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engineering
engineering fluid mechanics
Questions and Answers of
Engineering Fluid Mechanics
The Churchill formula for the friction factor is\[ f=8\left[\left(\frac{8}{\operatorname{Re}}\right)^{12}+\frac{1}{(A+B)^{1.5}}\right]^{1 / 12} \]where\[ \begin{aligned} & A=\left\{-2.457 \ln
Air at standard temperature and pressure flows through a 1 -in.-diameter galvanized iron pipe with an average velocity of \(8 \mathrm{ft} / \mathrm{s}\). What length of pipe produces a head loss
Given \(90^{\circ}\) threaded elbows used in conjunction with copper pipe (drawn tubing) of 0.75-in. diameter, convert the loss for a single elbow to equivalent length of copper pipe for wholly
To conserve water and energy, a "flow reducer" is installed in the shower head as shown in Fig. P8.52. If the pressure at point (1) remains constant and all losses except for that in the flow reducer
Water flows at a rate of \(0.040 \mathrm{~m}^{3} / \mathrm{s}\) in a 0.12-m-diameter pipe that contains a sudden contraction to a \(0.06-\mathrm{m}\)-diameter pipe. Determine the pressure drop across
Water flows from the container shown in Fig. P8.54. Determine the loss coefficient needed in the valve if the water is to "bubble up" 3 in. above the outlet pipe. The entrance is slightly
The Wide World of Fluids article titled "New Hi-tech Fountains,". The fountain shown in Fig. P8.55 is designed to provide a stream of water that rises \(h=10 \mathrm{ft}\) to \(h=20 \mathrm{ft}\)
Water flows through the screen in the pipe shown in Fig. P8.56 as indicated. Determine the loss coefficient for the screen.Figure P8.56 V=20ft/s Screen Water 6 in. SG=3.2
Air flows though the mitered bend shown in Fig. P8.57 at a rate of \(5.0 \mathrm{cfs}\). To help straighten the flow after the bend, a set of 0.25-in.-diameter drinking straws is placed in the pipe
As shown in Fig. P8.58, water flows from one tank to another through a short pipe whose length is \(n\) times the pipe diameter. Head losses occur in the pipe and at the entrance and exit. Determine
Water flows steadily through the 0.75-in.-diameter galvanized iron pipe system shown in Fig. P8.59 at a rate of \(0.020 \mathrm{cfs}\). Your boss suggests that friction losses in the straight pipe
Given two rectangular ducts with equal cross-sectional area, but different aspect ratios (width/height) of 2 and 4 , which will have the greater frictional losses? Explain your answer.
A viscous oil with a specific gravity \(S G=0.85\) and a viscosity of \(0.10 \mathrm{~Pa} \cdot \mathrm{s}\) flows from tank \(A\) to \(\operatorname{tank} B\) through the six rectangular slots
Air at standard temperature and pressure flows at a rate of 7.0 cfs through a horizontal, galvanized iron duct that has a rectangular cross-sectional shape of 12 in. by 6 in. Estimate the pressure
Water at \(20{ }^{\circ} \mathrm{C}\) flows through a concentric annulus of inner diameter \(D_{1}=2.0 \mathrm{~cm}\) and outer diameter \(D_{2}=4.0 \mathrm{~cm}\). The surface roughness is \(0.002
Air at standard conditions flows through a horizontal \(1 \mathrm{ft}\) by \(1.5 \mathrm{ft}\) rectangular wooden duct at a rate of \(5000 \mathrm{ft}^{3} / \mathrm{min}\). Determine the head loss,
Assume a car's exhaust system can be approximated as \(14 \mathrm{ft}\) of 0.125-ft-diameter cast-iron pipe with the equivalent of six \(90^{\circ}\) flanged elbows and a muffler. The muffler acts
The pressure at section (2) shown in Fig. P8.66 is not to fall below 60 psi when the flowrate from the tank varies from 0 to \(1.0 \mathrm{cfs}\) and the branch line is shut off. Determine the
Repeat Problem 8.66 with the assumption that the branch line is open so that half of the flow from the tank goes into the branch, and half continues in the main line.Problem 8.66The pressure at
The \(\frac{1}{2}\)-in.-diameter hose shown in Fig. P8.68 can withstand a maximum pressure of \(200 \mathrm{psi}\) without rupturing. Determine the maximum length, \(\ell\), allowed if the friction
The hose shown in Fig. P8.68 will collapse if the pressure within it is lower than 10 psi below atmospheric pressure. Determine the maximum length, \(\ell\), allowed if the friction factor is 0.015
According to fire regulations in a town, the pressure drop in a commercial steel horizontal pipe must not exceed 1.0 psi per 150 \(\mathrm{ft}\) of pipe for flowrates up to \(500 \mathrm{gal} /
As shown in Fig. P8.71, water "bubbles up" 3 in. above the exit of the vertical pipe attached to three horizontal pipe segments. The total length of the 0.75-in.diameter galvanized iron pipe between
Water at \(10{ }^{\circ} \mathrm{C}\) is pumped from a lake as shown in Fig. P8.72. If the flowrate is \(0.011 \mathrm{~m}^{3} / \mathrm{s}\), what is the maximum length inlet pipe, \(\ell\), that
At a ski resort, water at \(40{ }^{\circ} \mathrm{F}\) is pumped through a 3-in.diameter, 2000-ft-long steel pipe from a pond at an elevation of \(4286 \mathrm{ft}\) to a snow-making machine at an
Crude oil having a specific gravity of 0.80 and a viscosity of \(6.0 \times 10^{-5} \mathrm{ft}^{2} / \mathrm{sec}\) flows through a pumping station at a rate of \(10,000 \mathrm{barrels} /
A motor-driven centrifugal pump delivers \(15{ }^{\circ} \mathrm{C}\) water at the rate of \(10 \mathrm{~m}^{3} / \mathrm{min}\) from a reservoir, through a \(2500-\mathrm{m}\)-long,
An emergency flooding system for a nuclear reactor core is shown in Fig. P8.76. Find the power input required to flood the core at the rate of \(5000 \mathrm{gal} / \mathrm{min}\). Assume a
A hydraulic turbine takes water from a lake with the piping system shown in Figure P8.77. Find the head \(h_{t}\) available to the turbine for flow rates of \(0,5000,10,000,15,000\), and \(20,000
Water flows through a 2-in.-diameter pipe with a velocity of \(15 \mathrm{ft} / \mathrm{s}\) as shown in Fig. P8.78. The relative roughness of the pipe is 0.004, and the loss coefficient for the exit
Figure P7.79 shows the \(60{ }^{\circ} \mathrm{F}\) water flow rates from the branches of a main supply line. Find the total pressure drop \(\left(p_{A}-p_{E}\right)\) for soldered copper pipe.
Water is pumped through a \(60-\mathrm{m}\)-long, \(0.3-\mathrm{m}\)-diameter pipe from a lower reservoir to a higher reservoir whose surface is \(10 \mathrm{~m}\) above the lower one. The sum of the
Natural gas ( \(ho=0.0044\) slugs \(/ \mathrm{ft}^{3}\) and \(\left.u=5.2 \times 10^{-5} \mathrm{ft}^{2} / \mathrm{s}\right)\) is pumped through a horizontal 6-in.-diameter cast-iron pipe at a rate
As shown in Fig. P8.82, a standard household water meter is incorporated into a lawn irrigation system to measure the volume of water applied to the lawn. Note that these meters measure volume, not
A fan is to produce a constant air speed of \(40 \mathrm{~m} / \mathrm{s}\) throughout the pipe loop shown in Fig. P8.83. The 3-m-diameter pipes are smooth, and each of the four \(90^{\circ}\) elbows
Air flows in a horizontal 100-ft-long, 24-in. \(\times 24\)-in. duct at the rate of \(5000 \mathrm{ft}^{3} / \mathrm{min}\). The air then flows through an expansion into \(200 \mathrm{ft}\) of 36-in.
The turbine shown in Fig. P8.85 develops 400 kW. Determine the flowrate if(a) head losses are negligible (b) head loss due to friction in the pipe is considered. Assume \(f=0.02\). There may be more
Water flows from the nozzle attached to the spray tank shown in Fig. P8.86. Determine the flowrate if the loss coefficient for the nozzle (based on upstream conditions) is 0.75 and the friction
Water flows through the pipe shown in Fig. P8.87. Determine the net tension in the bolts if minor losses are neglected and the wheels on which the pipe rests are frictionless.Figure P8.87 80 mm 3.0 m
When the pump shown in Fig. P8.88 adds 0.2 horsepower to the flowing water, the pressures indicated by the two gages are equal. Determine the flowrate.Length of pipe between gages \(=60
The pump shown in Fig. P8.89 adds \(25 \mathrm{~kW}\) to the water and causes a flowrate of \(0.04 \mathrm{~m}^{3} / \mathrm{s}\). Determine the flowrate expected if the pump is removed from the
The vented storage tank shown in Fig. P8.90 is used to refuel race cars at a race track. A total of \(40 \mathrm{ft}\) of steel pipe (I.D. \(=0.957 \mathrm{in}\).), two \(90^{\circ}\) regular elbows,
Gasoline is unloaded from the tanker truck shown in Fig. P8.91 through a 4-in.-diameter rough-surfaced hose. This is a "gravity dump" with no pump to enhance the flowrate. It is claimed that the 8800
Calculate the water flow rate in the system shown in Fig. P8.92. The piping system includes four gate valves, two half-open globe valves, fourteen \(90^{\circ}\) regular elbows, and \(250
The pump shown in Fig. P8.93 delivers a head of \(250 \mathrm{ft}\) to the water. Determine the power that the pump adds to the water. The difference in elevation of the two ponds is \(200
For the standpipe system shown in Fig. P8.94, calculate the flow rate for \(H=4.0 \mathrm{ft}, D=6.77\) in., \(d=0.125\) in., and \(L=48\) in. The fluid is \(70^{\circ} \mathrm{F}\) water. Assume
Water flows through two sections of the vertical pipe shown in Fig. P8.95. The bellows connection cannot support any force in the vertical direction. The 0.4-ft-diameter pipe weights \(0.2
Water is circulated from a large tank, through a filter, and back to the tank as shown in Fig. P8.96. The power added to the water by the pump is \(200 \mathrm{ft} \cdot \mathrm{lb} / \mathrm{s}\).
A thief siphoned \(15 \mathrm{gal}\) of gasoline from a gas tank in the middle of the night. The gas tank is \(12 \mathrm{in}\). wide, \(24 \mathrm{in}\). long, and 18 in. high and was full when the
Estimate the time required for the water depth in the reservoir shown in Fig. P8. 98 to drop from a height of \(25 \mathrm{~m}\) to \(5 \mathrm{~m}\). The connections are threaded.Figure P8.98 500 m
Sheldon and Leonard come home from a long day of studying to discover that their basement is flooded with water. They have a submersible pump for such an emergency and connect the pump discharge to a
A company markets ethylene glycol antifreeze in halfgallon bottles. A machine fills and caps the bottles at a rate of 60 per minute. The \(68{ }^{\circ} \mathrm{F}\) ethylene glycol \(\left(ho=69.3
A certain process requires \(2.3 \mathrm{cfs}\) of water to be delivered at a pressure of \(30 \mathrm{psi}\). This water comes from a large-diameter supply main in which the pressure remains at \(60
Water is pumped between two large open reservoirs through \(1.5 \mathrm{~km}\) of smooth pipe. The water surfaces in the two reservoirs are at the same elevation. When the pump adds \(20
Determine the diameter of a steel pipe that is to carry 2000 \(\mathrm{gal} / \mathrm{min}\) of gasoline with a pressure drop of \(5 \mathrm{psi}\) per \(100 \mathrm{ft}\) of horizontal pipe.
Water is to be moved from a large, closed tank in which the air pressure is \(20 \mathrm{psi}\) into a large, open tank through \(2000 \mathrm{ft}\) of smooth pipe at the rate of \(3 \mathrm{ft}^{3}
A commercial steel flow channel in a heat exchanger has an equilateral triangle cross section with each side measuring \(5.0 \mathrm{in}\). and a length measuring \(96.0 \mathrm{in}\). Water at
Rainwater flows through the galvanized iron downspout shown in Fig. P8.106 at a rate of \(0.006 \mathrm{~m}^{3} / \mathrm{s}\). Determine the size of the downspout cross section if it is a rectangle
Repeat Problem 8.106 if the downspout is circular.Problem 8.106Rainwater flows through the galvanized iron downspout shown in Fig. P8.106 at a rate of \(0.006 \mathrm{~m}^{3} / \mathrm{s}\).
For a given head loss per unit length, what effect on the flowrate does doubling the pipe diameter have if the flow is(a) laminar,(b) completely turbulent?
It is necessary to deliver \(270 \mathrm{ft}^{3} / \mathrm{min}\) of water from reservoir \(A\) to reservoir \(B\), as shown in Fig. P8.109. The connecting piping consists of four fully open gate
A 10-m-long, 5.042-cm I.D. copper pipe has two fully open gate valves, a swing check valve, and a sudden enlargement to a 9.919-cm I.D. copper pipe. The \(9.919 \mathrm{~cm}\) copper pipe is \(5.0
Air, assumed incompressible, flows through the two pipes shown in Fig. P8.111. Determine the flowrate if minor losses are neglected and the friction factor in each pipe is 0.015. Determine the
Repeat Problem 8.111 if the pipes are galvanized iron and the friction factors are not known a priori.Problem 8.111Air, assumed incompressible, flows through the two pipes shown in Fig. P8.111.
Estimate the power that the human heart must impart to the blood to pump it through the two carotid arteries from the heart to the brain. List all assumptions and show all calculations.
Normal octane at \(68{ }^{\circ} \mathrm{F}\left(u=8.31 \times 10^{-6} \mathrm{ft}^{2} / \mathrm{s}\right)\) is to be delivered at a flow rate of \(3.0 \mathrm{gal} / \mathrm{min}\) through a
The flowrate between tank \(A\) and tank \(B\) shown in Fig. P8.115 is to be increased by \(30 \%\) (i.e., from \(Q\) to \(1.30 Q\) ) by the addition of a second pipe (indicated by the dotted lines)
A 250-ft-high building has a 6.065-in.-diameter steel standpipe and a \(100-\mathrm{ft}\)-long \(2 \frac{9}{16}\)-in. diameter fire hose on each floor. The nearest fireplug is \(100 \mathrm{ft}\)
With the valve closed, water flows from \(\operatorname{tank} A\) to \(\operatorname{tank} B\) as shown in Fig. P8.117. What is the flowrate into \(\operatorname{tank} B\) when the valve is opened to
Repeat Problem 8.117 if the friction factors are not known, but the pipes are steel pipes.Problem 8.117With the valve closed, water flows from \(\operatorname{tank} A\) to \(\operatorname{tank} B\)
The three water-filled tanks shown in Fig. P8.119 are connected by pipes as indicated. If minor losses are neglected, determine the flowrate in each pipe.Figure P8.119 Elevation = 20 m Elevation = 60
Five oil fields, each producing an output of \(Q\) barrels per day, are connected to the 28 -in.-diameter "mainline pipe" \((A-B-C)\) by 16-in.-diameter "lateral pipes" as shown in Fig. P8.120. The
As shown in Fig. P8.121, cold water \(\left(T=50^{\circ} \mathrm{F}\right)\) flows from the water meter to either the shower or the hot water heater. In the hot water heater it is heated to a
Water flows through the orifice meter shown in Fig. P8.122 at a rate of \(0.10 \mathrm{cfs}\). If \(d=0.1 \mathrm{ft}\), determine the value of \(h\) and the pressure difference associated with this
Water flows through the orifice meter shown in Fig P8.122 such that \(h=1.6 \mathrm{ft}\) with \(d=1.5 \mathrm{in}\). Determine the flowrate.Fig P8.122 0- 2 in. h
Water flows through the orifice meter shown in Fig. P8.122 at a rate of \(0.10 \mathrm{cfs}\). If \(h=3.8 \mathrm{ft}\), determine the value of \(d\).Fig. P8.122 0- 2 in. h
Water flows through a 40 -mm-diameter nozzle meter in a 75 - \(\mathrm{mm}\)-diameter pipe at a rate of \(0.015 \mathrm{~m}^{3} / \mathrm{s}\). Determine the pressure difference across the nozzle if
Gasoline flows through a \(35-\mathrm{mm}\)-diameter pipe at a rate of \(0.0032 \mathrm{~m}^{3} / \mathrm{s}\). Determine the pressure drop across a flow nozzle placed in the line if the nozzle
Air at \(200^{\circ} \mathrm{F}\) and 60 psia flows in a 4-in.-diameter pipe at a rate of \(0.52 \mathrm{lb} / \mathrm{s}\). Determine the pressure at the 2-in.-diameter throat of a Venturi meter
A 2.5-in.-diameter flow nozzle meter is installed in a 3.8-in.-diameter pipe that carries water at \(160{ }^{\circ} \mathrm{F}\). If the air-water manometer used to measure the pressure difference
A 0.064-m-diameter nozzle meter is installed in a 0.097-m-diameter pipe that carries water at \(60{ }^{\circ} \mathrm{C}\). If the inverted air-water U-tube manometer used to measure the pressure
A 50-mm-diameter nozzle meter is installed at the end of a 80 -mm-diameter pipe through which air flows. A manometer attached to the static pressure tap just upstream from the nozzle indicates a
Water flows through the Venturi meter shown in Fig. P8.131. The specific gravity of the manometer fluid is 1.52. Determine the flowrate.Figure P8.131 6 in. 3 in. 2 in. SG 1.52
If the fluid flowing in Problem 8.131 were air, what would the flowrate be? Would compressibility effects be important? Explain.Problem 8.131Water flows through the Venturi meter shown in Fig.
The scale reading on the rotameter shown in Fig. P8.133 (also see Fig. 8.44) is directly proportional to the volumetric flowrate. With a scale reading of 2.6 the water bubbles up approximately 3 in.
A mixing basin in a sewage filtration plant is stirred by mechanical agitation (paddlewheel) with a power input \(\dot{W}(\mathrm{ft} \cdot \mathrm{lb} / \mathrm{s})\). The degree of mixing of fluid
An equation used to evaluate vacuum filtration is\[ Q=\frac{\Delta p A^{2}}{\alpha\left(\forall R w+A R_{f}\right)} \]Where \(Q \doteq L^{3} / T\) is the filtrate volume flow rate, \(\Delta p
Verify the left-hand side of Eq. 7.2 is dimensionless using the MLT system.Eq. 7.2 D Ape PV2 = (DVD)
The Reynolds number, \(ho V D / \mu\), is a very important parameter in fluid mechanics. Verify that the Reynolds number is dimensionless, using both the FLT system and the MLT system for basic
For the flow of a thin film of a liquid with a depth \(h\) and a free surface, two important dimensionless parameters are the Froude number, \(V / \sqrt{g h}\), and the Weber number, \(ho V^{2} h /
The Mach number for a body moving through a fluid with velocity \(V\) is defined as \(V / c\), where \(c\) is the speed of sound in the fluid. This dimensionless parameter is usually considered to be
A mixing basin in a sewage filtration plant is stirred by a mechanical agitator with a power input \(\dot{W} \doteq F \cdot L / T\). Other parameters describing the performance of the mixing process
The excess pressure inside a bubble (discussed in Chapter 1) is known to be dependent on bubble radius and surface tension. After finding the pi terms, determine the variation in excess pressure if
At a sudden contraction in a pipe the diameter changes from \(D_{1}\) to \(D_{2}\). The pressure drop, \(\Delta p\), which develops across the contraction is a function of \(D_{1}\) and \(D_{2}\), as
Water sloshes back and forth in a tank as shown in Fig. P7.10. The frequency of sloshing, \(\omega\), is assumed to be a function of the acceleration of gravity, \(g\), the average depth of the
Assume that the flowrate, \(Q\), of a gas from a smokestack is a function of the density of the ambient air, \(ho_{a}\), the density of the gas, \(ho_{g}\), within the stack, the acceleration of
The pressure rise, \(\Delta p\), across a pump can be expressed as\[ \Delta p=f(D, ho, \omega, Q) \]where \(D\) is the impeller diameter, \(ho\) the fluid density, \(\omega\) the rotational speed,
A thin elastic wire is placed between rigid supports. A fluid flows past the wire, and it is desired to study the static deflection, \(\delta\), at the center of the wire due to the fluid drag.
Because of surface tension, it is possible, with care, to support an object heavier than water on the water surface as shown in Fig. P7.14. The maximum thickness, \(h\), of a square of material that
Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency \(\omega\). See Fig. P7.15. Assume that \(\omega\) is a function of the
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