bernoulli and continuity equations are important. Print this photo and write a brief paragraph that describes the situation involved.

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 ft/s. Determine the pressure in the pipe if viscous effects are negligible.

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 section? The water flow is inviscid.

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 (lb/s) of the gasoline in the pipe.

A fire hose nozzle has a diameter of 11 8 in. According to some fire codes, the nozzle must be capable of delivering at least 250 gal/min. If the nozzle is attached to a 3-in.-diameter hose, what pressure must be maintained just upstream of the nozzle to deliver this flowrate?

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.

A fire hose has a nozzle outlet velocity of 30 mph. What is the maximum height the water can reach?

At what rate does oil (SG = 0.85) flow from the tank shown in Fig. P3.47?

Find the water height hB in tank B shown in Fig. P3.48 for steady-state conditions.

The pressure and average velocity at point A in the pipe shown in Fig. P3.49 are 16.0 psia and 4.0 ft/sec, respectively. Find the height h and the pressure and average velocity at point B. Fluid fills the 1-in.-diameter discharge pipe.

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 kPa.

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 mph. Note that there is a 1-in. column of oil on the water in the manometer. (b) Determine the difference between the stagnation pressure on the front of the automobile and the pressure in the test section

Figure P3.52 shows a duct for testing a centrifugal fan. Air is drawn from the atmosphere (patm = 14.7 psia, Tatm = 70 F). The inlet box is 4 ft 2 ft. At section 1, the duct is 2.5 ft square. At section 2, the duct is circular and has a diameter of 3 ft. A water manometer in the inlet box measures a static pressure of 2.0 in. of water. Calculate the volume flow rate of air into the fan and the average fluid velocity at both sections 1 and 2. Assume constant density.

Natural gas (methane) flows from a 3-in.-diameter gas main, through a 1-in.-diameter pipe, and into the burner of a furnace at a rate of 100 ft3 /hour. Determine the pressure in the gas main if the pressure in the 1-in. pipe is to be 6 in. of water greater than atmospheric pressure. Neglect viscous effects.

Air flows radially outward between the two parallel circular plates shown in Fig. P3.54. The pressure at the outer radius Ro = 5.0 cm is atmospheric. Find the pressure at the inner radius Ri = 0.5 cm if the air density is constant, the air flow is inviscid, the volume flow rate is 4.0 L/s, and the plate spacing is h = 0.125 cm.

Repeat Problem 3.54 for air flowing radially inward.

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/ft3 , and the flow is inviscid.

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 50 kN/m2 . Determine (a) the height h, to which the water rises, (b) the water velocity in the pipe, and (c) the pressure in the horizontal part of the pipe.

Water (assumed inviscid and incompressible) flows steadily with a speed of 10 ft/s from the large tank shown in Fig. P3.50. Determine the depth, H, of the layer of light liquid (specific weight = 50 lb/ft3 ) that covers the water in the tank.

Water flows through the pipe contraction shown in Fig. P3.59. For the given 0.2-m difference in the manometer level, determine the flowrate as a function of the diameter of the small pipe, D.

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 psi and 30 ft/s, respectively. At location B the pressure and velocity are 23 psi and 14 ft/s. Which point is at the higher elevation and by how much?

Water flows from a 20-mm-diameter pipe with a flowrate Q as shown in Fig. P3.61. Plot the diameter of the water stream, d, as a function of distance below the faucet, h, for values of 0 h 1 m and 0 Q 0.004 m3 /s. Discuss the validity of the one-dimensional assumption used to calculate d = d(h), noting, in particular, the conditions of small h and small Q.

A liquid stream directed vertically upward leaves a nozzle with a steady velocity V0 and cross-sectional area A0. Find the velocity V and cross-sectional area A as a function of the vertical position z.

Water leaves a pump at 200 kPa and a velocity of 12 m/s. It then enters a diffuser to increase its pressure to 250 kPa. What must be the ratio of the outlet area to the inlet area of the diffuser?

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 D1 if the pressure is to remain constant throughout the pipe. That is, p(z) = p1.

The circular stream of water from a faucet is observed to taper from a diameter of 20 mm to 10 mm in a distance of 50 cm. Determine the flowrate.

Water is siphoned from the tank shown in Fig. P3.66. The water barometer indicates a reading of 30.2 ft. Determine the maximum value of h allowed without cavitation occurring. Note that the pressure of the vapor in the closed end of the barometer equals the vapor pressure

Water is siphoned from a tank as shown in Fig. P3.67. Determine the flowrate and the pressure at point A, a stagnation point.

A 50-mm-diameter plastic tube is used to siphon water from the large tank shown in Fig. P3.68. If the pressure on the outside of the tube is more than 35 kPa greater than the pressure within the tube, the tube will collapse and siphon will stop. If viscous effects are negligible, determine the minimum value of h allowed without the siphon stopping.

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.

Redo Problem 3.69 if a 1-in.-diameter nozzle is placed at the end of the tube.

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) Determine the velocity and pressure at section (1).

Water flows steadily from a large, closed tank as shown in Fig. P3.72. The deflection in the mercury manometer is 1 in. and viscous effects are negligible. (a) Determine the volume flowrate. (b) Determine the air pressure in the space above the surface of the water in the tank.

Carbon dioxide flows at a rate of 1.5 ft3 /s from a 3-in. pipe in which the pressure and temperature are 20 psi (gage) and 120 F into a 1.5-in. pipe. If viscous effects are neglected and incompressible conditions are assumed, determine the pressure in the smaller pipe.

Oil of specific gravity 0.83 flows in the pipe shown in Fig. P3.74. If viscous effects are neglected, what is the flowrate?

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 m3 /s and the density of the manometer fluid is 500 kg/m3 .

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) gasoline, or (c) air at standard conditions

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 becomes less than 10 psi below atmospheric pressure. Determine the maximum value that h can have without causing collapse of the tubing.

Helium flows through a 0.30-m-diameter horizontal pipe with a temperature of 20 C and a pressure of 200 kPa (abs) at a rate of 0.30 kg/s. If the pipe reduces to 0.25-m-diameter, determine the pressure difference between these two sections. Assume incompressible, inviscid flow.

Water is pumped from a lake through an 8-in. pipe at a rate of 10 ft3 s. If viscous effects are negligible, what is the pressure in the suction pipe (the pipe between the lake and the pump) at an elevation 6 ft above the lake?

Air is drawn into a small open-circuit wing tunnel as shown in Fig. P3.80. Atmospheric pressure is 98.7 kPa (abs) and the temperature is 27 C. If viscous effects are negligible, determine the pressure at the stagnation point on the nose of the airplane. Also determine the manometer reading, h, for the manometer attached to the static pressure tap within the test section of the wind tunnel if the air velocity within the test section is 50 m/s.

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, Q, and the pressure needed at section (1) to draw the water into section (2). Neglect compressibility and viscous effects.

Water flows steadily from the large open tank shown in Fig. 3.82. If viscous effects are negligible, determine (a) the flowrate, Q, and (b) the manometer reading, h.

Water from a faucet fills a 16-oz glass (volume = 28.9 in.3 ) in 20 s. If the diameter of the jet leaving the faucet is 0.60 in., what is the diameter of the jet when it strikes the water surface in the glass which is positioned 14 in. below the faucet?

The nozzle shown in Fig. P3.84 has two water manometers to indicate the static pressures at sections 1 and 2. The diameters D1 and D2 are 8 in. and 2 in., respectively. Air flows through the nozzle, and the air and water temperatures are 60 F. Find the air volume flow rate. Assume constant density and inviscid flow. Neglect elevation changes.

Air flows steadily through a convergingdiverging 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 H0 and V0 respectively. The channel is to be shaped so that the distance, d, that water is drawn up into tubes attached to static pressure taps along the channel wall is linear with distance along the channel. That is d = (dmax/L) x, where L is the channel length and dmax is the maximum water depth (at the minimum channel height: x = L). Determine the height, H(x), as a function of x and the other important parameters.

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 = A0[1 x(1 x/)/2], where A0 is the area at the beginning (x = 0) and end (x = ) of the pipe. Plot graphs of the pressure within the pipe as a function of distance along the pipe for water depths of h = 1, 4, 10, and 25 m.

If viscous effects are neglected and the tank is large, determine the flowrate from the tank shown in Fig. P3.87.

Water flows steadily downward in the pipe shown in Fig. P.3.88 with negligible losses. Determine the flowrate.

Water flows steadily from a large open tank and discharges into the atmosphere though a 3-in.-diameter pipe as shown in Fig. P3.89. Determine the diameter, d, in the narrowed section of the pipe at A if the pressure gages at A and B indicate the same pressure.

Water flows from a large tank as shown in Fig. P3.90. Atmospheric pressure is 14.5 psia, and the vapor pressure is 1.60 psia. If viscous effects are neglected, at what height, h, will cavitation begin? To avoid cavitation, should the value of D1 be increased or decreased? To avoid cavitation, should the value of D2 be increased or decreased? Explain.

Water flows into the sink shown in Fig. P3.91 and Video V5.1 at a rate of 2 gal/min. If the drain is closed, the water will eventually flow through the overflow drain holes rather than over the edge of the sink. How many 0.4-in.-diameter drain holes are needed to ensure that the water does not overflow the sink? Neglect viscous effects.

What pressure, p1, is needed to produce a flowrate of 0.09 ft3 /s from the tank shown in Fig. P3.92?

The vent on the tank shown in Fig. P3.93 is closed and the tank pressurized to increase the flowrate. What pressure, p1, is needed to produce twice the flowrate of that when the vent is open?

A sump pump is submerged in 60 F ordinary water that vaporizes at a pressure of 0.256 psia. The pump inlet has an inside diameter of 2.067 in. and is 15 ft below the water surface. Find the maximum possible flow rate before cavitation (vaporization) occurs

Water is siphoned from a large tank and discharges into the atmosphere through a 2-in.-diameter tube as shown in Fig. P3.95. The end of the tube is 3 ft below the tank bottom, and viscous effects are negligible. (a) Determine the volume flowrate from the tank. (b) Determine the maximum height, H, over which the water can be siphoned without cavitation occurring. Atmospheric pressure is 14.7 psia, and the water vapor pressure is 0.26 psia.

Water flows in the system shown in Fig. P3.96. Assume frictionless flow. (a) Calculate the rate Q at which water must be added at the inlet to maintain the 16-ft height. (b) Calculate the height h in feet of water in the static-pressure tube.

Water flows steadily from the pipe shown in Fig. P3.97 with negligible viscous effects. Determine the maximum flowrate if the water is not to flow from the open vertical tube at A.

JP-4 fuel (SG = 0.77) flows through the Venturi meter shown in Fig. P3.98 with a velocity of 15 ft/s in the 6-in. pipe. If viscous effects are negligible, determine the elevation, h, of the fuel in the open tube connected to the throat of the Venturi meter

Water, considered an inviscid, incompressible fluid, flows steadily as shown in Fig. P3.99. Determine h.

Determine the flowrate through the submerged orifice shown in Fig. P3.100 if the contraction coefficient is Cc = 0.63.

The water clock (clepsydra) shown in Fig. P3.101 is an ancient device for measuring time by the falling water level in a large glass container. The water slowly drains out through a small hole in the bottom. Determine the approximate shape R(z) of a container of circular cross section required for the water level to fall at a constant rate of 5 cm/hr if the drain hole is 1.5 mm in diameter. What size container (h and R0) permits the clock to run for 24 hr without refilling?

A long water trough of triangular cross section is formed from two planks as is shown in Fig. P3.102. A gap of 0.1 in. remains at the junction of the two planks. If the water depth initially was 2 ft, how long a time does it take for the water depth to reduce to 1 ft?

Pop (with the same properties as water) flows from a 4-in.-diameter pop container that contains three holes as shown in Fig. P3.103 (see Video 3.9). The diameter of each fluid stream is 0.15 in., and the distance between holes is 2 in. If viscous effects are negligible and quasi-steady conditions are assumed, determine the time at which the pop stops draining from the top hole. Assume the pop surface is 2 in. above the top hole when t = 0. Compare your results with the time you measure from the video.

A spherical tank of diameter D has a drain hole of diameter d at its bottom. A vent at the top of the tank maintains atmospheric pressure at the liquid surface within the tank. The flow is quasisteady and inviscid and the tank is full of water initially. Determine the water depth as a function of time, h = h(t), and plot graphs of h(t) for tank diameters of 1, 5, 10, and 20 ft if d = 1 in.

A small hole develops in the bottom of the stationary rowboat shown in Fig. P3.105. Estimate the amount of time it will take for the boat to sink. List all assumptions and show all calculations.

When the drain plug is pulled, water flows from a hole in the bottom of a large, open cylindrical tank. Show that if viscous effects are negligible and if the flow is assumed to be quasisteady, then it takes 3.41 times longer to empty the entire tank than it does to empty the first half of the tank. Explain why this is so.

Someone siphoned 15 gal of gasoline from a gas tank in the middle of the night. The gas tank measures 12 in. wide 24 in. long 18 in. high and was full when the thief started. If the siphoning tube has an inside diameter of 1 2 in., find the minimum amount of time needed to siphon the 15 gal from the tank. Assume that at any instant of time the steady-state equations are adequate to predict the gasoline velocity in the siphon tube. Also assume that the end of the siphon tube outside the gas tank is at the same level as the bottom of the tank. You may consider the gasoline to be inviscid.

The surface area, A, of the pond shown in Fig. P3.108 varies with the water depth, h, as shown in the table. At time t = 0 a valve is opened and the pond is allowed to drain through a pipe of diameter D. If viscous effects are negligible and quasisteady conditions are assumed, plot the water depth as a function of time from when the valve is opened (t = 0) until the pond is drained for pipe diameters of D = 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 ft. Assume h = 18 ft at t = 0.

Water flows through a horizontal branching pipe as shown in Fig. P3.109. Determine the pressure at section (3).

The wye fitting shown in Fig. P.3.110 lies in a horizontal plane. The fitting splits the inlet flow into two equal parts. At section 1, the water velocity is 12 ft/sec and the pressure is 20 psig. Calculate the water pressure at sections 2 and 3. Assume inviscid flow and a water temperature of 60 F.

Water flows through the branching pipe shown in Fig. P3.111. If viscous effects are negligible, determine the pressure at section (2) and the pressure at section (3).

Water flows through the horizontal branching pipe shown in Fig. P3.112 at a rate of 10 ft3 /s. If viscous effects are negligible, determine the water speed at section (2), the pressure at section (3), and the flowrate at section (4).

Water flows from a large tank through a large pipe that splits into two smaller pipes as shown in Fig. P3.113. If viscous effects are negligible, determine the flowrate from the tank and the pressure at point (1).

A gutter running along the side of a house is 6 in. wide and 40 ft long. During a hard downpour, water is 1 in. deep in the gutter. The gutter has only one downspout, and it is 3 in. in diameter. What is the velocity of the water entering the downspout? The pressure at the downspout entrance is atmospheric pressure.

Air, assumed incompressible and inviscid, flows into the outdoor cooking grill through nine holes of 0.40-in. diameter as shown in Fig. P3.115. If a flowrate of 40 in.3 /s into the grill is required to maintain the correct cooking conditions, determine the pressure within the grill near the holes.

An air cushion vehicle is supported by forcing air into the chamber created by a skirt around the periphery of the vehicle as shown in Fig. P3.116. The air escapes through the 3-in. clearance between the lower end of the skirt and the ground (or water). Assume the vehicle weighs 10,000 lb and is essentially rectangular in shape, 30 by 65 ft. The volume of the chamber is large enough so that the kinetic energy of the air within the chamber is negligible. Determine the flowrate, Q, needed to support the vehicle. If the ground clearance were reduced to 2 in., what flowrate would be needed? If the vehicle weight were reduced to 5000 lb and the ground clearance maintained at 3 in., what flowrate would be needed?

Water flows from the pipe shown in Fig. P3.117 as a free jet and strikes a circular flat plate. The flow geometry shown is axisymmetrical. Determine the flowrate and the manometer reading, H.

A conical plug is used to regulate the airflow from the pipe shown in Fig. P3.118. The air leaves the edge of the cone with a uniform thickness of 0.02 m. If viscous effects are negligible and the flowrate is 0.50 m3 /s, determine the pressure within the pipe.

Figure P3.119 shows two tall towers. Air at 10 C is blowing toward the two towers at V0 = 30 km/hr. If the two towers are 10 m apart and half the air flow approaching the two towers passes between them, find the minimum air pressure between the two towers. Assume constant air density, inviscid flow, and steady-state conditions. The atmospheric pressure is 101 kPa.

Water flows steadily from a nozzle into a large tank as shown in Fig. P3.120. The water then flows from the tank as a jet of diameter d. Determine the value of d if the water level in the tank remains constant. Viscous effects are negligible.

A small card is placed on top of a spool as shown in Fig. P3.121. It is not possible to blow the card off the spool by blowing air through the hole in the center of the spool. The harder one blows, the harder the card sticks to the spool. In fact by blowing hard enough it is possible to keep the card against the spool with the spool turned upside down. Give this experiment a try. (Note: It may be necessary to use a thumb tack to prevent the card from sliding from the spool.) Explain this phenomenon.

Observations show that it is not possible to blow the table tennis ball from the funnel shown in Fig. P3.122a. In fact, the ball can be kept in an inverted funnel, Fig. P3.122b, by blowing through it. The harder one blows through the funnel, the harder the ball is held within the funnel. Try this experiment on your own. Explain this phenomenon.

Water flows down the sloping ramp shown in Fig. P3.123 with negligible viscous effects. The flow is uniform at sections (1) and (2). For the conditions given show that three solutions for the downstream depth, h2, are obtained by use of the Bernoulli and continuity equations. However, show that only two of these solutions are realistic. Determine these values.

Water flows in a rectangular channel that is 2.0 m wide as shown in Fig. P3.124. The upstream depth is 70 mm. The water surface rises 40 mm as it passes over a portion where the channel bottom rises 10 mm. If viscous effects are negligible, what is the flowrate?