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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

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}
Obtain a photograph/image of a situation in which the viscosity of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved.
For flowing water, what is the magnitude of the velocity gradient needed to produce a shear stress of \(1.0 \mathrm{~N} / \mathrm{m}^{2}\) ?
The viscosity of a soft drink was determined by using a capillary tube viscometer. For this device the kinematic viscosity, \(u\), is directly proportional to the time, \(t\), that it takes for a
The viscosity of a certain fluid is \(5 \times 10^{-4}\) poise. Determine its viscosity in both SI and BG units.
The kinematic viscosity and specific gravity of a liquid are \(3.5 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\) and 0.79, respectively. What is the dynamic viscosity of the liquid in SI units?
A liquid has a specific weight of \(59 \mathrm{lb} / \mathrm{ft}^{3}\) and a dynamic viscosity of \(2.75 \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\). Determine its kinematic viscosity.
The kinematic viscosity of oxygen at \(20^{\circ} \mathrm{C}\) and a pressure of \(150 \mathrm{kPa}\) (abs) is 0.104 stokes. Determine the dynamic viscosity of oxygen at this temperature and pressure.
Fluids for which the shearing stress, \(\tau\), is not linearly related to the rate of shearing strain, \(\dot{\gamma}\), are designated as nonNewtonian fluids. Such fluids are commonplace and can
Water flows near a flat surface and some measurements of the water velocity, \(u\), parallel to the surface, at different heights, \(y\), above the surface are obtained. At the surface \(y=0\). After
For air at standard atmospheric pressure the values of the constants that appear in the Sutherland equation are \(C=1.458 \times 10^{-6} \mathrm{~kg} /\left(\mathrm{m} \cdot \mathrm{s} \cdot
Use the values of viscosity of air given in Table B. 4 at temperatures of \(0,20,40,60,80\), and \(100{ }^{\circ} \mathrm{C}\) to determine the constants \(C\) and \(S\) which appear in the
The viscosity of a fluid plays a very important role in determining how a fluid flows. (See Video V1.3.) The value of the viscosity depends not only on the specific fluid but also on the fluid
Use the value of the viscosity of water given in Table B. 2 at temperatures of \(0,20,40,60,80\), and \(100^{\circ} \mathrm{C}\) to determine the constants \(D\) and \(B\) which appear in Andrade's
For a certain liquid \(\mu=7.1 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\) at \(40^{\circ} \mathrm{F}\) and \(\mu=\) \(1.9 \times 10^{-5} \mathrm{lb} \cdot \mathrm{s} /
For a parallel plate arrangement of the type shown in Fig. 1.5 it is found that when the distance between plates is \(2 \mathrm{~mm}\), a shearing stress of \(150 \mathrm{~Pa}\) develops at the upper
Two flat plates are oriented parallel above a fixed lower plate as shown in Fig. P1.73. The top plate, located a distance \(b\) above the fixed plate, is pulled along with speed \(V\). The other thin
Three large plates are separated by thin layers of ethylene glycol and water, as shown in Fig. P1.74. The top plate moves to the right at \(2 \mathrm{~m} / \mathrm{s}\). At what speed and in what
The sled shown in Fig. P1.76 slides along on a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to \(1.2 \mathrm{lb}\)
A 25-mm-diameter shaft is pulled through a cylindrical bearing as shown in Fig. P1.77. The lubricant that fills the \(0.3-\mathrm{mm}\) gap between the shaft and bearing is an oil having a kinematic
A hydraulic lift in a service station has a \(32.50-\mathrm{cm}\)-diameter ram that slides in a \(32.52-\mathrm{cm}\)-diameter cylinder. The annular space is filled with SAE 10 oil at \(20^{\circ}
A 10-kg block slides down a smooth inclined surface as shown in Fig. P1.80. Determine the terminal velocity of the block if the \(0.1-\mathrm{mm}\) gap between the block and the surface contains SAE
A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. P1.81. Determine the magnitude and direction of the shearing stress that the water exerts on the fixed
Oil (absolute viscosity \(=0.0003 \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\), density \(=50\) \(\mathrm{lbm} / \mathrm{ft}^{3}\) ) flows in the boundary layer, as shown in Fig. P1.82. The plate
Standard air flows past a flat surface, and velocity measurements near the surface indicate the following distribution:The coordinate \(y\) is measured normal to the surface and \(u\) is the velocity
A new computer drive is proposed to have a disc, as shown in Fig. P1.84. The disc is to rotate at \(10,000 \mathrm{rpm}\), and the reader head is to be positioned 0.0005 in. above the surface of the
The space between two 6-in.-long concentric cylinders is filled with glycerin (viscosity \(=8.5 \times 10^{-3} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\) ). The inner cylinder has a radius of 3
A pivot bearing used on the shaft of an electrical instrument is shown in Fig. P1.86. An oil with a viscosity of \(\mu=0.010 \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\) fills the \(0.001-\) in.
The viscosity of liquids can be measured through the use of a rotating cylinder viscometer of the type illustrated in Fig. P1.87. In this device the outer cylinder is fixed and the inner cylinder is
The concentric cylinder viscometer shown in Fig. P1.88 has a cylinder height of \(10.0 \mathrm{~cm}\), a cylinder radius of \(3.0 \mathrm{~cm}\), and a uniform gap between the cylinder and the
A 12-in.-diameter circular plate is placed over a fixed bottom plate with a -in. gap between the two plates filled with glycerin as shown in Fig. P1.89. Determine the torque required to rotate the
Vehicle shock absorbers damp out oscillations caused by road roughness. Describe how a temperature change may affect the operation of a shock absorber.
Some measurements on a blood sample at \(37^{\circ} \mathrm{C}\left(98.6^{\circ} \mathrm{F}\right)\) indicate a shearing stress of \(0.52 \mathrm{~N} / \mathrm{m}^{2}\) for a corresponding rate of
Obtain a photograph/image of a situation in which the compressibility of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved.
A sound wave is observed to travel through a liquid with a speed of \(1500 \mathrm{~m} / \mathrm{s}\). The specific gravity of the liquid is 1.5. Determine the bulk modulus for this fluid.
A rigid-walled cubical container is completely filled with water at \(40^{\circ} \mathrm{F}\) and sealed. The water is then heated to \(100^{\circ} \mathrm{F}\). Determine the pressure that develops
Estimate the increase in pressure (in psi) required to decrease a unit volume of mercury by \(0.1 \%\).
A \(1-\mathrm{m}^{3}\) volume of water is contained in a rigid container. Estimate the change in the volume of the water when a piston applies a pressure of \(35 \mathrm{MPa}\).
Determine the speed of sound at \(20^{\circ} \mathrm{C}\) in (a) air, (b) helium, and (c) natural gas (methane). Express your answer in \(\mathrm{m} / \mathrm{s}\).
Air is enclosed by a rigid cylinder containing a piston. A pressure gage attached to the cylinder indicates an initial reading of 25 psi. Determine the reading on the gage when the piston has
Carbon dioxide at \(30^{\circ} \mathrm{C}\) and \(300 \mathrm{kPa}\) absolute pressure expands isothermally to an absolute pressure of \(165 \mathrm{kPa}\). Determine the final density of the gas.
Natural gas at \(70{ }^{\circ} \mathrm{F}\) and standard atmospheric pressure of 14.7 psi (abs) is compressed isentropically to a new absolute pressure of 70 psi. Determine the final density and
A compressed air tank in a service station has a volume of \(10 \mathrm{ft}^{3}\). It contains air at \(70{ }^{\circ} \mathrm{F}\) and 150 psia. How many tubeless tires can it fill to \(44.7
Oxygen at \(30{ }^{\circ} \mathrm{C}\) and \(300 \mathrm{kPa}\) absolute pressure expands isothermally to an absolute pressure of \(120 \mathrm{kPa}\). Determine the final density of the gas.
Compare the isentropic bulk modulus of air at \(101 \mathrm{kPa}\) (abs) with that of water at the same pressure.
Often the assumption is made that the flow of a certain fluid can be considered as incompressible flow if the density of the fluid changes by less than \(2 \%\). If air is flowing through a tube such
An important dimensionless parameter concerned with very high-speed flow is the Mach number, defined as \(V / c\), where \(V\) is the speed of the object such as an airplane or projectile, and \(c\)
The "power available in the wind" of velocity \(V\) through an area \(A\) is\[ \dot{W}=\frac{1}{2} ho A V^{3} \]where \(ho\) is the air density \(\left(0.075 \mathrm{lbm} / \mathrm{ft}^{3}\right)\).
Air enters the converging nozzle at \(T_{1}=70^{\circ} \mathrm{F}\) and \(V_{1}=50 \mathrm{ft} / \mathrm{s}\). At the exit of the nozzle, \(V_{2}\) is given by\[ V_{2}=\sqrt{V_{1}^{2}+2
The Wide World of Fluids article titled "This water jet is a blast,". By what percent is the volume of water decreased if its pressure is increased to an equivalent to 3000 atmospheres \((44,100
During a mountain climbing trip it is observed that the water used to cook a meal boils at \(90^{\circ} \mathrm{C}\) rather than the standard \(100{ }^{\circ} \mathrm{C}\) at sea level. At what
When a fluid flows through a sharp bend, low pressures may develop in localized regions of the bend. Estimate the minimum absolute pressure (in psi) that can develop without causing cavitation if the
A partially filled closed tank contains ethyl alcohol at \(68^{\circ} \mathrm{F}\). If the air above the alcohol is evacuated, what is the minimum absolute pressure that develops in the evacuated
Estimate the minimum absolute pressure (in pascals) that can be developed at the inlet of a pump to avoid cavitation if the fluid is carbon tetrachloride at \(20^{\circ} \mathrm{C}\).
When water at \(70{ }^{\circ} \mathrm{C}\) flows through a converging section of pipe, the pressure decreases in the direction of flow. Estimate the minimum absolute pressure that can develop without
At what atmospheric pressure will water boil at \(35^{\circ} \mathrm{C}\) ? Express your answer in both SI and BG units.
Obtain a photograph/image of a situation in which the surface tension of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved.
When a 2-mm-diameter tube is inserted into a liquid in an open tank, the liquid is observed to rise \(10 \mathrm{~mm}\) above the free surface of the liquid (see Video V1.10). The contact angle
A soda straw with an inside diameter of 0.125 in. is inserted into a pan of water at \(60^{\circ} \mathrm{F}\). The water in the straw rises to a height of \(0.150 \mathrm{in}\). above the water
Small droplets of carbon tetrachloride at \(68^{\circ} \mathrm{F}\) are formed with a spray nozzle. If the average diameter of the droplets is \(200 \mu \mathrm{m}\), what is the difference in
A 12-mm-diameter jet of water discharges vertically into the atmosphere. Due to surface tension the pressure inside the jet will be slightly higher than the surrounding atmospheric pressure.
A method used to determine the surface tension of a liquid is to determine the force necessary to raise a wire ring through the air-liquid interface. What is the value of the surface tension if a
Calculate the pressure difference between the inside and outside of a spherical water droplet having a diameter of \(\frac{1}{32} \mathrm{in}\). and a temperature of \(50^{\circ} \mathrm{F}\).
As shown in Video V1.9, surface tension forces can be strong enough to allow a double-edge steel razor blade to "float" on water, but a single-edge blade will sink. Assume that the surface tension
Explain how sweat soldering of copper pipe works from a fluid mechanics viewpoint.
Under the right conditions, it is possible, due to surface tension, to have metal objects float on water. Consider placing a short length of a small diameter steel \((\gamma=490\) \(\left.\mathrm{lb}
An open, clean glass tube \(\left(\theta=0^{\circ}\right)\) is inserted vertically into a pan of water. What tube diameter is needed if the water level in the tube is to rise one tube diameter (due
Determine the height that water at \(60^{\circ} \mathrm{F}\) will rise due to capillary action in a clean, \(\frac{1}{4}\)-in.-diameter tube. What will be the height if the diameter is reduced to
Two vertical, parallel, clean glass plates are spaced a distance of \(2 \mathrm{~mm}\) apart. If the plates are placed in water, how high will the water rise between the plates due to capillary
A torpedo-like device is being designed to travel just below the water surface. Which dimensionless numbers in Section 8.4 would be significant in this problem? Give a rationale for your answer.
What is f for the flow of water at 10°C through a 30-cm cast iron pipe with a mean velocity of 24 m/s?
Briefly explain each of the following ideas.a. Post processorb. Verificationc. Validation
Briefly explain each of the following ideas.a. DNSb. k-epsilon methodc. LES
Briefly explain each of the following ideas.a. Gridb. Time stepc. Solution time for a CFD program versus the accuracyd. Boundary conditione. Initial condition
Using the Internet, find one example of a publicly available CFD program (either a commercial or noncommercial code) and describe the code so that others can understand it. Address the following
Would you prefer to write your own CFD programs, or would you prefer to use codes that have been written by others? Discuss the advantages and disadvantages of each approach.
If someone asked you why CFD codes are useful for engineers, how would you answer? List your top three reasons in priority order.
Stress, as introduced in the derivation of the Navier-Stokes equation, is a second-order tensor. Using the Internet, find some articles on tensors and answer the following questions:a. Why do people
For the propeller and conditions described in Problem 14.10, determine the thrust and the power input. Assume ρ = 1.2 kg/m3.Data from Problem 14.10A propeller 2 m in diameter, like the one for which
A propeller 8 ft in diameter, like the one for which characteristics are given in Fig. 14.3, is to be used on a swamp boat and is to operate at maximum efficiency when cruising. If the cruising speed
Water at 50°F is piped from a reservoir to a channel like that shown. The pipe from the reservoir to the channel is a 4 in. steel pipe 100 ft in total length. There are two 90° bends, r/D = 1, in
Consider the rectangular weir described in Prob. 13.50. When the head is doubled, the discharge is (a) Doubled, (b) Less than doubled(c) More than doubled.Data from Prob. 13.50A 3 m long
A 3 m long rectangular weir is to be constructed in a 3 m wide rectangular channel, as shown (a). The maximum flow in the channel will be 4 m3/s. What should be the height P of the weir to yield a
A 1 ft high rectangular weir (weir 1) is installed in a 2 ft wide rectangular channel, and the head on the weir is observed for a discharge of 10 cfs. Then the 1 ft weir is replaced by a 2 ft high
Water flows over two rectangular weirs. Weir A is 5 ft long in a channel 10 ft wide; weir B is 5 ft long in a channel 5 ft wide. Both weirs are 2 ft high. If the head on both weirs is 1.00 ft , then
The head on a 60° triangular weir is 25 cm. What is the discharge over the weir in cubic meters per second?
Water flows over a rectangular weir that is 3 m wide and 35 cm high. If the head on the weir is 15 cm, what is the discharge in cubic meters per second?
On the Internet, locate technically reliable resources about weirs to answer the following questions. a. What are five important considerations for using weirs?b. What variables influence flow
Ultrasonic flowmeters are used to measure velocity in systems where it is important to not disrupt the flow, such as for blood velocity. One mode of operation of ultrasonic flowmeters is to measure
A rotameter is used to measure the flow rate of a gas with a density of 1.0 kg/m3. The scale on the rotameter indicates 5 liters/s. However, the rotameter is calibrated for a gas with a density of
A rotameter operates by aerodynamic suspension of a weight in a tapered tube. The scale on the side of the rotameter is calibrated in scfm of air—that is, cubic feet per minute at standard
A vortex flowmeter is used to measure the discharge in a duct 5 cm in diameter. The diameter of the shedding element is 1 cm. The Strouhal number based on the shedding frequency from one side of the
What is the head loss in terms of V0 2/2g for the flow nozzle shown? Vo D 3
Water flows through an annular venturi consisting of a body of revolution mounted inside a pipe. The pressure is measured at the minimum area and upstream of the body. The pipe is 5 cm in diameter,
A flow nozzle has a throat diameter of 2 cm and a beta ratio (d/D) of 0.5. Water flows through the nozzle, creating a pressure difference across the nozzle of 8 kPa. The viscosity of the water is
The differential-pressure gage on the venturi meter reads 40 kPa, d = 20 cm, D = 40 cm, and h = 75 cm. What is the discharge of gasoline (SG = 0.69; μ = 3 × 10−4 N∙s/m2) in the system? D - Ap h
The differential-pressure gage on the venturi meter shown reads 5.4 psi, h = 25 in., d = 7 in., and D = 12 in. What is the discharge of water in the system? Assume T = 50°F.
The pressure differential across this venturi meter is 92 kPa. What is the discharge of water (T = 20°C) through it? The value of flow coefficient you calculate should be K = 1.02. Ap d= 1.00 m D =
When no flow occurs through the venturi meter, the indicator on the differential-pressure gage is straight up and indicates a Δp of zero. When 5 cfs of water flows to the right, the

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