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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

For a 40 cm pipe, the resistance coefficient f was found to be 0.06 when the mean velocity was 3 m/s and the kinematic viscosity was 10–5 m2/s. If the velocity were doubled, would you expect the
A pipe can be used to measure the viscosity of a fluid. A liquid flows in a 1.7-cm smooth pipe 0.52 m long with an average velocity of 8 m/s. A head loss of 5 cm is measured. Estimate the kinematic
Points A and B are 1.5 km apart along a 15-cm new steel pipe (ks = 4.6 × 10–5 m). Point B is 20 m higher than A. With a flow from A to B of 0.03 m3/s of crude oil (S = 0.82) at 10°C (μ = 10–2
Determine the head loss in 800 ft of a concrete pipe with a 6 in. diameter (ks = 0.0002 ft ) carrying 2.5 cfs of fluid. The properties of the fluid are ν = 3.33 × 10–3 ft 2/s and ρ = 1.5
Water at 20°C flows through a 2 cm ID smooth brass tube at a rate of 0.003 m3/s. What is f for this flow? Use the Swamee-Jain equation (10.39), given in §10.6. 0.25 (10.39) f = 5.74 k, log10 3.7D
Water (20°C) flows in a 35-cm cast iron pipe at a rate of 0.5 m3/s. For these conditions, determine or estimate the following:a. The Reynolds numberb. Friction factor f (use Swamee-Jain Eq. (10.39)
Fluid (μ = 10–2 N∙s/m2; ρ = 800 kg/m3) flows with a mean velocity of 500 mm/s in a 100 mm diameter smooth pipe. Answer the following questions relating to the given flow conditions.a. What is
Water (10°C) flows through a 50-cm smooth pipe at a rate of 0.05 m3/s. What is the resistance coefficient f ?
Use Fig. 10.14, Table 10.3, and Table 10.4 (in §10.6) to assess the following statements as true or false:In Figure 10.14In table 10.3In table 10.4a. If ks/D is 0.05 or larger, and the flow is
Water (70°F) flows through a nominal 4-in., schedule 40, PVC pipe at the rate of 6 cfs. What is the resistance coefficient f? Use the Swamee-Jain equation (10.39), given in §10.6. 0.25 (10.39) f =
liquid flows in a round pipeline. The mass flow rate is 9800 kg/s. The Reynolds number is 6 million. Kinematic viscosity is 1.4E-6 m2/s and SG = 0.9. Calculate the pipe diameter in meters. Choose the
Newtonian fluid flows in a round pipe. The flow is fully developed, steady, and laminar. Determine whether the following statement is true or false: The head loss in a pipe with a rusty and rough
Water is pumped through a heat exchanger consisting of tubes 8 mm in diameter and 6 m long. The velocity in each tube is 12 cm/s. The water temperature increases from 20°C at the entrance to 30°C
The velocity of oil (SG = 0.8) through the 2 in. smooth pipe is 5 ft/s. Here L = 30 ft, z1 = 2 ft, z2 = 4 ft, and the manometer deflection is 4 in. Determine the flow direction, the resistance
The velocity of oil (SG = 0.8) through the 5-cm smooth pipe is 1.2 m/s. Here L = 12 m, z1 = 1 m, z2 = 2 m, and the manometer deflection is 10 cm. Determine the flow direction, the resistance
Velocity measurements are made in a 35-cm pipe. The velocity at the center is found to be 2 m/s, and the velocity distribution is observed to be parabolic. If the pressure drop is found to be 2 kPa
What nominal size of steel pipe should be used to carry 0.2 cfs of castor oil at 90°F a distance of 0.5 mi with an allowable pressure drop of 10 psi (μ = 0.085 lbf-s/ft 2)? Assume SG = 0.85.
Glycerine (T = 20°C) flows through a funnel with D = 1.3 cm as shown. Calculate the mean velocity of the glycerine exiting the tube. Assume the only head loss is due to friction in the tube. 30 cm
In the pipe system shown, for a given discharge, the ratio of the head loss in a given length of the 1 m pipe to the head loss in the same length of the 2 m pipe is (a) 2, (b) 4, (c)
As shown, SAE-10W-30 oil is pumped through an 8 m length of 1-cm-diameter drawn tubing at a discharge of 7.85 × 10–4 m3/s. The pipe is horizontal, and the pressures at points 1 and 2 are equal.
Oil (SG = 0.94; μ = 0.048 N∙s/m2) is pumped through a horizontal 10 cm pipe. Mean velocity is 0.3 m/s. What is the pressure drop per 10 m of pipe?
Kerosene (SG = 0.80 and T = 68°F) flows from the tank shown and through the 1/4 in. diameter (ID) tube. Determine the mean velocity in the tube and the discharge. Assume the only head loss is in the
A liquid (ρ = 1000 kg/m3; μ = 10–1 N∙s/2 m2; v = 10–4 m2/s) flows uniformly with a mean velocity of 0.9 m/s in a pipe with a diameter of 175 mm. Show that the flow is laminar. Also, find the
Oil (SG = 0.97, μ = 10–2 lbf-s/ft 2) is pumped through a nominal 1 in., schedule 80 pipe at the rate of 0.005 cfs. What is the head loss per 100 ft of level pipe?
Liquid (γ = 9.6 kN/m3) is flowing in a pipe at a steady rate, but the direction of flow is unknown. Is the liquid moving upward or moving downward in the pipe? If the pipe diameter is 12 mm and the
As shown, a round tube of diameter 0.5 mm and length 750 mm is connected to plenum. A fan produces a negative gage pressure of –1.5 inch H2O in the plenum and draws air (20°C) into the
Flow of a liquid in a smooth 3 cm pipe yields a head loss of 2 m per meter of pipe length when the mean velocity is 1 m/s. Calculate f and the Reynolds number. Prove that doubling the flow rate will
Water (15°C) flows in a horizontal schedule 40 pipe that has a nominal diameter of 0.5 in. The Reynolds number is Re = 1000. Work in SI units. a. What is mass flow rate?b. What is the magnitude
A Newtonian fluid is flowing in a round conduit. The flow is laminar, steady, and fully developed. The Darcy friction factor is 16. Calculate ReD. Choose the closest answer: (a) 4.0, (b)
A fluid (μ = 10–2 N∙s/m2; ρ = 800 kg/m3) flows with a mean velocity of 4 cm/s in a 10 cm smooth pipe.a. What is the value of the Reynolds number?b. What is the magnitude of the maximum velocity
Water flows in the pipe shown, and the manometer deflects 120 cm. What is f for the pipe if V = 3 m/s? D = 5 cm Elevation = 10 m 4 m Elevation = 11 m V = 3 m/s S= 2.5
As shown, water (15°C) is flowing from a tank through a tube and then discharging to ambient. The tube has an ID of 8 mm and a length of L = 6 m, and the resistance coefficient is f = 0.015. The
Water (15°C) flows through a garden hose (ID = 25 mm) with a mean velocity of 1.5 m/s. Find the pressure drop for a section of hose that is 20 meters long and situated horizontally. Assume that f =
In Case A, water flows through an 8-inch schedule 40 pipe with a discharge of 75 liters per second. In Case B, the schedule is changed to 80. The mean velocity is the same in both cases. Calculate
The head loss from section 1 to 2 is 1.0 m. The Darcy friction factor is 0.01. D = 1.0 m. L = 100 m. The flow is steady and fully developed. Calculate the mean velocity in m/s. Choose the closest
A Newtonian fluid is flowing in a round conduit. The flow is laminar, steady, and fully developed. Determine whether the following statement is true or false: The head loss will vary linearly with
Air (ρ = 1.4 kg/m3) flows in a straight round tube. The mean velocity is 22 m/s. The friction factor is 0.03. Flow is fully developed. Calculate the wall shear stress in units of Pa. Choose the
As shown, air (20°C) is flowing from a large tank, through a horizontal pipe, and then discharging to ambient. The pipe length is L = 50 m, and the pipe is schedule 40 PVC with a nominal diameter of
For each case that follows, apply the Darcy-Weisbach equation from Eq. (10.12) in §10.3 to calculate the head loss in a pipe. Apply the grid method to carry and cancel units. a. Water flows at
Using §10.3 and other resources, answer the following questions. Strive for depth, clarity, and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness of
A newly designed dam is to be modeled in the laboratory. The prime objective of the general model study is to determine the adequacy of the spillway design and to observe the water velocities,
A model of a spillway is to be built at 1/80 scale. If the prototype has a discharge of 800 m3/s, what must be the water discharge in the model to ensure dynamic similarity? The total force on part
A tidal estuary is to be modeled at 1/600 scale. In the actual estuary, the maximum water velocity is expected to be 3.6 m/s, and the tidal period is approximately 12.5 h. What corresponding velocity
A solid particle falls through a viscous fluid. The falling velocity, V, is believed to be a function of the fluid density, ρf, the particle density, ρp, the fluid viscosity, μ, the particle
Oil (v = 10–4 m2/s; SG = 0.9) flows past a plate in a tangential direction so that a boundary layer develops. If the velocity of approach is 0.3 m/s, what is the oil velocity 0.2 m downstream
Oil (v = 10–4 m2/s) flows tangentially past a thin plate. If the free-stream velocity is 1 m/s, what is the velocity 5 m downstream from the leading edge and 15 mm away from the plate?
A liquid (ρ = 1000 kg/m3; μ = 2 × 10–2 N∙s/m2; v = 2 × 10–5 m2/s) flows tangentially past a flat plate. If the approach velocity is 1 m/s, what is the liquid velocity 2 m downstream from
Which of the following are features of a laminar boundary layer? (Select all that are correct.)a. Flow is smooth.b. The boundary layer thickness increases in the downstream direction.c. A decreasing
a. Explain in your own words what is meant by “boundary layer.” b. Define “boundary layer thickness.”
An engineer is designing a very thin, horizontal channel for cooling electronic circuitry. The channel is 3 cm wide and 6 cm long. The distance between the plates is 0.4 mm. The average fluid
One type of bearing that can be used to support very large structures is shown. Here, fluid under pressure is forced from the bearing midpoint (slot A) to the exterior zone B. Thus, a pressure
Two parallel plates are spaced 0.09 in. apart, and motor oil (SAE-30) with a temperature of 100°F flows at a rate of 0.009 cfs per foot of width between the plates. What is the pressure gradient in
Two vertical parallel plates are spaced 0.012 ft apart. If the pressure decreases at a rate of 100 psf/ft in the vertical z direction in the fluid between the plates, what is the maximum fluid
Glycerine at 20°C flows downward between two vertical parallel plates separated by a distance of 0.6 cm. The ends are open, so there is no pressure gradient. Calculate the discharge per unit width,
A viscous fluid fills the space between these two plates, and the pressures at A and B are 150 psf and 100 psf, respectively. The fluid is not accelerating. If the specific weight of the fluid is 100
Two horizontal parallel plates are spaced 0.015 ft apart. The pressure decreases at a rate of 25 psf/ft in the horizontal x direction in the fluid between the plates. What is the maximum fluid
The velocity distribution that is shown represents laminar flow. Indicate which of the following statements are true:a. The velocity gradient at the boundary is infinitely large.b. The maximum shear
Under certain conditions (pressure decreasing in the x direction, the upper plate fixed, and the lower plate moving to the right in the positive x direction), the laminar velocity distribution will
Uniform, steady flow is occurring between horizontal parallel plates as shown.a. In a few words, tell what other condition must be present to cause the odd velocity distribution.b. Where is the
Uniform, steady flow is occurring between horizontal parallel plates as shown.a. The flow is Poiseuille; therefore, what is causing the fluid to move?b. Where is the maximum velocity located?c. Where
Often in liquid lubrication applications, there is a heat generated that is transferred across the lubricating layer. Consider a Couette flow with one wall at a higher temperature than the other. The
A bearing uses SAE-30 oil with a viscosity of 0.1 N∙s/m2. The bearing is 30 mm in diameter, and the gap between the shaft and the casing is 1 mm. The bearing has a length of 1 cm. The shaft turns
A plate 2 mm thick and 3 m wide (normal to the page) is pulled between the walls shown in the figure at a speed of 0.5 m/s. Note that the space that is not occupied by the plate is filled with
A circular horizontal disk with a 27 cm diameter has a clearance of 3.0 mm from a horizontal plate. What torque is required to rotate the disk about its center at an angular speed of 31 rad/s when
The upper plate shown is moving to the right with a velocity V, and the lower plate is free to move laterally under the action of the viscous forces applied to it. For steady-state conditions, derive
A flat plate is pulled to the right at a speed of 30 cm/s. Oil with a viscosity of 4 N∙s/m2 fills the space between the plate and the solid boundary. The plate is 1 m long (L = 1 m) by 30 cm wide,
Information is needed about the thickness of oil necessary to lubricate metal parts sliding down an inclined plane. A square metal part with 0.9 m sides that weighs 20 N is required to slide down the
A board 1 m by 1 m that weighs 55 N slides down an inclined ramp with a velocity of 40 cm/s. The board is separated from the ramp by a layer of oil 0.6 mm thick. Neglecting the edge effects of the
A board 3 ft by 3 ft that weighs 32 lbf slides down an inclined ramp with a velocity of 0.6 ft /s. The board is separated from the ramp by a layer of oil 0.02 in. thick. Calculate the dynamic
The cube shown weighing 110 N and measuring 39 cm on a side is allowed to slide down an inclined surface on which there is a film of oil having a viscosity of 10–2 N∙s/m2. What is the velocity of
The velocity distribution in a Couette flow is linear if the viscosity is constant. If the moving plate is heated and the viscosity of the liquid is decreased near the hot plate, how will the
A model of a high-rise office building at 1/550 scale is tested in a wind tunnel to estimate the pressures and forces on the full-scale structure. The wind-tunnel air speed is 20 m/s at 20°C and
The wave resistance of a model of a ship at 1/25 scale is 2 lbf at a model speed of 5 ft /s. What are the corresponding velocity and wave resistance of the prototype?
The maximum wave force on a 1/36 model seawall was found to be 80 N. For a corresponding wave in the full-scale wall, what full-scale force would you expect? Assume freshwater is used in the model
A 1/25-scale model of a spillway is tested. The discharge in the model is 0.1 m3/s. To what prototype discharge does this correspond? If it takes 1 min for a particle to float from one point to
Flow around a bridge pier is studied using a model at 1/12 scale. When the velocity in the model is 0.9 m/s, the standing wave at the pier nose is observed to be 2.5 cm in height. What are the
A 1/40-scale model of a spillway is tested in a laboratory. If the model velocity and discharge are 3.2 ft/s and 3.53 cfs, respectively, what are the corresponding values for the prototype?
If the scale ratio between a model spillway and its prototype is 1/36, what velocity and discharge ratio will prevail between model and prototype? If the prototype discharge is 3000 m3/s, what is the
A seaplane model is built at a one-sixth scale. To simulate takeoff conditions at 117 km/h, what should be the corresponding model speed to achieve Froude-number scaling?
To study flow over a spillway in a new dam, a 1/20-scale model is constructed. The maximum design flow rate in the actual spillway will be 150 m3/s. Calculate the corresponding flow rate in the
A hydraulic model, 1/20 scale, is built to simulate the flow conditions of a spillway of a dam. For a particular run, the waves downstream were observed to be 8 cm high. How high would be similar
Determine the relationship between the kinematic viscosity ratio vm/vP and the scale ratio if both the Reynolds-number and the Froude number criteria are to be satisfied in a given model test.
Water is sprayed from a nozzle at 20 m/s into air at atmospheric pressure and 20°C. Estimate the size of the droplets produced if the Weber number for breakup is 6.0 based on the droplet diameter.
Experimental studies have shown that the condition for breakup of a droplet in a gas stream is We/Re1/2 = 0.5 where Re is the Reynolds number and We is the Weber number based on the droplet diameter.
A model hydrofoil is tested in a water tunnel. For a given angle of attack, the lift of the hydrofoil is measured to be 25 kN when the water velocity is 15 m/s in the tunnel. If the prototype
The moment acting on a submarine rudder is studied by a 1/40-scale model. If the test is made in a water tunnel and if the moment measured on the model is 2 N∙m when the freshwater speed in the
A 60 cm valve is designed for control of flow in a petroleum pipeline. A one-third-scale model of the full-size valve is to be tested with water in the laboratory. If the prototype flow rate is to be
An experiment is being designed to measure aerodynamic forces on a building. The model is a 1/500-scale replica of the prototype. The wind velocity on the prototype is 47 ft/s, and the density is
The “noisemaker” B is towed behind the mine-sweeper A to set off enemy acoustic mines such as that shown at C. The drag force of the “noisemaker” is to be studied in a water tunnel at a
A flow meter to be used in a 40 cm pipeline carrying oil (v = 10–5 m2/s, ρ = 860 kg/m3) is to be calibrated by means of a model (1/12 scale) carrying water (T = 20°C and standard atmospheric
A drying tower at an industrial site is 10 m in diameter. The air inside the tower has a kinematic viscosity of 4 × 10–5 m2/s and enters at 18 m/s. A 1/20-scale model of this tower is fabricated
Colonization of the moon will require an improved understanding of fluid flow under reduced gravitational forces. The gravitational force on the moon is one-fifth that on the surface of the earth. An
A student is competing in a contest to design a radio controlled blimp. The drag force acting on the blimp depends on the Reynolds number, Re = (ρVD)/μ, where V is the speed of the blimp, D is the
A smooth pipe designed to carry crude oil (D = 60 in., ρ = 1.75 slugs/ft3, and μ = 4 × 10–4 lbf-s/ft 2) is to be modeled with a smooth pipe 4 in. in diameter carrying water (T = 60°F). If the
Flow in a given pipe is to be tested with air and then with water. Assume that the velocities (VA and VW) are such that the flow with air is dynamically similar to the flow with water. Then for this
The Boeing 787-3 Dreamliner has a wing span of 52 m. It flies at a cruise Mach number of 0.85, which corresponds to a velocity of 945 km/hr at an altitude of 10,000 m. You are going to estimate the
An airplane travels in air (p = 100 kPa, T = 10°C) at 150 m/s. If a one-eighth-scale model of the plane is tested in a wind tunnel at 25°C, what must the density of the air in the tunnel be so that
An engineer needs a value of lift force for an airplane that has a coefficient of lift (CL) of 0.4. The π-group is defined asWhere FL is the lift force, ρ is the density of ambient air, V is the
A spherical balloon that is to be used in air at 60°F and atmospheric pressure is tested by towing a 1/12-scale model in a lake. The model is 1.4 ft in diameter, and a drag of 37 lbf is measured
A one-eighth-scale model of an experimental deep sea submersible that will operate at great depths is to be tested to determine its drag characteristic by towing it behind a submarine. For true

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