Fox And McDonald's Introduction To Fluid Mechanics 9th Edition Philip J. Pritchard, John W. Mitchell - Solutions

Water flows in a pipeline. At a point in the line where the diameter is 7 in., the velocity is \(12 \mathrm{fps}\) and the pressure is \(50 \mathrm{psi}\). At a point \(40 \mathrm{ft}\) away the diameter reduces to 3 in. Calculate the pressure here when the pipe is (a) horizontal, (b) vertical with
In a pipe \(0.3 \mathrm{~m}\) in diameter, \(0.3 \mathrm{~m}^{3} / \mathrm{s}\) of water are pumped up a hill. On the hilltop (elevation 48), the line reduces to \(0.2 \mathrm{~m}\) diameter. If the pump maintains a pressure of \(690 \mathrm{kPa}\) at elevation 21 , calculate the pressure in the
A jet of air from a nozzle is blown at right angles against a wall in which two pressure taps are located. A manometer connected to the tap directly in front of the jet shows a head of \(25 \mathrm{~mm}\) of mercury above atmospheric. Determine the approximate speed of the air leaving the nozzle if
The inlet contraction and test section of a laboratory wind tunnel are shown. The air speed in the test section is \(U=50 \mathrm{~m} / \mathrm{s}\). A totalhead tube pointed upstream indicates that the stagnation pressure on the test section centerline is \(10 \mathrm{~mm}\) of water below
Maintenance work on high-pressure hydraulic systems requires special precautions. A small leak can result in a high-speed jet of hydraulic fluid that can penetrate the skin and cause serious injury (therefore troubleshooters are cautioned to use a piece of paper or cardboard, not a finger, to
An open-circuit wind tunnel draws in air from the atmosphere through a well-contoured nozzle. In the test section, where the flow is straight and nearly uniform, a static pressure tap is drilled into the tunnel wall. A manometer connected to the tap shows that static pressure within the tunnel is
Water is flowing. Calculate \(H(\mathrm{~m})\) and \(p(\mathrm{kPa})\). 175 mm- -125 mm d -100 mm d Hg (13.57) P6.36 75 mm d H
If each gauge shows the same reading for a flow rate of \(1.00 \mathrm{cfs}\), what is the diameter of the constriction? 3-in.-dia. El. 100 - El. 90 P6.37 El. 108 3-in.-dia.
Derive a relation between \(A_{1}\) and \(A_{2}\) so that for a flow rate of \(0.28 \mathrm{~m}^{3} / \mathrm{s}\) the static pressure will be the same at sections (1) and (2). Also calculate the manometer reading for this condition and state which leg has the higher mercury column.' 1.5 m 1 2. -A-
Water flows steadily up the vertical 1-in.-diameter pipe and out the nozzle, which is 0.5 in. in diameter, discharging to atmospheric pressure. The stream velocity at the nozzle exit must be \(30 \mathrm{ft} / \mathrm{s}\). Calculate the minimum gage pressure required at section (1). If the device
Your car runs out of gas unexpectedly and you siphon gas from another car. The height difference for the siphon is \(1 \mathrm{ft}\). The hose diameter is 0.5 in. What is your gasoline flow rate?
A tank at a pressure of \(50 \mathrm{kPa}\) gage gets a pinhole rupture and benzene shoots into the air. Ignoring losses, to what height will the benzene rise?
The water flow rate through the siphon is \(5 \mathrm{~L} / \mathrm{s}\), its temperature is \(20^{\circ} \mathrm{C}\), and the pipe diameter is \(25 \mathrm{~mm}\). Compute the maximum allowable height, \(h\), so that the pressure at point \(A\) is above the vapor pressure of the water. Assume the
Water flows from a very large tank through a \(5 \mathrm{~cm}\) diameter tube. The dark liquid in the manometer is mercury. Estimate the velocity in the pipe and the rate of discharge from the tank. Assume the flow is frictionless. - 4 m 75 cm 5 cm 157 Flow 15 cm Mercury P6.43
Consider frictionless, incompressible flow of air over the wing of an airplane flying at \(200 \mathrm{~km} / \mathrm{hr}\). The air approaching the wing is at \(65 \mathrm{kPa}\) and \(-10^{\circ} \mathrm{C}\). At a certain point in the flow, the pressure is \(60 \mathrm{kPa}\). Calculate the
A closed tank contains water with air above it. The air is maintained at a gage pressure of \(150 \mathrm{kPa}\) and \(3 \mathrm{~m}\) below the water surface a nozzle discharges into the atmosphere. At what velocity will water emerge from the nozzle?
Water jets upward through a 3-in.-diameter nozzle under a head of \(10 \mathrm{ft}\). At what height \(h\) will the liquid stand in the pitot tube? What is the cross-sectional area of the jet at section \(B\) ? 10 ft Water 5 ft B Nozzle is 3 in. in diameter (A=0.0491 ft2) P6.46
Calculate the rate of flow through this pipeline and the pressures at \(A, B, C\), and \(D\). Sketch the EL and HGL showing vertical distances. 5 ft B 20 ft 6 in. dl Water A P6.47 12 ft 2 in. d 8 ft
A mercury barometer is carried in a car on a day when there is no wind. The temperature is \(20^{\circ} \mathrm{C}\) and the corrected barometer height is \(761 \mathrm{~mm}\) of mercury. One window is open slightly as the car travels at \(105 \mathrm{~km} / \mathrm{hr}\). The barometer reading in
A racing car travels at \(235 \mathrm{mph}\) along a straightaway. The team engineer wishes to locate an air inlet on the body of the car to obtain cooling air for the driver's suit. The plan is to place the inlet at a location where the air speed is \(60 \mathrm{mph}\) along the surface of the
The velocity field for a plane source at a distance \(h\) above an infinite wall aligned along the \(x\) axis was given in Problem 6.6. Using the data from that problem, plot the pressure distribution along the wall from \(x=-10 h\) to \(x=+10 h\) (assume the pressure at infinity is atmospheric).
A smoothly contoured nozzle, with outlet diameter \(d=20 \mathrm{~mm}\), is coupled to a straight pipe by means of flanges. Water flows in the pipe, of diameter \(D=50 \mathrm{~mm}\), and the nozzle discharges to the atmosphere. For steady flow and neglecting the effects of viscosity, find the
Water flows steadily through a 3.25-in.-diameter pipe and discharges through a 1.25-in.-diameter nozzle to atmospheric pressure. The flow rate is \(24.5 \mathrm{gpm}\). Calculate the minimum static pressure required in the pipe to produce this flow rate. Evaluate the axial force of the nozzle
A flow nozzle is a device for measuring the flow rate in a pipe. This particular nozzle is to be used to measure low-speed air flow for which compressibility may be neglected. During operation, the pressures \(p_{1}\) and \(p_{2}\) are recorded, as well as upstream temperature, \(T_{1}\). Find the
The head of water on a \(50 \mathrm{~mm}\) diameter smooth nozzle is \(3 \mathrm{~m}\). If the nozzle is directed upward at angles of(a) \(30^{\circ}\),(b) \(45^{\circ}\),(c) \(60^{\circ}\),(d) \(90^{\circ}\), how high above the nozzle will the jet rise, and how far from the nozzle will the jet
Water flows from one reservoir in a \(200-\mathrm{mm}\) pipe, while water flows from a second reservoir in a \(150-\mathrm{mm}\) pipe. The two pipes meet in a "tee" junction with a \(300-\mathrm{mm}\) pipe that discharges to the atmosphere at an elevation of \(20 \mathrm{~m}\). If the water surface
Barometric pressure is 14.0 psia. What is the maximum flow rate that can be obtained by opening the valve? (a) if cavitation is not a consideration and (b) if cavitation needs to be prevented? CCI4 (68F) 6 in. d 4 in. d 20 ft 25 ft P6.56 6 in. d
A spray system is shown in the diagram. Water is supplied at \(p=10 \mathrm{kPa}\) gage, through the flanged opening of area \(A=1900 \mathrm{~mm}^{2}\). The water leaves in a steady free jet at atmospheric pressure. The jet area and speed are \(A=650 \mathrm{~mm}^{2}\) and \(V=4.6 \mathrm{~m} /
Water flows out of a kitchen faucet of 1.25 -in.-diameter at the rate of \(0.1 \mathrm{~L} / \mathrm{s}\). The bottom of the sink is \(45 \mathrm{~cm}\) below the faucet outlet. Will the cross-sectional area of the fluid stream increase, decrease, or remain constant between the faucet outlet and
A horizontal axisymmetric jet of air with 0.4-in.-diameter strikes a stationary vertical disk of \(7.5 \mathrm{in}\). diameter. The jet speed is \(225 \mathrm{ft} / \mathrm{s}\) at the nozzle exit. A manometer is connected to the center of the disk. Calculate (a) the deflection, if the manometer
The water level in a large tank is maintained at height \(H\) above the surrounding level terrain. A rounded nozzle placed in the side of the tank discharges a horizontal jet. Neglecting friction, determine the height \(h\) at which the orifice should be placed so the water strikes the ground at
Many recreation facilities use inflatable "bubble" structures. A tennis bubble to enclose four courts is shaped roughly as a circular semicylinder with a diameter of \(50 \mathrm{ft}\) and a length of \(50 \mathrm{ft}\). The blowers used to inflate the structure can maintain the air pressure inside
Water flows at low speed through a circular tube with inside diameter of 2 in. A smoothly contoured body of \(1.5 \mathrm{in}\). diameter is held in the end of the tube where the water discharges to atmosphere. Neglect frictional effects and assume uniform velocity profiles at each section.
Describe the pressure distribution on the exterior of a multistory building in a steady wind. Identify the locations of the maximum and minimum pressures on the outside of the building. Discuss the effect of these pressures on infiltration of outside air into the building.
An aspirator provides suction by using a stream of water flowing through a venturi. Analyze the shape and dimensions of such a device. Comment on any limitations on its use.
Carefully sketch the energy grade lines (EGL) and hydraulic grade lines (HGL) for the system shown in Fig. 6.6 if the pipe is horizontal (i.e., the outlet is at the base of the reservoir), and a water turbine (extracting energy) is located at point (2), or at point (3). In Chapter 8 we will
Carefully sketch the energy grade lines (EGL) and hydraulic grade lines (HGL) for the system shown in Fig. 6.6 if a pump adding energy to the fluid is located at point (2), such that flow is into the reservoir. In Chapter 8 we will investigate the effects of friction on internal flows. Can you
Water is being pumped from the lower reservoir through a nozzle into the upper reservoir. If the vacuum gauge at \(A\) reads \(2.4 \mathrm{psi}\) vacuum,(a) find the flow velocity through the nozzle,(b) find the horsepower the pump must add to the water,(c) draw the energy line and the hydraulic
The turbine extracts power from the water flowing from the reservoir. Find the horsepower extracted if the flow through the system is 1000 cfs. Draw the energy line and the hydraulic grade line. El. 1000 ft de 12 ft P6.68 -EI.500 ft T El.475 ft
Consider a two-dimensional fluid flow: \(u=a x+b y\) and \(v=\) \(c x+d y\), where (a,b, c, and d) are constant. If the flow is incompressible and irrotational, find the relationships among (a,b, c, and d. Find the stream function and velocity potential function of this flow.
The velocity field for a two-dimensional flow is \(\vec{V}=\) \((A x-B y) t \hat{i}-(B x+A y) t \hat{j}\), where \(A=1 \mathrm{~s}^{-2} B=2 \mathrm{~s}^{-2}, t\) is in seconds, and the coordinates are measured in meters. Is this a possible incompressible flow? Is the flow steady or unsteady? Show
A flow field is characterized by the stream function \(\psi=A x y\), where \(A=2 \mathrm{~s}^{-1}\) and the coordinates are measured in feet. Verify that the flow is irrotational and determine the velocity potential \(\phi\). Plot the streamlines and potential lines and visually verify that they
The flow field for a plane source at a distance \(h\) above an infinite wall aligned along the \(x\) axis is given by \[\begin{aligned}\vec{V} & =\frac{q}{2 \pi\left[x^{2}+(y-h)^{2}\right]}[x \hat{i}+(y-h) \hat{j}] \\& +\frac{q}{2 \pi\left[x^{2}+(y+h)^{2}\right]}[x \hat{i}+(y+h)
The stream function of a flow field is \(\psi=A x^{2} y-B y^{3}\), where \(A=1 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}, B=\frac{1}{3} \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\), and the coordinates are measured in meters. Find an expression for the velocity potential.
A flow field is characterized by the stream function\[\psi=2 y+\frac{1}{2 \pi}\left(\tan ^{-1} \frac{y-a}{x}-\tan ^{-1} \frac{y+a}{x}\right)\]Derive an expression for the location of the stagnation points. Sketch the flow field.
A flow field is characterized by the stream function\[\psi=x y^{2}+B x^{3}\]What does the value of \(B\) need to be for the flow to be irrotational? For that value of \(B\), determine the velocity potential \(\phi\). Sketch the streamlines and potential lines.
The stream function of a flow field is \(\psi=A x^{3}-B x y^{2}\), where \(A=1 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\) and \(B=3 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\), and coordinates are measured in meters. Find an expression for the velocity potential.
A flow field is represented by the stream function \(\psi=x^{5}-\) \(15 x^{4} y^{2}+15 x^{2} y^{4}-y^{6}\). Find the corresponding velocity field. Show that this flow field is irrotational and obtain the potential function.
Consider the flow field represented by the potential function \(\phi=x^{5}-10 x^{3} y^{2}+5 x y^{4}-x^{2}+y^{2}\). Verify that this is an incompressible flow, and obtain the corresponding stream function.
Show by expanding and collecting real and imaginary terms that \(f=z^{6}\) (where \(z\) is the complex number \(z=x+i y\) ) leads to a valid velocity potential (the real part of \(f\) ) and a corresponding stream function (the negative of the imaginary part of \(f\) ) of an irrotational and
Consider the flow field represented by the velocity potential \(\phi=A x+B x^{2}-B y^{2}\), where \(A=1 \mathrm{~m} \cdot \mathrm{s}^{-1}, B=1 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\), and the coordinates are measured in meters. Obtain expressions for the velocity field and the stream function.
An incompressible flow field is characterized by the stream function \(\psi=3 A x^{2} y-A y^{3}\), where \(A=1 \mathrm{~m}^{-1} \cdot \mathrm{s}^{-1}\). Show that this flow field is irrotational. Derive the velocity potential for the flow. Plot the streamlines and potential lines, and visually
Consider an air flow over a flat wall with an upstream velocity of \(6 \mathrm{~m} / \mathrm{s}\). There is a narrow slit through which air is drawn in at a flow rate of \(0.2 \mathrm{~m}^{3} / \mathrm{s}\) per meter of width. Represent the flow as a combination of a uniform flow and a sink.
A source with a strength of \(q=3 \pi \mathrm{m}^{2} / \mathrm{s}\) and a sink with a strength of \(q=\pi \mathrm{m}^{2} / \mathrm{s}\) are located on the \(x\) axis at \(x=-1 \mathrm{~m}\) and \(x=1 \mathrm{~m}\), respectively. Determine the stream function and velocity potential for the combined
The velocity distribution in a two-dimensional, steady, inviscid flow field in the \(x y\) plane is \(\vec{V}=(A x+B) \hat{i}+(C-A y) \hat{j}\), where \(A=3 \mathrm{~s}^{-1}, B=6 \mathrm{~m} / \mathrm{s}, C=4 \mathrm{~m} / \mathrm{s}\), and the coordinates are measured in meters. The body force
Consider the flow past a circular cylinder, of radius \(a\), used in Example 6.11. Show that \(V_{r}=0\) along the lines \((r, \theta)=(r, \pm \pi / 2)\). Plot \(V_{\theta} / U\) versus radius for \(r \geq a\), along the line \((r, \theta)=(r, \pi / 2)\). Find the distance beyond which the
The flow in a corner with an angle \(\alpha\) can be described in radial coordinates by the stream function as \(\psi=A r^{\frac{\pi}{\alpha}} \sin \frac{\pi \theta}{\alpha}\). Determine the velocity potential for the flow and plot streamlines for flow for \(\alpha=60^{\circ}\).
Consider the two-dimensional flow against a flat plate that is characterized by the stream function \(\psi=A x y\). Superimpose a plane source of strength \(B\) placed at the origin. Determine the relation between the height of the stagnation point \(h\), the constant \(A\), and the strength \(B\).
A source and a sink with strengths of equal magnitude, \(q=3 \pi \mathrm{m}^{2} / \mathrm{s}\), are placed on the \(x\) axis at \(x=-a\) and \(a\), respectively. A uniform flow, with speed \(U=20 \mathrm{~m} / \mathrm{s}\), in the positive \(x\) direction, is added to obtain the flow past a Rankine
A flow field is formed by combining a uniform flow in the positive \(x\) direction, with \(U=10 \mathrm{~m} / \mathrm{s}\), and a counterclockwise vortex, with strength \(K=16 \pi \mathrm{m}^{2} / \mathrm{s}\), located at the origin. Obtain the stream function, velocity potential, and velocity
Consider the flow field formed by combining a uniform flow in the positive \(x\) direction and a source located at the origin. Obtain expressions for the stream function, velocity potential, and velocity field for the combined flow. If \(U=25 \mathrm{~m} / \mathrm{s}\), determine the source
The slope of the free surface of a steady wave in one-dimensional flow in a shallow liquid layer is described by the equation\[\frac{\partial h}{\partial x}=-\frac{u}{g} \frac{\partial u}{\partial x}\]Use a length scale, \(L\), and a velocity scale, \(V_{0}\), to nondimensionalize this equation.
One-dimensional unsteady flow in a thin liquid layer is described by the equation\[\frac{\partial u}{\partial t}+u \frac{\partial u}{\partial x}=-g \frac{\partial h}{\partial x}\]Use a length scale, \(L\), and a velocity scale, \(V_{0}\), to nondimensionalize this equation. Obtain the dimensionless
In atmospheric studies the motion of the earth's atmosphere can sometimes be modeled with the equation\[\frac{D \vec{V}}{D t}+2 \vec{\Omega} \times \vec{V}=-\frac{1}{ho} abla p\]where \(\vec{V}\) is the large-scale velocity of the atmosphere across the Earth's surface, \(abla p\) is the climatic
Fluid fills the space between two parallel plates. The differential equation that describes the instantaneous fluid velocity for unsteady flow with the fluid moving parallel to the walls is\[ho \frac{\partial u}{\partial t}=\mu \frac{\partial^{2} u}{\partial y^{2}}\]The lower plate is stationary
By using order of magnitude analysis, the continuity and Navier-Stokes equations can be simplified to the Prandtl boundarylayer equations. For steady, incompressible, and two-dimensional flow, neglecting gravity, the result is\[\begin{aligned} & \frac{\partial u}{\partial x}+\frac{\partial
Consider a disk of radius \(R\) rotating in an incompressible fluid at a speed \(\omega\). The equations that describe the boundary layer on the disk are:\[\begin{aligned}& \frac{1}{r}\left(\frac{\partial\left(r v_{r}\right)}{\partial r}\right)+\frac{\partial v_{z}}{\partial z}=0 \\&
An unsteady, two-dimensional, compressible, inviscid flow can be described by the equation\[\begin{aligned}\frac{\partial^{2} \psi}{\partial t^{2}}+\frac{\partial}{\partial t} & \left(u^{2}+v^{2}\right)+\left(u^{2}-c^{2}\right) \frac{\partial^{2} \psi}{\partial x^{2}} \\& +\left(v^{2}-c^{2}\right)
Experiments show that the pressure drop for flow through an orifice plate of diameter \(d\) mounted in a length of pipe of diameter . You are asked to organize some experimental data. Obtain the resulting dimensionless parameters. Ap P1 P2 f(p, , V, d, D)
At very low speeds, the drag on an object is independent of fluid density. Thus the drag force, \(F\), on a small sphere is a function only of speed, \(V\), fluid viscosity, \(\mu\), and sphere diameter, \(D\). Use dimensional analysis to determine how the drag force \(F\) depends on the speed
We saw in Chapter 3 that the buoyant force, \(F_{B}\), on a body submerged in a fluid is directly proportional to the specific weight of the fluid, \(\gamma\). Demonstrate this using dimensional analysis, by starting with the buoyant force as a function of the volume of the body and the specific
Assume that the velocity acquired by a body falling from rest (without resistance) depends on weight of body, acceleration due to gravity, and distance of fall. Prove by dimensional analysis that \(V=C \sqrt{g_{n} h}\) and is thus independent of the weight of the body.
Derive by dimensional analysis an expression for the local velocity in established pipe flow through a smooth pipe if this velocity depends only on mean velocity, pipe diameter, distance from pipe wall, and density and viscosity of the fluid.
The speed of shallow water waves in the ocean (e.g., seismic sea waves or tsunamis) depends only on the still water depth and the acceleration due to gravity. Derive an expression for wave speed.
The speed, \(V\), of a free-surface wave in shallow liquid is a function of depth, \(D\), density, \(ho\), gravity, \(g\), and surface tension, \(\sigma\). Use dimensional analysis to find the functional dependence of \(V\) on the other variables. Express \(V\) in the simplest form possible.
The boundary-layer thickness, \(\delta\), on a smooth flat plate in an incompressible flow without pressure gradients depends on the freestream speed, \(U\), the fluid density, \(ho\), the fluid viscosity, \(\mu\), and the distance from the leading edge of the plate, \(x\). Express these variables
The speed, \(V\), of a free-surface gravity wave in deep water is a function of wavelength, \(\lambda\), depth, \(D\), density, \(ho\), and acceleration of gravity, \(g\). Use dimensional analysis to find the functional dependence of \(V\) on the other variables. Express \(V\) in the simplest form
Derive an expression for the velocity of very small ripples on the surface of a liquid if this velocity depends only on ripple length and density and surface tension of the liquid.
Derive an expression for the axial thrust exerted by a propeller if the thrust depends only on forward speed, angular speed, size, and viscosity and density ofthe fluid. How would the expression change if gravity were a relevant variable in the case of a ship propeller?
Derive an expression for drag force on a smooth submerged object moving through incompressible fluid if this force depends only on speed and size of object and viscosity and density of the fluid.
The energy released during an explosion, \(E\), is a function of the time after detonation \(t\), the blast radius \(R\) at time \(t\), and the ambient air pressure \(p\), and density \(ho\). Determine, by dimensional analysis, the general form of the expression for \(E\) in terms of the other
Measurements of the liquid height upstream from an obstruction placed in an open-channel flow can be used to determine volume flow rate. (Such obstructions, designed and calibrated to measure rate of open-channel flow, are called weirs.) Assume the volume flow rate, \(Q\), over a weir is a function
The load-carrying capacity, \(W\), of a journal bearing is known to depend on its diameter, \(D\), length, \(l\), and clearance, \(c\), in addition to its angular speed, \(\omega\), and lubricant viscosity, \(\mu\). Determine the dimensionless parameters that characterize this problem.
Derive an expression for the drag force on a smooth object moving through compressible fluid if this force depends only on speed and size of object, and viscosity, density, and modulus of elasticity of the fluid.
A circular disk of diameter \(d\) and of negligible thickness is rotated at a constant angular speed, \(\omega\), in a cylindrical casing filled with a liquid of viscosity \(\mu\) and density \(ho\). The casing has an internal diameter \(D\), and there is a clearance \(y\) between the surfaces of
Two cylinders are concentric, the outer one fixed and the inner one movable. A viscous incompressible fluid fills the gap between them. Derive an expression for the torque required to maintain constant-speed rotation of the inner cylinder if this torque depends only on the diameters and lengths of
The time, \(t\), for oil to drain out of a viscosity calibration container depends on the fluid viscosity, \(\mu\), and density, \(ho\), the orifice diameter, \(d\), and gravity, \(g\). Use dimensional analysis to find the functional dependence of \(t\) on the other variables. Express \(t\) in the
You are asked to find a set of dimensionless parameters to organize data from a laboratory experiment, in which a tank is drained through an orifice from initial liquid level \(h_{0}\). The time, \(\tau\), to drain the tank depends on tank diameter, \(D\), orifice diameter, \(d\), acceleration of
A continuous belt moving vertically through a bath of viscous liquid drags a layer of liquid, of thickness \(h\), along with it. The volume flow rate of liquid, \(Q\), is assumed to depend on \(\mu, ho, g, h\), and \(V\), where \(V\) is the belt speed. Apply dimensional analysis to predict the form
Derive an expression for the frictional torque exerted on the journal of a bearing if this torque depends only on the diameters of journal and bearing, their axial lengths (these are the same), viscosity of the lubricant, angular speed of the journal, and the transverse load (force) on the bearing.
Tests on the established flow of six different liquids in smooth pipes of various sizes yield the following data:Make a dimensional analysis of this problem and a plot of the resulting dimensionless numbers as ordinate and abscissa. What conclusions may be drawn from the plot? Diameter Velocity
The power, \(\mathscr{P}\), required to drive a fan is believed to depend on fluid density, \(ho\), volume flow rate, \(Q\), impeller diameter, \(D\), and angular velocity, \(\omega\). Use dimensional analysis to determine the dependence of \(\mathscr{P}\) on the other variables.
The sketch shows an air jet discharging vertically. Experiments show that a ball placed in the jet is suspended in a stable position. The equilibrium height of the ball in the jet is found to depend on \(D\), \(d\), \(V\), \(ho, \mu\), and \(W\), where \(W\) is the weight of the ball. Dimensional
The diameter, \(d\), of bubbles produced by a bubble-making toy depends on the soapy water viscosity, \(\mu\), density, \(ho\), and surface tension, \(\sigma\), the ring diameter, \(D\), and the pressure differential, \(\Delta p\), generating the bubbles. Use dimensional analysis to find the
Choked-flow nozzles are often used to meter the flow of gases through piping systems. The mass flow rate of gas is thought to depend on nozzle area \(A\), pressure \(p\), and temperature \(T\) upstream of the meter, and the gas constant \(R\). Determine how many independent \(\Pi\) parameters can
A large tank of liquid under pressure is drained through a smoothly contoured nozzle of area \(A\). The mass flow rate is thought to depend on nozzle area, \(A\), liquid density, \(ho\), difference in height between the liquid surface and nozzle, \(h\), tank gage pressure, \(\Delta p\), and
Spin plays an important role in the flight trajectory of golf, ping-pong, and tennis balls. Therefore, it is important to know the rate at which spin decreases for a ball in flight. The aerodynamic torque, \(T\), acting on a ball in flight, is thought to depend on flight speed, \(V\), air density,
The power loss, \(\mathscr{P}\), in a journal bearing depends on length, \(l\), diameter, \(D\), and clearance, \(c\), of the bearing, in addition to its angular speed, \(\omega\). The lubricant viscosity and mean pressure are also important. Obtain the dimensionless parameters that characterize
The thrust of a marine propeller is to be measured during "open-water" tests at a variety of angular speeds and forward speeds ("speeds of advance"). The thrust, \(F_{T}\), is thought to depend on water density, \(ho\), propeller diameter, \(D\), speed of advance, \(V\), acceleration of gravity,
The rate \(d T / d t\) at which the temperature \(T\) at the center of a rice kernel falls during a food technology process is critical-too high a value leads to cracking of the kernel, and too low a value makes the process slow and costly. The rate depends on the rice specific heat, \(c\), thermal

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Fox And McDonald's Introduction To Fluid Mechanics 9th Edition Philip J. Pritchard, John W. Mitchell - Solutions

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