Questions and Answers of Engineering Fluid Mechanics

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
A large venturi meter is calibrated by means of a onetenth-scale model using the prototype liquid. What is the discharge ratio Qm/Qp for dynamic similarity? If a pressure difference of 400 kPa is
Oil with a kinematic viscosity of 4 × 10–6 m2/s flows through a smooth pipe 15 cm in diameter at 3 m/s. What velocity should water have at 20°C in a smooth pipe 5 cm in diameter to be dynamically
Water with a kinematic viscosity of 10–6 m2/s flows through a 4 cm pipe. What would the velocity of water have to be for the water flow to be dynamically similar to oil (v = 10–5 m2/s) flowing
In a study of the power required to overcome drag, an engineer is using a π-group given byWhere P is the power lost, ρ is the fluid density, A is area, and V is the fluid velocity. In laboratory
A wind tunnel operates by drawing air through a contraction, passing this air through a test section, and then exhausting the air using a large axial fan. Experimental data are recorded in the test
High-speed passenger trains are streamlined to reduce shear force. Th e cross section of a passenger car of one such train is shown. For a train 81 m long, estimate the shear force (a) for a speed of
A motor boat pulls a long, smooth, water-soaked log (0.5 m in diameter and 40 m long) at a speed of 3 m/s. Assuming total submergence, estimate the force required to overcome the shear force of the
A model is being developed for the entrance region between two flat plates. As shown in the figure, it is assumed that the region is approximated by a turbulent boundary layer originating at the
An engineer is designing a horizontal, rectangular conduit that will be part of a system that allows fish to bypass a dam. Inside the conduit, a flow of water at 40°F will be divided into two
A flat plate is oriented parallel to a 45 m/s airflow at 20°C and atmospheric pressure. The plate is L = 1 m in the flow direction and 0.5 m wide. On one side of the plate, the boundary layer is
A model airplane descends in a vertical dive through air at standard conditions (1 atmosphere and 20°C). Th e majority of the drag is due to skin friction on the wing (like that on a flat plate).
A turbulent boundary layer develops from the leading edge of a flat plate with water at 20°C flowing tangentially past the plate with a free-stream velocity of 7.7 m/s. Determine the drag force
The plate shown in the figure is weighted at the bottom so it will fall stably and steadily in a liquid. The weight of the plate in air is 23.5 N, and the plate has a volume of 0.002 m3. Estimate the
A turbulent boundary layer exists in the flow of water at 20°C over a flat plate. The local shear stress measured at the surface of the plate is 0.4 N/m2. What is the velocity at a point 0.3 cm from
An element for sensing local shear stress is positioned in a flat plate 1 meter from the leading edge. The element simply consists of a small plate, 1 cm × 1 cm, mounted flush with the wall, and the
A thin plastic panel (3 mm thick) is lowered from a ship to a construction site on the ocean floor. Th e plastic panel weighs 300 N in air and is lowered at a rate of 3 m/s. Assuming that the panel
Calculate the power required to pull the sign shown if it is towed at 48 m/s and if it is assumed that the sign has the same drag force as an equivalent flat plate. Assume standard atmospheric
For the hypothetical boundary layer on the flat plate shown, what is the shear stress on the plate at the downstream end (point A)? Here ρ = 1.2 kg/m3 and μ = 3.0 × 10–5 N∙s/m2. Free stream
What is the ratio of the drag force of a plate 30 m long and 5 m wide to that of a plate 10 m long and 5 m wide if both plates are towed lengthwise through water (T = 20°C) at 10 m/s?
An airplane wing of 2 m chord length (leading edge to trailing edge distance) and 11 m span flies at 200 km/hr in air at 30°C. Assume that the drag force of the wing surfaces is like that of a flat
Assume that a turbulent gas boundary layer was adjacent to a cool wall and the viscosity in the wall region was reduced. How may this affect the features of the boundary layer? Give some rationale
A flat plate 1.5 m long and 1.0 m wide is towed in water at 20°C in the direction of its length at a speed of 15 cm/s. Determine the resistance of the plate and the boundary layer thickness at its
A thin plate 0.7 m long and 1.5 m wide is submerged and held stationary in a stream of water (T = 10°C) that has a velocity of 1.5 m/s. What is the thickness of the boundary layer on the plate for
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 with total length of 4 m (parallel to the flow direction), a velocity of 1 m/s,
Oil (μ = 10–2 N∙s/m2; ρ = 900 kg/m3) flows past a plate in a tangential direction so that a boundary layer develops. If the velocity of approach is 4 m/s, then at a section 30 cm downstream of
A ship 600 ft long steams at a rate of 25 ft/s through still freshwater (T = 50°F). If the submerged area of the ship is 50,000 ft 2, what is the skin friction drag of this ship?
A compressor draws 0.4 m3/s of ambient air (20°C) in from the outside through a round duct that is 10 m long and 175 mm in diameter. Determine the entrance length and establish whether the flow is
Classify each of the following features into one of two categories: laminar boundary layer (L), or turbulent boundary layer (T).a. The flow occurs in smooth layers.b. The boundary layer contains
A model airplane has a wing span of 6 ft and a chord (leading edge–trailing edge distance) of 4.5 in. The model flies in air at 60°F and atmospheric pressure. The wing can be regarded as a flat
What is the ratio of the boundary layer thickness on a smooth, flat plate to the distance from the leading edge just before transition to turbulent flow?
A thin plate 6 ft long and 3 ft wide is submerged and held stationary in a stream of water (T = 60°F) that has a velocity of 17 ft/s. What is the thickness of the boundary layer on the plate for Rex
Assume the wall adjacent to a liquid laminar boundary is heated and the viscosity of the fluid is lower near the wall and increases the free-stream value at the edge of the boundary layer. How would
A river barge has the dimensions shown. It draws 2ft of water when empty. Estimate the skin friction drag of the barge when it is being towed at a speed of 10ft/s through still freshwater at 60°F. 2
A supertanker has length, breadth, and draught (fully loaded) dimensions of 325 m, 48 m, and 19 m, respectively. In open seas, the tanker normally operates at a speed of 18 kt (1 kt = 0.515 m/s). For
A hydroplane 3 m long skims across a very calm lake (T = 20°C) at a speed of 15 m/s. For this condition, what will be the minimum shear stress along the smooth bottom?
Estimate the power required to overcome the shear force of a water skier if he or she is towed at 30 mph and each skin is 4 ft by 6 in. Assume the water temperature is 60°F.
If the wetted area of an 80 m ship is 1500 m2, approximately how great is the skin friction drag when the ship is traveling at a speed of 15 m/s? What is the thickness of the boundary layer at the
Kerosene (20°C) flows at a rate of 0.04 m3/s in a 25 cm diameter pipe. Would you expect the flow to be laminar or turbulent? Calculate the entrance length.
For each item ahead, which π-group (Re, We, M, or Fr) would best match the given description?a. (kinetic force)/(surface-tension force)b. (kinetic force)/(viscous force)c. (kinetic
One of the shortcomings of mounting a model of an automobile in a wind tunnel and measuring drag is that the effect of the road is not included. Give some thought as to your impressions of what the
Many automobile companies advertise products with low drag for improved performance. Research the technical literature on the Internet regarding wind-tunnel testing of automobiles, and summarize your
The drag on a submarine moving below the free surface is to be determined by a test on a 1/19-scale model in a water tunnel. Th e velocity of the prototype in seawater (ρ = 1015 kg/m3, v = 1.4 ×
What is meant by geometric similitude?
The hydrodynamic drag on a sailboat is very important to the performance of the craft , especially in competitive races such as the America’s Cup. Investigate on the Internet or other sources the
One of the largest wind tunnels in the United States is the NASA Ames Research Center in Moff at Field, California. Look up information on this facility (size, test section velocity, etc.) and
The Womersley number (α) is a π-group given by the ratio of [pulsatile transient force]/[viscous force]. Biomedical engineers have applied this to flow in blood vessels. The Womersley number is
Using the Internet, read about the Womersley number (α) and answer the following questions.a. Is α dimensionless? How do you know? Show that all the units in fact cancel out.b. Like other
Drag tests show that the drag of a square plate placed normal to the free-stream velocity is a function of the velocity V, the density ρ, the plate dimensions B, the viscosity μ, the free-stream
The discharge of a centrifugal pump is a function of the rotational speed of the pump, N, the diameter of the impeller, D, the head across the pump, hp, the viscosity of the fluid, μ, the density of
The rise velocity Vb of a bubble with diameter D in a liquid of density ρl and viscosity μ depends on the acceleration due to gravity, g, and the density difference between the bubble and the
Flow situations in biofluid mechanics involve the flow through tubes that change in size with time (such as blood vessels) or are supplied by an oscillatory source (such as a pulsing gland). The
By dimensional analysis, determine the π-groups for the change in pressure that occurs when water or oil flows through a horizontal pipe with an abrupt contraction as shown. Express your answer in
An engineer is using an experiment to characterize the power P consumed by a fan (see photo) to be used in an electronics cooling application. Power depends on four variables: P = f(ρ, D, Q, n),
A general study is to be made of the height of rise of liquid in a capillary tube as a function of time after the start of a test. Other significant variables include surface tension, mass density,
The force on a satellite in the earth’s upper atmosphere depends on the mean path of the molecules λ (a length), the density ρ, the diameter of the body D, and the molecular speed c: F = f (λ,
It is known that the differential pressure developed by a centrifugal pump, Δp, is a function of the diameter D of the impeller, the speed of rotation n, the discharge Q, and the fluid density ρ.
Consider steady viscous flow through a small horizontal tube. For this type of flow, the pressure gradient along the tube, Δp/Δℓ should be a function of the viscosity μ, the mean velocity V, and
Determine which of the following equations are dimensionally homogeneous:a.where Q is discharge, C is a pure number, L is length, g is acceleration due to gravity, and H is head.b.where V is
Refer to Figure 7.16. Assume that the head loss in the pipe is given by hL = 0.02(L/D)(V 2/2g), where V is the mean velocity in the pipe, D is the pipe diameter, and L is the pipe length. The
Observations show that the side thrust, F, for a rough spinning ball in a fluid is a function of the ball diameter, D, the free-stream velocity, V0, the density, ρ, the viscosity, μ, the roughness
For very low velocities it is known that the drag force FD of a small sphere is a function solely of the velocity V of flow past the sphere, the diameter d of the sphere, and the viscosity μ of the
The maximum rise of a liquid in a small capillary tube is a function of the diameter of the tube, the surface tension, and the specific weight of the liquid. What are the significant π-groups for
It takes a certain length of time for the liquid level in a tank of diameter D to drop from position h1 to position h2 as the tank is being drained through an orifice of diameter d at the bottom.
Determine the dimensions of the following variables and combinations of variables in terms of primary dimensions:a. T (torque)b. ρV2/2, where V is velocity and ρ is mass densityc. √τ/ρ, where
Explain what is meant by dimensional homogeneity.
According to the Buckingham Π theorem, if there are six dimensional variables and three primary dimensions, how many dimensionless variables will there be?
Find the primary dimensions of density (ρ), viscosity (μ), and pressure (p).
What power is required to pump water at a rate of 3 m3/s from the lower to the upper reservoir? Assume the pipe head loss is given by hL = 0.018(L/D)(V 2/2g), where L is the length of pipe, D is the
Water flows from the reservoir on the left to the reservoir on the right at a rate of 16 cfs. Th e formula for the head losses in the pipes is hL = 0.02(L/D)(V 2/2g). What elevation in the left
Water flows from reservoir A to reservoir B in a desert retirement community. The water temperature in the system is 100°F, the pipe diameter D is 2 ft, and the pipe length L is 160 ft. If H = 35
Water flows from reservoir A to reservoir B. Th e water temperature in the system is 10°C, the pipe diameter D is 1 m, and the pipe length L is 300 m. If H = 16 m, h = 2 m, and the pipe head loss is
What horsepower must be supplied to the water to pump 3.0 cfs at 68°F from the lower to the upper reservoir? Assume that the head loss in the pipes is given by hL = 0.018(L/D) (V 2/2g), where L is
Refer to Figure 7.14. Assume that the head loss in the pipes is given by hL = 0.02(L/D)(V 2/2g), where V is the mean velocity in the pipe, D is the pipe diameter, and L is the pipe length. The water
Water flows from the reservoir through a pipe and then discharges from a nozzle as shown. The head loss in the pipe itself is given as hL = 0.025(L/D)(V 2/2g), where L and D are the length and
The discharge of water through this turbine is 1000 cfs. What power is generated if the turbine efficiency is 85% and the total head loss is 4 ft? H = 100 ft. Also, carefully sketch the EGL and the
Assume that the head loss in the pipe is given by hL = 0.014(L/D)(V 2/2g), where L is the length of pipe and D is the pipe diameter. Assume α = 1.0 at all locations.a. Determine the discharge of

Showing 300 - 400 of 1194