Questions and Answers of Introduction To Fluid Mechanics

A fire nozzle is supplied through \(300 \mathrm{ft}\) of 3-in.-diameter canvas hose with \(e=0.001 \mathrm{ft}\). Water from a hydrant is supplied at \(50 \mathrm{psig}\) to a booster pump on board
Manufacturer's data for a submersible utility pump areThe owner's manual also states, These ratings are based on discharge into 25 -mm-diameter pipe with friction loss neglected. Using 20-mm-diameter
Water is pumped from a lake at \(z=0\) to a large storage tank located on a bluff above the lake. The pipe is 3-in.-diameter galvanized iron. The inlet section between the lake and the pump includes
Performance data for a centrifugal fan of 3-ft diameter tested at \(750 \mathrm{rpm}\) arePlot the performance data versus volume flow rate. Calculate static efficiency, and show the curve on the
The performance data of Problem 10.57 are for a 36-in.diameter fan wheel. The fan also is manufactured with 42-, 48-, 54-, and 60-in.-diameter wheels. Pick a standard fan to deliver \(600
Performance characteristics of a Howden Buffalo axial flow fan are presented below. The fan is used to power a wind tunnel with \(1-\mathrm{ft}\)-square test section. The tunnel consists of a smooth
Experimental test data for an aircraft engine fuel pump are presented below. This gear pump is required to supply jet fuel at 450 pounds per hour and \(150 \mathrm{psig}\) to the engine fuel
Preliminary calculations for a hydroelectric power generation site show a net head of \(2350 \mathrm{ft}\) is available at a water flow rate of \(75 \mathrm{ft}^{3} / \mathrm{s}\). Compare the
Conditions at the inlet to the nozzle of a Pelton wheel are \(p=700 \mathrm{psig}\) and \(V=15 \mathrm{mph}\). The jet diameter is \(d=7.5 \mathrm{in}\). and the nozzle loss coefficient is \(K_{\text
A Francis turbine is to operate under a head of \(46 \mathrm{~m}\) and deliver 18.6 MW while running at \(150 \mathrm{rpm}\). The runner diameter is \(4 \mathrm{~m}\). A 1-m-diameter model is
A Kaplan (propeller with variable-pitch blades) turbine with a rated capacity of \(83 \mathrm{MW}\) at a head of \(24 \mathrm{~m}\) and \(86 \mathrm{rpm}\) was one of 14 units installed at the McNary
Francis turbine Units 19, 20, and 21, installed at the Grand Coulee Dam on the Columbia River, are very large [55]. Each runner is \(32.6 \mathrm{ft}\) in diameter and contains 550 tons of cast
Measured data for performance of the reaction turbines at Shasta Dam near Redding, California, are shown in Fig. 10.38. Each turbine is rated at \(103,000 \mathrm{hp}\) when operating at \(138.6
For a flow rate of \(12 \mathrm{~L} / \mathrm{s}\) and turbine speed of \(65 \mathrm{rpm}\), estimate the power transferred from jet to turbine wheel. 3 m 50 mm Pipe Water -1.2 md- P10.67
The velocity of the water jet driving this impulse turbine is \(45 \mathrm{~m} / \mathrm{s}\). The jet has a \(75-\mathrm{mm}\) diameter. After leaving the buckets the absolute velocity of the water
An impulse turbine is to develop \(15 \mathrm{MW}\) from a single wheel at a location where the net head is \(350 \mathrm{~m}\). Determine the appropriate speed, wheel diameter, and jet diameter for
An impulse turbine under a net head of \(33 \mathrm{ft}\) was tested at a variety of speeds. The flow rate and the brake force needed to set the impeller speed were recorded:Calculate and plot the
The absolute velocities and directions of the jets entering and leaving the blade system are as shown. Calculate the power transferred from the jet to the blade system and the blade angles required.
A small hydraulic impulse turbine is supplied with water through a penstock with diameter \(D\) and length \(L\); the jet diameter is \(d\). The elevation difference between the reservoir surface and
A fanboat in the Florida Everglades is powered by a propeller with \(D=1.5 \mathrm{~m}\) driven at maximum speed, \(N=1800 \mathrm{rpm}\), by a \(125 \mathrm{~kW}\) engine. Estimate the maximum
A jet-propelled aircraft traveling at \(225 \mathrm{~m} / \mathrm{s}\) takes in \(50 \mathrm{~kg} / \mathrm{s}\) of air. If the propulsive efficiency (defined as the ratio of the useful work output
When an air jet of 1-in.-diameter strikes a series of blades on a turbine rotor, the absolute velocities are as shown. If the air is assumed to have a constant specific weight of \(0.08 \mathrm{lb} /
The volume flow rate through the propeller of an airboat (a boat driven by a propeller moving air) is \(50 \mathrm{~m}^{3} / \mathrm{s}\). When the boat is docked, the speed of the slipstream behind
The propeller for the Gossamer Condor human-powered aircraft has \(D=12 \mathrm{ft}\) and rotates at \(N=107 \mathrm{rpm}\). The wing loading is \(0.4 \mathrm{lbf} / \mathrm{ft}^{2}\) of wing area,
A typical American multiblade farm windmill has \(D=7 \mathrm{ft}\) and is designed to produce maximum power in winds with \(V=15 \mathrm{mph}\). Estimate the rate of water delivery as a function of
An airplane flies at \(200 \mathrm{~km} / \mathrm{h}\) through still air of specific weight \(12 \mathrm{~N} / \mathrm{m}^{3}\). The propeller is \(2.4 \mathrm{~m}\) in diameter and its slipstream
This ducted propeller unit drives a ship through still water at a speed of \(4.5 \mathrm{~m} / \mathrm{s}\). Within the duct the mean velocity of the water relative to the unit is \(15 \mathrm{~m} /
A model of an American multiblade farm windmill is to be built for display. The model, with \(D=1 \mathrm{~m}\), is to develop full power at \(V=10 \mathrm{~m} / \mathrm{s}\) wind speed. Calculate
A large Darrieus vertical axis wind turbine was built by the U.S. Department of Energy near Sandia, New Mexico [48]. This machine is \(18 \mathrm{~m}\) tall and has a \(5-\mathrm{m}\) radius; the
Show that this ducted propeller system when moving forward at velocity \(V_{1}\) will have an efficiency given by \(2 V_{1} /\left(V_{4}+V_{1}\right)\). If for a specific design and point of
This ducted propeller unit (now operating as a turbine) is towed through still water at a speed of \(7.5 \mathrm{~m} / \mathrm{s}\). Calculate the maximum power that the propeller can develop.
Aluminum extrusions, patterned after NACA symmetric airfoil sections, frequently are used to form Darrieus wind turbine "blades." Below are section lift and drag coefficient data [57] for a NACA 0012
What is the maximum power that can be expected from a windmill \(30 \mathrm{~m}\) in diameter in a wind of \(50 \mathrm{~km} / \mathrm{h}\) ? Assume air density \(1.225 \mathrm{~kg} /
If an ideal windmill is operating at best efficiency in a wind of \(48 \mathrm{~km} / \mathrm{h}\), what is the velocity through the disk and at some distance behind the windmill? What is the thrust
A prototype air compressor with a compression ratio of 7 is designed to take \(8.9 \mathrm{~kg} / \mathrm{s}\) air at 1 atmosphere and \(20^{\circ} \mathrm{C}\). The design point speed, power
A compressor has been designed for entrance conditions of \(14.7 \mathrm{psia}\) and \(70^{\circ} \mathrm{F}\). To economize on the power required, it is being tested with a throttle in the entry
We have seen many examples in Chapter 7 of replacing working fluids in order to more easily achieve similitude between models and prototypes. Describe the effects of testing an air compressor using
The roof of a minivan is approximated as a horizontal flat plate. Plot the length of the laminar boundary layer as a function of minivan speed, \(V\), as the minivan accelerates from \(10
A model of a river towboat is to be tested at \(1: 18\) scale. The boat is designed to travel at \(3.5 \mathrm{~m} / \mathrm{s}\) in fresh water at \(10^{\circ} \mathrm{C}\). Estimate the distance
For flow over a smooth plate, what approximately is the maximum length of the laminar boundary layer if \(V_{o}=9.0 \mathrm{~m} / \mathrm{s}\) in the irrotational uniform flow and the fluid is air?
A model of a thin streamlined body is placed in a flow for testing. The body is \(0.9 \mathrm{~m}\) long and the flow velocity is \(0.6 \mathrm{~m} / \mathrm{s}\). What \(u\) is needed to ensure that
A student is to design an experiment involving dragging a sphere through a tank of fluid to illustrate(a) "creeping flow" \(\left(R e_{D}
A \(1 \mathrm{~m} \times 2 \mathrm{~m}\) sheet of plywood is attached to the roof of your vehicle after being purchased at the hardware store. At what speed (in kilometers per hour) in \(20^{\circ}
The extent of the laminar boundary layer on the surface of an aircraft or missile varies with altitude. For a given speed, will the laminar boundary-layer length increase or decrease with altitude?
Velocity profiles in laminar boundary layers often are approximated by the equationsCompare the shapes of these velocity profiles by plotting \(y / \delta\) (on the ordinate) versus \(u / U\) (on the
An approximation for the velocity profile in a laminar boundary layer isDoes this expression satisfy boundary conditions applicable to the laminar boundary-layer velocity profile? Evaluate
Evaluate \(\theta / \delta\) for each of the laminar boundary-layer velocity profiles given in Problem 9.8.Data From Problem 9.8 9.8 Velocity profiles in laminar boundary layers often are approxi-
Evaluate the displacement thickness \(\delta^{*}\) and the momentum thickness \(\theta\) for a velocity profile given by \(\frac{u}{U}=\frac{y}{\delta}\). Plot the nondimensional velocity profile and
Evaluate the displacement thickness \(\delta^{*}\) and the momentum thickness \(\theta\) for a power law velocity profile given by \(\frac{u}{U}=\left(\frac{y}{\delta}\right)^{1 / 7}\). Plot the
A fluid, with density \(ho=1.5 \mathrm{slug} / \mathrm{ft}^{3}\), flows at \(U=10 \mathrm{ft} / \mathrm{s}\) over a flat plate \(10 \mathrm{ft}\) long and \(3 \mathrm{ft}\) wide. At the trailing
Solve Problem 9.13 with the velocity profile at section \(b c\) given by the parabolic expression from Problem 9.8.Data From Problem 9.13Data From Problem 9.8 9.13 A fluid, with density p = 1.5
Air flows in a horizontal cylindrical duct of diameter \(D=100 \mathrm{~mm}\). At a section a few meters from the entrance, the turbulent boundary layer is of thickness \(\delta_{1}=5.25
Evaluate the displacement thickness \(\delta^{*}\) and the momentum thickness \(\theta\) for the profile given by \(\frac{u}{U}=2\left(\frac{y}{\delta}\right)-\left(\frac{y}{\delta}\right)^{2}\).
Evaluate the displacement thickness \(\delta^{*}\) and the momentum thickness \(\theta\) for a velocity profile given by \(\frac{u}{U}=\sin \left(\frac{\pi y}{2 \delta}\right)\). Plot the
A laboratory wind tunnel has a test section \(25 \mathrm{~cm}\) square and \(50 \mathrm{~cm}\) long. With nominal air speed \(U_{1}=25 \mathrm{~m} / \mathrm{s}\) at the test section inlet, turbulent
Air flows in the entrance region of a square duct, as shown. The velocity is uniform, \(U_{0}=100 \mathrm{ft} / \mathrm{s}\), and the duct is \(3 \mathrm{in}\). square. At a section \(1 \mathrm{ft}\)
A flow of \(68^{\circ} \mathrm{F}\) air develops in a flat horizontal duct following a well-rounded entrance section. The duct height is \(H=1 \mathrm{ft}\). Turbulent boundary layers grow on the
A flow of air develops in a horizontal cylindrical duct, of diameter \(D=15\) in., following a well-rounded entrance. A turbulent boundary grows on the duct wall, but the flow is not yet fully
Using numerical results for the Blasius exact solution for laminar boundary-layer flow on a flat plate, plot the dimensionless velocity profile, \(u / U\) (on the abscissa), versus dimensionless
Using numerical results obtained by Blasius (Table 9.1, on the web), evaluate the distribution of shear stress in a laminar boundary layer on a flat plate. Plot \(\tau / \tau_{w}\) versus \(y /
Using numerical results obtained by Blasius (Table 9.1, on the web), evaluate the vertical component of velocity in a laminar boundary layer on a flat plate. Plot \(v / U\) versus \(y / \delta\) for
Consider flow of air over a flat plate. On one graph, plot the laminar boundary-layer thickness as a function of distance along the plate (up to transition) for freestream speeds \(U=1 \mathrm{~m} /
A thin flat plate, \(L=9 \mathrm{in}\). long and \(b=3 \mathrm{ft}\) wide, is installed in a water tunnel as a splitter. The freestream speed is \(U=5 \mathrm{ft} / \mathrm{s}\), and the velocity
For a laminar boundary layer on a flat plate, evaluate the kinetic energy lost between the free stream and any point in the boundary layer. Assume that the boundary layer is linear (see Problem 9.8)
Air at atmospheric pressure and \(20^{\circ} \mathrm{C}\) flows over both sides of a flat plate that is \(0.8 \mathrm{~m}\) long and \(0.3 \mathrm{~m}\) wide at a velocity of \(5 \mathrm{~m} /
A thin flat plate is installed in a water tunnel as a splitter. The plate is \(0.3 \mathrm{~m}\) long and \(1 \mathrm{~m}\) wide. The freestream speed is \(1.6 \mathrm{~m} / \mathrm{s}\). Laminar
Assume laminar boundary-layer flow to estimate the drag on the flat plate shown when it is placed parallel to a \(15 \mathrm{ft} / \mathrm{s}\) air flow. The air is at \(70^{\circ} \mathrm{F}\) and
A horizontal surface, with length \(L=1.8 \mathrm{~m}\) and width \(b=0.9 \mathrm{~m}\), is immersed in a stream of standard air flowing at \(U=3.2 \mathrm{~m} / \mathrm{s}\). Assume a laminar
Use the momentum integral equation to derive expressions for the displacement thickness \(\delta^{*}\), the momentum thickness \(\theta\), and the friction coefficient \(C_{f}\) for a linear velocity
A horizontal surface, with length \(L=0.8 \mathrm{~m}\) and width \(b=1.9 \mathrm{~m}\), is immersed in a stream of standard air flowing at \(U=5.3 \mathrm{~m} / \mathrm{s}\). Assume a laminar
Assume the flow conditions given in Example 9.3. Plot \(\delta, \delta^{*}\), and \(\tau_{w}\) versus \(x / L\) for the plate.Data From Example 9.3 Example 9.3 TURBULENT BOUNDARY LAYER ON A FLAT
European InterCity Express trains operate at speeds of up to \(280 \mathrm{~km} / \mathrm{hr}\). Suppose that a train is \(120 \mathrm{~m}\) long. Treat the sides and top of the train as a smooth
Repeat Problem 9.32, for an air flow at \(80 \mathrm{ft} / \mathrm{s}\), assuming a turbulent boundary layer.Data From Problem 9.32 9.32 Assume laminar boundary-layer flow to estimate the drag on the
The U.S. Navy has built the Sea Shadow, which is a small waterplane twin-hull (SWATH) ship whose object is to achieve the same reduced radar profile as the STEALTH aircraft. This catamaran is \(160
The two rectangular smooth flat plates are to have the same drag in the same fluid stream. Calculate the required value of \(x\). If the two plates are combined into the \(\mathrm{T}\)-shape
Standard air flows over a horizontal smooth flat plate at freestream speed \(U=20 \mathrm{~m} / \mathrm{s}\). The plate length is \(L=1.5 \mathrm{~m}\) and its width is \(b=0.8 \mathrm{~m}\). The
A uniform flow of standard air at \(60 \mathrm{~m} / \mathrm{s}\) enters a plane-wall diffuser with negligible boundary-layer thickness. The inlet width is \(75 \mathrm{~mm}\). The diffuser walls
Air flows in a cylindrical duct of diameter \(D=6\) in. At section (1), the turbulent boundary layer is of thickness \(\delta_{1}=0.4 \mathrm{in}\). and the velocity in the inviscid central core is
Table 9.1 (on the web) shows the numerical results obtained from Blasius exact solution of the laminar boundary-layer equations. Plot the velocity distribution. On the same graph, plot the turbulent
A fluid flow enters the plane-wall diffuser that has an entrance area of \(A_{o}\) at a velocity of \(U_{o}\). (a) Assuming the fluid is inviscid, determine the velocity gradient \(\frac{d U}{d x}\)
Boundary-layer separation occurs when the shear stress at the surface becomes zero. Assume a polynomial representation for the laminar boundary layer of the form, \(u / U=a+b \lambda+c \lambda^{2}+d
For flow over a flat plate with zero pressure gradient, will the shear stress increase, decrease, or remain constant along the plate? Justify your answer. Does the momentum flux increase, decrease,
A laboratory wind tunnel has a test section that is square in cross section, with inlet width \(W_{1}\) and height \(H_{1}\), each equal to \(1 \mathrm{ft}\). At freestream speed \(U_{1}=80
A flat-bottomed barge, \(80 \mathrm{ft}\) long and \(35 \mathrm{ft}\) wide, submerged to a depth of \(5 \mathrm{ft}\), is to be pushed up a river at \(60^{\circ} \mathrm{F}\). Estimate and plot the
A towboat for river barges is tested in a towing tank. The towboat model is built at a scale ratio of 1:13.5. Dimensions of the model are overall length \(3.5 \mathrm{~m}\), beam \(1 \mathrm{~m}\),
Plot the local friction coefficient \(c_{f}\), the boundary layer thickness ratio \(\delta / x\), and the drag coefficient \(C_{f}\), for both laminar and turbulent boundary layers on a flat plate
A smooth plate \(3 \mathrm{~m}\) long and \(0.9 \mathrm{~m}\) wide moves through still sea level air at \(4.5 \mathrm{~m} / \mathrm{s}\). Assuming the boundary layer to be wholly laminar, calculate
A nuclear submarine cruises fully submerged at 27 knots. The hull is approximately a circular cylinder with diameter \(D=11.0 \mathrm{~m}\) and length \(L=107 \mathrm{~m}\). Estimate the percentage
The drag coefficient of a circular disk when placed normal to the flow is 1.12. Calculate the force and power necessary to drive a 12 in. \((0.3 \mathrm{~m})\) disk at \(48 \mathrm{~km} /
A steel sphere \((\mathrm{SG}=7.8)\) of \(13 \mathrm{~mm}\) diameter falls at a constant velocity of \(0.06 \mathrm{~m} / \mathrm{s}\) through an oil \((\mathrm{SG}=0.90)\). Calculate the viscosity
The wave resistance and viscous resistance on a model and prototype ship were discussed. For the prototype, \(L=130 \mathrm{~m}\) and \(A=1800 \mathrm{~m}^{2}\). From the data of Figs 7.2 and 7.3,
What constant speed will be attained by a lead \((\mathrm{SG}=1.4)\) sphere of \(0.5 \mathrm{in}\). diameter falling freely through an oil of kinematic viscosity \(0.12 \mathrm{ft}^{2} / \mathrm{s}\)
Glass spheres of 0.1 in. diameter fall at constant velocities of 0.1 and \(0.05 \mathrm{ft} / \mathrm{s}\) through two different oils of the same specific gravity in very large tanks. If the
As a design engineer you are asked to design an emergency braking parachute system for use with a military aircraft of mass \(9500 \mathrm{~kg}\). The plane lands at \(350 \mathrm{~km} /
Calculate the drag of a smooth sphere of \(0.3 \mathrm{~m}\) diameter in a stream of standard sea level air at Reynolds numbers of 1,10,100, and 1000 .
A cylindrical chimney \(0.9 \mathrm{~m}\) in diameter and \(22.5 \mathrm{~m}\) high is exposed to a \(56 \mathrm{~km} / \mathrm{h}\) wind \(\left(15^{\circ} \mathrm{C}\right.\) and \(\left.101.3
Ballistic data obtained on a firing range show that aerodynamic drag reduces the speed of a .44 magnum revolver bullet from \(250 \mathrm{~m} / \mathrm{s}\) to \(210 \mathrm{~m} / \mathrm{s}\) as it
A standard marine torpedo is \(0.533 \mathrm{~m}\) in diameter and about \(7.2 \mathrm{~m}\) long. Make an engineering estimate of the power required to drive this torpedo at \(80 \mathrm{~km} /
A large truck has an essentially boxlike body that causes flow separation at the front edges of the cab at any speed. The drag is mostly profile drag and \(C_{D}=0.75\). If the projected frontal area
At a surprise party for a friend you've tied a series of \(20-\mathrm{cm}-\) diameter helium balloons to a flagpole, each tied with a short string. The first one is tied \(1 \mathrm{~m}\) above the

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