Questions and Answers of Fox And McDonald S Introduction To Fluid Mechanics

6.36 Consider an air flow over a flat wall with an upstream velocity of 6 m s. There is a narrow slit through which air is drawn in at a flow rate of 0 2m3 s per meter of width. Represent the flow as
6.35 Consider the flow field represented by the velocity potentialϕ=Ax+Bx2−By2, where A=1m s−1, B=1m−1 s−1, and the coordinates are measured in meters. Obtain expressions for the velocity
6.34 A flow field is represented by the stream function ψ =x5−15x4y2 +15x2y4−y6. Find the corresponding velocity field. Show that this flow field is irrotational and obtain the potential
6.20 Determine the flow rate through the pipeline shown in the figure and the pressures at A, B, C, and D. 20 ft 5' C B 12' -6 in. d D 2 in. d Water A P6.20
6.19 The water jet is directed upward through a 3-in.-diameter nozzle under a head of 10 ft as shown in the figure. Determine the height h of the liquid in the pitot tube. Determine the
6.4 Water flows in a circular channel as shown in the figure. The velocity is 12 m/s and uniform across the channel. The pressure is 120 kPa at the centerline (point 1). Determine the pressures at
6.3 For a water flow in a pipe, determine the pressure gradient required to accelerate the water at 20 ft/s2 for (a) a horizontal pipe,(b) a vertical pipe with the water flowing upward, and (c) a
6.2 The velocity field for a two-dimensional downward flow of water against a plate is given by V =Axi−Ayj. Plot the pressure gradient along the centerline and determine the pressure gradient
6.1 An incompressible frictionless flow field is given by V = Ax+By i + Bx−Ay j where A = 2 s−1 and B = 2 s−1 and x and y are in meters. The fluid is water and g =gj . Determine the magnitude
A viscous liquid fills the annular gap between vertical concentric cylinders. The inner cylinder is stationary, and the outer cylinder rotates at constant speed. The flow is laminar. Simplify the
A liquid flows down an inclined plane surface in a steady, fully developed laminar film of thickness h. Simplify the continuity and Navier–Stokes equations to model this flow field. Obtain
The velocity field V =Axi−Ayj represents flow in a “corner,” as shown in Example 5.4, where A=0 3 s−1 and the coordinates are measured in meters. A square is marked in the fluid as shown at t
A viscometric flow in the narrow gap between large parallel plates is shown. The velocity field in the narrow gap is given by V =U y h i, where U =4mm s and h=4 mm. At t =0 line segments ac and bd
Consider flow fields with purely tangential motion (circular streamlines): Vr =0 and Vθ =f r . Evaluate the rotation, vorticity, and circulation for rigid-body rotation, a forced vortex. Show that
Consider two-dimensional, steady, incompressible flow through the plane converging channel shown. The velocity on the horizontal centerline (x axis) is given by V =V1 1+ x L i. Find an expression for
6.5 A tornado moves in a circular pattern with a vertical axis. The wind speed is 200 mph, and the diameter of the tornado is 200 ft.Determine the radial pressure gradient. If it is desired to model
6.6 The y component of velocity in a two-dimensional incompressible flow field is given by v = −Axy, where v is in m/s, the coordinates are measured in meters, and A = 1/m s. There is no velocity
6.18 Consider frictionless, incompressible flow of air over the wing of an airplane flying at 200 km hr. The air approaching the wing is at 65 kPa and −10 C. At a certain point in the flow, the
6.16 The water flow rate through the siphon is 5 L s, its temperature is 20 C, and the pipe diameter is 25 mm. Compute the maximum allowable height, h, so that the pressure at point A is above the
6.15 Water flows steadily through the vertical 1-in.-diameter pipe and out the 0.5 in. in diameter nozzle to the atmosphere. Determine the minimum gage pressure required at section 1 to produce a
6.14 Determine the relation between A1 and A2 so that for a flow rate of 0:28 m3/s the static pressure will be the same at sections 1 and 2.Determine the manometer reading for this condition and
6.13 Water flows in a pipeline. At a point in the line where the diameter is 7 in., the velocity is 12 fps and the pressure is 50 psi. At a point 40 ft away the diameter reduces to 3 in. Calculate
6.12 Determine the height H (m) and the pressure p (kPa) for the water flow in the system shown in the figure. 175 mm- -125 mm d Z100 mm d P6.12 Hg (13.57) 75 mm d H
6.11 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
6.9 In a pipe 0.3 m in diameter, 0 3m3 s of water are pumped up a hill. On the hilltop (elevation 48), the line reduces to 0.2 m diameter.If the pump maintains a pressure of 690 kPa at elevation 21,
6.8 Determine the dynamic and stagnation pressure of water flowing at a speed of 25 ft/s. Express your answer in psi, kPa, and inches of mercury.
6.7 Air flows in a two-dimensional bend of width w in a duct as shown in the figure. The velocity profile is similar to a free vortex(irrotational) profile given by Vθ =cr, where c is a constant.
Given the velocity field for steady, incompressible flow in a corner (Example 2.1), V =Axi−Ayj, with A=0 3 s−1, determine the stream function that will yield this velocity field. Plot and
An inclined-tube reservoir manometer is constructed as shown. Derive a general expression for the liquid deflection, L, in the inclined tube, due to the applied pressure difference, Δp. Also obtain
4.4 The velocity field in the region shown is given by V = aj+byk where a=10m s and b=5 s−1. For the 1 m× 1 m triangular control volume (depth w=1 m perpendicular to the diagram), an element of
4.5 A0.3mby 0.5mrectangular air duct carries a flowof 0 45 m3 s at a density of 2 kg m3. Calculate the mean velocity in the duct. If the duct tapers to 0.15 m by 0.5 m size, determine the mean
4.6 Across a shock wave in a gas flow there is a change in gas density ρ. If a shock wave occurs in a duct such that V =660 m s and ρ=1 0 kg m3 before the shock and V =250 m s after the shock,
4.7 Calculate the mean velocities for these two-dimensional velocity profiles if υc =3m s Parabola, Circle Parabola Equal Equal (a) (b) (c) (d) (e) P4-7
4.8 Fluid passes through this set of thin closely spaced blades.Determine flow rate q is required for the velocity V to be 10 ft s. 2 ft Radial line 30 V P4.8
4.9 A pipeline 0.3 m in diameter divides at a Y into two branches 200 mm and 150 mm in diameter. If the flow rate in the main line is 0 3m3 s and the mean velocity in the 200-mm pipe is 2 5m s,
4.10 Find V for this mushroom cap on a pipeline. 3 m/s- 1 md 45 18 mr P4.10 2 mr
4.11 You are trying to pump stormwater out of your basement during a storm. The basement is 20 ft × 30 ft and the pump extracts 27.5 gpm. The water level in the basement is dropping 4
4.12 A cylindrical tank, of diameter D=50 mm, drains through an opening, d =5 mm., in the bottom of the tank. The speed of the liquid leaving the tank is approximately V = 2gy where y is the height
4.13 A 100-mm nozzle is bolted with 6 bolts to the flange of a 300-mm-diameter horizontal pipeline and discharges water into the atmosphere. Calculate the tension load on each bolt when the gage
4.3 A block of copper of mass 5 kg is heated to 90 C and then plunged into an insulated container containing 4 L of water at 10 C. Find the final temperature of the system. For copper, the specific
Normal blood pressure for a human is 120 80 mm Hg. Bymodeling a sphygmomanometer pressure gage as a U-tube manometer, convert these pressures to psig.
Water flows through pipes A and B. Lubricating oil is in the upper portion of the inverted U. Mercury is in the bottom of the manometer bends. Determine the pressure difference, pA−pB, in units of
The maximum power output capability of a gasoline or diesel engine decreases with altitude because the air density and hence the mass flow rate of air decreases. A truck leaves Denver (elevation 5280
The inclined surface shown, hinged along edge A, is 5 m wide. Determine the resultant force, FR, of the water and the air on the inclined surface.
The door shown in the side of the tank is hinged along its bottom edge. A pressure of 100 psfg is applied to the liquid free surface.Find the force, Ft , required to keep the door closed
The gate shown is hinged at O and has constant width, w=5 m. The equation of the surface is x =y2a, where a=4 m. The depth of water to the right of the gate is D=4 m. Find the magnitude of the force,
A hot air balloon (approximated as a sphere of diameter 50 ft) is to lift a basket load of 600 lbf. To what temperature must the air be heated in order to achieve liftoff?
As a result of a promotion, you are transferred from your present location. You must transport a fish tank in the back of your minivan. The tank is 12 in ×24 in × 12 in. How much water can you
A cylindrical container, partially filled with liquid, is rotated at a constant angular speed, ω, about its axis as shown in the diagram. After a short time there is no relative motion; the liquid
4.1 A hot air balloon with an initial volume of 2600 m3 rises from sea level to 1000 m elevation. The temperature of the air inside the balloon is 100 C at the start and drops to 90 C at 1000 m.
4.2 A fully loaded Boeing 777-200 jet transport aircraft has a mass of 325,000 kg. The pilot brings the 2 engines to full takeoff thrust of 450 kN each before releasing the brakes. Neglecting
4.14 The water flow rate through the vertical bend shown in the figure is 2.83 m3/s. Calculate the magnitude, direction, and location of the resultant force of the water on the pipe bend. 34.5 kPa
4.15 Water flows through a tee in a horizontal pipe system as shown in the figure. The incoming velocity is 15 ft/s, the pressure is 20 psi, and the pipe diameter is 12 in. Each branch of the tee is
4.29 A solid-fuel rocket motor is fired on a test stand. The combustion chamber is circular, with 100 mm diameter. Fuel, of density 1660 kg/ = m3, burns uniformly at the rate of 12.7 mm/s.
4.30 Crude oil SG=0 95 from a tanker dock flows through a pipe of 0.25 m diameter in the configuration shown. The flow rate is 0 58 m3 s, and the gage pressures are shown in the diagram. Determine
4.31 Calculate the torque about the pipe’s centerline in the plane of the bolted flange that is caused by the flow through the nozzle. The nozzle centerline is 0.3 m above the flange centerline.
4.32 A fire truck is equipped with a 66 ft long extension ladder which is attached at a pivot and raised to an angle of 45 . A 4-in.-diameter fire hose is laid up the ladder and a 2-in.-diameter
4.33 The lawn sprinkler shown in the figure rotates in the horizontal plane. A water flow of 15 L/min of water enters the center vertically and discharges in the horizontal plane from the two jets.
4.34 A water flow rate of 4 L/min enters the lawn sprinkler shown in the figure in a vertical direction. The velocity of the jets leaving the nozzles is 17 m/s relative to the sprinkler arm and
4.35 The impeller of a radial water pump has an outer diameter of 10 in. and rotates at 1600 rpm. A water flow of 1200 gpm enters the impeller axially and leaves at an absolute velocity of 90 ft/s
4.36 The simplified lawn sprinkler shown rotates in the horizontal plane. At the center pivot, Q=15 L min of water enters vertically.Water discharges in the horizontal plane from each jet. If the
4.37 Water flows at the rate of 0 15 m3 s through a nozzle assembly that rotates steadily at 30 rpm. The arm and nozzle masses are negligible compared with the water inside. Determine the torque
4.38 A turbine is supplied with 0 6m3 s of water from a 0.3 m diameter pipe; the discharge pipe has a 0.4 m diameter. Determine the pressure drop across the turbine if it delivers 60 kW.
4.28 A sled used to test rockets is slowed lowering a scoop into a water trough. The scoop is 0.3 m wide and deflects water through 150 . The mass of the sled is 8000 kg. At the initial speed, it
4.27 A pressurized tank of water is mounted on a cart as shown.A jet issues from a nozzle in the tank at a constant speed and propels the cart along a horizontal track. The initial mass of the cart
4.16 Water flows steadily through a fire hose and nozzle. The hose is 75-mm-ID, and the nozzle tip is 35-mm-ID; water gage pressure in the hose is 510 kPa, and the stream leaving the nozzle is
4.17 Water is flowing steadily through the 180 elbow shown. At the inlet to the elbow, the gage pressure is 103 psi. The water discharges to atmospheric pressure. Assume that properties are uniform
4.18 Water flows steadily through the nozzle shown, discharging to atmosphere. Calculate the horizontal component of force in the flanged joint. Indicate whether the joint is in tension or
4.20 The lower tank weighs 224 N, and the water in it weighs 897 N. If this tank is on a platform scale, determine the weight that will register on the scale beam. 1.8 m 6.0 m 1.8 m P4.20 - 75 mm d
4.21 A fluid with a density of 1040 kg/m3 density flows steadily through the rectangular box shown in the figure. The areas are A1 = 0:046 m2, A2 = 0:009 m2, and A3 = 0:056 m2, and the velocities are
4.22 An incompressible fluid flows steadily through the twodimensional reducing bend shown in the figure. The width of the bend is 1 m. The velocity profile is linear at section 1 and uniform at
4.23 An incompressible fluid with a density of 850 kg/m3 flows steadily in the entrance region of a circular tube of radius R = 75 mm. The flow rate is Q = 0.1 m3/s. The velocity profile entering the
4.24 A water flow from a nozzle impinges on a moving vane as shown in the figure. The water leaves the nozzle at 30 m/s, and the exit area of the nozzle is 0.004 m2. The vane moves away from the
4.25 A inboard jet boat takes in water through side vents and ejects it through a nozzle at the stern. The drag on the boat is given by Fdrag =kV2, where V is the boat speed and k is a constant that
4.26 The cart in the figure below is accelerated along a level track by a jet of water that strikes the curved vane. Determine the time it takes to accelerate the cart from rest to U 10 m/s. U = 10.0
4.39 Air is drawn from the atmosphere into a turbomachine. At the exit, conditions are 500 kPa gage and 130 C. The exit speed is 100 m s and the mass flow rate is 0 8 kg s. Flow is steady and there
Consider a one-dimensional radial flow in the rθ plane, given by Vr =f r and Vθ =0. Determine the conditions on f r required for the flow to be incompressible.
A tank of 0 1m3 volume is connected to a high-pressure air line; both line and tank are initially at a uniform temperature of 20 C.The initial tank gage pressure is 100 kPa. The absolute line
5.13 A flow field given by V =xy2 i− 1 3y3j +xyk Determine(a) whether this is a one-, two-, or three-dimensional flow and(b) whether it is a possible incompressible flow. Determine the acceleration
5.14 The velocity field within a laminar boundary layer is represented by the expression V =AU yx1 2 i+AU 4y2 x3 2 j, where A = 141 m-1/2 and the free stream velocity is U = 0.240 m/s. Demonstrate
5.15 A 4 m diameter tank is filled with water and then rotated at a rate of ω=2π 1−e−t rad s. At the tank walls, viscosity prevents relative motion between the fluid and the wall. Determine the
5.16 A fluid flows parallel to the x axis with a constant shear rate given by du dy=A where A = 0.1 s−1. Determine an expression for the velocity field V. Determine the rate of rotation and the
5.17 The velocity field given by V =Axi−Ayj represents flow in a rectangular corner. Evaluate the circulation around the unit square with corners at (x,y) = (1,1), (1,2), (2,2) and (2,1) for the
5.18 Fluid passes through the set of thin, closely spaced blades at a velocity of 3 m s. Determine the circulation for the flow. D=0.6 m P5.18 30
5.19 A velocity field is given by V =2i−4x j m s. Determine an equation for the streamline. Calculate the vorticity of the flow.
5.20 The flow between stationary parallel plates separated by distance 2b is driven by a pressure gradient. The velocity field is given by u=U 1−y b2, where U is the centerline velocity and y is
5.21 As a weather reconnaissance airplane flies through a cold front, the outside air temperature instrument measures a rate of change of – 0.7 F/min. The air speed is 400 mph and the airplane is
5.22 Consider a steady, laminar, fully developed incompressible flow between two infinite parallel plates as shown. The flow is due to a pressure gradient applied in the x direction. Given that V V z
5.12 The velocity in a parallel one-dimensional flow in the positive x direction varies linearly from zero at y = 0 to 30 m/s at y = 1.5 m.Determine the stream function. Calculate the volume flow
5.11 Determine the stream function for the flow field specified by u = 4y; = −4x, where x and y are in meters and u and v are in m/s. Plot the streamlines passing between the points (x,y) =
5.1 Determine which of the following velocity distributions are possible three-dimensional incompressible flows.(a) u=2y2 +2xz; υ= −2xy+6x2yz; w=3x2z2 +x3y4(b) u=xyzt; υ= −xyzt2; w=z2
5.2 Determine which of the following flow fields represent a possible incompressible flow.(a) Vr =U cos θ; Vθ = −U sin θ(b) Vr = −q 2πr; Vθ =K 2πr(c) Vr =U cos θ 1− a r 2 ; Vθ = −U
5.3 The x component of velocity in a steady, incompressible flow field in the xy plane is u=A x, where A=2m2 s, and x is measured in meters. Find the simplest y component of velocity for this flow
5.4 The velocity components for an incompressible steady flow field are u=A x2 +z2 and v=B xy+yz . Determine the z component of velocity for steady and for unsteady flow.
5.5 For the laminar boundary layer flow of an incompressible fluid, the x component of velocity can be approximated as a linear variation from u = 0 at the surface to the u = U at the boundary-layer
5.6 The x component of velocity for a flow field is given as u=Ax2y2 where A = 0.3 m−3 s−1 and x and y are in meters. Determine the y component of velocity for a steady incompressible flow.
5.7 A viscous liquid is sheared between two parallel disks of radius R, one of which rotates while the other is fixed. The velocity field is purely tangential, and the velocity varies linearly with z
5.8 Determine the stream function that will yield the velocity field V =2y 2x+1 i+ x x+1 −2y2 j V
5.9 The stream function for a certain incompressible flow field is given by the expression ψ = −Ur sin θ +qθ 2π. Obtain an expression for the velocity field. Find the stagnation point(s) where
5.10 An incompressible frictionless flow field is specified by the stream function ψ =5Ax−2Ay where A = 2 m/s, and x and y are in meters. Determine the velocity field. Plot the streamlines passing

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