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

7.6 Experiments on flow through an orifice plate of diameter d mounted in a length of pipe of diameter D show that the pressure drop is a function of the orifice diameter, pipe diameter, fluid
For two-dimensional, incompressible, irrotational flow, the superposition of a doublet, a uniform flow, and a free vortex represents the flow around a circular cylinder with circulation. Obtain the
For two-dimensional, incompressible, irrotational flow, the superposition of a doublet and a uniform flow represents flow around a circular cylinder. Obtain the stream function and velocity potential
Consider the flow field given by ψ =ax2−ay2, where a=3 s−1. Show that the flow is irrotational. Determine the velocity potential for this flow.
A long pipe is connected to a large reservoir that initially is filled with water to a depth of 3 m. The pipe is 150mmin diameter and 6 m long. Determine the flow velocity leaving the pipe as a
Water flows steadily from a large open reservoir through a short length of pipe and a nozzle with cross-sectional area A=0 864 in 2 A well-insulated 10 kW heater surrounds the pipe. Find the
A light plane flies at 150 km hr in standard air at an altitude of 1000 m. Determine the stagnation pressure at the leading edge of the wing. At a certain point close to the wing, the air speed
Water flows under a sluice gate on a horizontal bed at the inlet to a flume. Upstream from the gate, the water depth is 1.5 ft and the speed is negligible. At the vena contracta downstream from the
A U-tube acts as a water siphon. The bend in the tube is 1 m above the water surface; the tube outlet is 7 m below the water surface. The water issues from the bottom of the siphon as a free jet at
Air flows steadily at low speed through a horizontal nozzle (by definition a device for accelerating a flow), discharging to atmosphere.The area at the nozzle inlet is 0 1m2. At the nozzle exit, the
A pitot tube is inserted in an air flow (at STP) to measure the flow speed. The tube is inserted so that it points upstream into the flow and the pressure sensed by the tube is the stagnation
3.18 The inclined-tube manometer shown has D=96 mm and d =8 mm. Determine the angle q that will give a deflection of 15 cm for a gage pressure in the tank of 25 mm water. Compare to the deflection
3.19 Water flows downward along a pipe that is inclined at 30 below the horizontal, as shown. Pressure difference pA−pB is due partly to gravity and partly to friction. Derive an algebraic
3.22 A rectangular gate (width w=2 m) is hinged as shown, with a stop on the lower edge. Determine the depth H that will tip the gate. Water H Hinge 0.55 m -Stop 0.45 m P3.22
3.23 A plane gate of uniform thickness holds back a depth of water as shown. Find the minimum weight needed to keep the gate closed. 0=30 Water w=2m P3.23 L=3m
3.25 Gates in the Poe Lock at Sault Ste. Marie, Michigan, close a channel W =34 m wide, L=360 m long, and D=10 m deep. The geometry of one pair of gates is shown; each gate is hinged at the channel
3.26 For the situation shown, find the air pressure in the tank in psi.Calculate the force exerted on the gate at the support B if the gate is 10 ft wide. Show a free body diagram of the gate with
3.17 The figure shows a sectional view through a submarine.Calculate the depth of submergence, y. Assume the specific weight of seawater is 10 0 kN m3. Atmos. pressure 74 mm Hg 60 Conventional
A piston-cylinder device contains 0 95 kg of oxygen initially at a temperature of 27 C and a pressure due to the weight of 150 kPa abs . Heat is added to the gas until it reaches a temperature of 627
2.6 For the free vortex flow the velocities are υt =5 r and υr =0.Assume that lengths are in feet or meters and times are in seconds.Plot the streamlines of this flow that pass through the points
2.5 When an incompressible, nonviscous fluid flows against a plate in a plane (two-dimensional) flow, an exact solution for the equations of motion for this flow is u=Ax, υ= −Ay,with A>0 for the
2.4 For the velocity field V =Ax2yi +Bxy2j, where A=2m−2s−1 and B=1m−2s−1, and the coordinates are measured in meters, obtain an equation for the flow streamlines. Plot the streamlines that
2.3 A fluid fills the space between two parallel disks. The lower one is stationary and the upper one rotates at a constant speed.The velocity field is given as V =eθrωz h, where the origin of the
2.2 A fluid is contained between two parallel plates spaced a distance h apart. The lower plate moves at a constant velocity U and the upper plate is stationary. Determine which of the following
2.1 Briefly state why the following flows are classified as either one-, two-, or three-dimensional, and as either steady or unsteady.The quantities a and b are constants. 1 V = [(ax+1)ei 2 V =
The label on a jar of peanut butter states its net weight is 510 g. Express its mass and weight in SI, BG, and EE units.
The air resistance (drag force) on a 200 g ball in free flight is given by FD =2×10−4V2, where FD is in newtons and V is in meters per second. If the ball is dropped from rest 500 m above the
A reducing water pipe section has an inlet diameter of 50 mm and exit diameter of 30 mm. If the steady inlet speed (averaged across the inlet area) is 2 5m s, find the exit speed.
3.27 Semicircular plane gate AB is hinged along B and held by horizontal force FA applied at A. The liquid to the left of the gate is water.Calculate the force FA required for equilibrium H= 25 ft R
3.28 Determine the pressure at A. Draw a free body diagram of the 10-ft wide gate showing all forces and the locations of their lines of action. Calculate the minimum force P necessary to keep the
3.29 Calculate magnitude and location of the resultant force of water on this annular gate. 1m Water Gate 3 md -Hub-- +1.5 m d P3.29
2.13 A flow is described by velocity field V =ai+bxj, where a=2m s and b=1 s−1. Coordinates are measured in meters.Obtain the equation for the streamline passing through point(2, 5). At t =2 s,
3.42 The timber weighs 40 lb ft3 and is held in a horizontal position by the concrete 150 lb ft3 anchor. Calculate the minimum total weight which the anchor may have. Timber 6 in. x 6 in. x 20 ft
3.43 Determine the specific weight of the cube when one-half is submerged as shown in the figure. Determine the position of the center of the cube relative to the water level when the weight is
3.44 The opening in the bottom of the tank is square and slightly less than 2 ft on each side. The opening is to be plugged with a wooden cube 2 ft on a side.(a) Determine the weight W that will
3.46 A sphere of 1-in.-radius made from material of specific gravity of SG =0 95, is submerged in a tank of water. The sphere is placed over a hole of 0.075-in.-radius in the tank bottom. When the
3.47 A rectangular container of water undergoes constant acceleration down an incline as shown. Determine the slope of the free surface using the coordinate system shown 100 0-30 P3.47 a = 3 m/s
3.40 A hydrometer is a specific gravity indicator, the value being indicated by the level at which the free surface intersects the stem when floating in a liquid. The 1.0 mark is the level when in
3.39 The barge show in the figure weighs 40 tons and carries a cargo of 30 tons. Determine the draft (distance from the water level to the bottom of the barge) in freshwater. Determine the draft when
3.38 A gate, in the shape of a quarter-cylinder, hinged at A and sealed at B, is 3 m wide. The bottom of the gate is 4.5 m below the water surface. Determine the force on the stop at B if the gate is
3.31 The gate AOC shown is 6 ft wide and is hinged along O.Neglecting the weight of the gate, determine the force in bar AB.The gate is sealed at C. V All Water 3 ft 12 ft 1 / -6 ft- 8 ft P3.31 B C
3.32 The gate shown is hinged at H. The gate is 3 m wide normal to the plane of the diagram. Calculate the force required at A to hold the gate closed 1.5 m H Water 3 m P3.32 30
3.33 A tank of water 4 m wide with a hinged gate is shown in the figure. Determine the magnitude and direction of the force at location A needed to hold the gate in the position shown and the moment
3.34 Determine the vertical force on the dam shown. Top 3 ft 3ft 3 ft 3 ft 3 ft 6 ft 33 Water 33 3 ft 3 ft 3 ft 3 ft #1# Front P3.34 Side 3 ft
3.36 Calculate the magnitude, direction and line of action of the resultant force exerted by the water on the cylindrical gate 30 ft long. P3.36 10 f
2.7 For the forced vortex flow the velocities are υt =ωr and υr =0.Plot the streamlines of this flow that pass through the points (0,1),(0,2), and (0,3). Plot the velocity as a function of radius
3.11 Consider the two-fluid manometer shown. Calculate the applied pressure difference. P1 P2 -Water- 1= 10.2 mm Carbon tetrachloride P3.11
3.12 The manometer shown contains water and kerosene. With both tubes open to the atmosphere, the free-surface elevations differ by H0 =20 0 mm. Determine the elevation difference when a pressure of
3.13 Determine the gage pressure in kPa at pointa, if liquid A has SG=1 20 and liquid B has SG=0 75. The liquid surrounding point a is water, and the tank on the left is open to the atmosphere. 0.9 m
3.14 Determine the pressure px in the bulb for the manometer readings shown Oil (SG 0.85) 30 in. U Mercury 60 in. Px P3.14
3.15 Calculate px−py for this inverted U-tube manometer 60 in. Oil(SG 0.90) 10 in. Water 20 in. Px P3.15
2.37 The cruising speed of a military airplane is 700 km/hr.Determine the Mach number of the plane as it flies at this speed from an altitude of 1 km to 15 km and plot the Mach number as a function
2.36 A seaplane flies at 80 mph in air at 45 F. The pontoons are 17 feet long. Assume that the flow over the underside of the pontoons can be treated as a flat plate and determine the Reynolds number
2.35 SAE 30 oil at 100 C flows through a 12-mm-diameter stainless-steel tube. Determine the specific gravity and specific weight of the oil. The oil discharged from the tube fills a 100-mL graduated
2.34 A supersonic aircraft travels at 2800 km/hr at an altitude of 27 km. Determine the Mach number for the airplane. The wing width(chord) is 7 m. Assume that the wing can be treated as a flat plate
2.33 Calculate the maximum capillary depression of mercury to be expected in a vertical glass tube 1 mm in diameter at 15.5 C.
3.6 A 125-mL cube of solid oak is held submerged by a tether as shown. Calculate the force of the water on the bottom surface of the cube and the tension in the tether Patm Oil D V 0.5 m SG = 0.8 t
3.5 A piston is placed on a tank filled with mercury at 20 C as shown below. A force is applied to the piston and the height of the mercury column rises. Determine the weight of the piston and the
An infinite plate is moved over a second plate on a layer of liquid as shown. For small gap width,d, we assume a linear velocity distribution in the liquid. The liquid viscosity is 0.65 centipoise
2.32 Calculate the maximum capillary rise of water (20 C) to be expected between two vertical, clean glass plates spaced 1 mm apart.
2.31 Small gas bubbles form in soda when a bottle or can is opened.The average bubble diameter is about 0.1 mm. Estimate the pressure difference between the inside and outside of such a bubble.
2.17 The variation with temperature of the viscosity of air is represented well by the empirical Sutherland correlationBest-fit values of b and S are given in Appendix A. Develop an equation in SI
2.16 A cubic element with sides 1 mm in length in a twodimensional flow is shown below. The stresses on each of the faces are given on the diagram. Determine the net force on the element and the
2.15 For each of the situations shown below, enter into the table whether the stresses on opposite sides are equal, unequal, or zeroa) A sheet of water flowing down an inclined plane.b) Water flowing
2.14 In a two-dimensional flow, a force of 20 lbf acts on a small square plate as shown below. Determine the normal stress σxx and the shear stress τyx. 20 lbf 60 0.8 ft P2.14
3.16 A rectangular tank that is open to the atmosphere is filled to a depth of 2.5 m. A U-tube manometer filled with Meriam blue manometer fluid (SG = 1.75) is connected to the tank 0.7 m above the
2.12 Consider the flow field V =axti+bj, where a=1 4 s−2 and b=1 3m s. Coordinates are measured in meters. For the particle that passes through the point x,y = 1,2 at the instant t =0, plot the
2.11 Consider the flow field given in Eulerian description by the expression V =axi+bytj, where a=0 2 s−1, b=0 04 s−2, and the coordinates are measured in meters. Derive the Lagrangian position
2.10 Consider the velocity field V =axi+by 1+ct j, where a=b=2 s−1 and c=0 4 s−1. Coordinates are measured in meters.For the particle that passes through the point x,y = 1,1 at the instant t =0,
2.9 A velocity field is given by V =a 1+bt yi+cxj , where x and y are in m and a = 0.5 s−1, b = 1 s−1, and c = 4 s−1. Determine an equation for the streamlines. Plot the streamlines that pass
2.8 Avelocity field is given byV =ax3i +bxy3j, where a=1m−2s−1 and b=1m−3s−1. Find the equation of the streamlines. Plot the streamlines that pass through the points (2, 0.25), (2, 0.5) and
2.18 The velocity distribution for laminar flow between parallel plates is given bywhere h is the distance separating the plates and the origin is placed midway between the plates. Consider a flow of
2.19 Calculate velocity gradients and shear stress for y=0, 0.2, 0.4, and 0.6 m, if the velocity profile is a quarter-circle having its center 0.6 m from the boundary. The fluid viscosity is 7
2.20 A very large thin plate is centered in a gap of width 0.06mwith different oils of unknown viscosities above and below; one viscosity is twice the other. When the plate is pulled at a velocity of
2.30 A viscometer is used to measure the viscosity of a patient’s blood. The deformation rate (shear rate)–shear stress data is shown below. Plot the apparent viscosity versus deformation rate.
2.29 The cone and plate viscometer shown is an instrument used frequently to characterize non-Newtonian fluids. It consists of a flat plate and a rotating cone with a very obtuse angle (typically θ
2.28 A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylinders. The annular gap is small so that a linear velocity profile will exist in the
2.27 Fluids of viscosities μ1 =0 1N s m2 and μ2 =0 15 N s m2are contained between two plates (each plate is 1 m2 in area). The thicknesses are h1 =0 5 mm and h2 =0 3 mm, respectively. And the upper
2.26 A piston-cylinder combination is shown in the figure. The piston velocity is 6 m/s and the oil has a kinematic viscosity of 2.8 × 10−5m2/s and a specific gravity of 0.92. Determine the power
2.25 The fluid drive shown transmits a torque T for steadystate conditions (ω1 and ω2 constant). Derive an expression for the slip ω1−ω2 in terms of T, μ,d, and h. For values d =6 in , h=0 2
2.24 A block 0.1 m square, with 5 kg mass, slides down a smooth incline, 30 below the horizontal, on a film of SAE 30 oil at 20 C that is 0.20 mm thick. If the block is released from rest at t =0,
2.23 Crude oil at 20 C fills the space between two concentric cylinders 250 mm high and with diameters of 150 mm and 156 mm. Find the torque is required to rotate the inner cylinder at 12 r min, the
2.22 A cylinder 8 in. in diameter and 3 ft long is concentric with a pipe of 8.25 in. i.d. Between the cylinder and pipe there is an oil film.Find the force required to move the cylinder along the
2.21 A vertical gap 25 mm wide of infinite extent contains oil of specific gravity 0.95 and viscosity 2 4 Pa s. A metal plate 1 5m×1 5m×1 6 mm weighing 45 N is to be lifted through the gap at a
3.48 Cast iron or steelmolds are used in a horizontal-spindlemachine to make tubular castings such as liners and tubes. A charge of molten metal is poured into the spinning mold. The radial
3.45 A balloon has a weight of 2.2 kN, not including gas, and a gasbag capacity of 566 m3. At the ground, it is partially inflated with 445 N of helium. Determine how high the balloon will rise.
3.41 A cylindrical can 75 mm in diameter and 150 mm high is filled with water to a depth of 80 mm. The can weighs 1.1 N. Determine the depth the can will sink when placed in water.
3.37 A hemispherical shell 1.2 m in diameter is connected to the vertical wall of a tank containing water. If the center of the shell is 1.8 m below the water surface, determine the vertical and
3.24 A vertical rectangular gate 2.4 m wide and 2.7 m high is subjected to water pressure on one side, the water surface being at the top of the gate. The gate is hinged at the bottom and is held by
3.21 Compare the height due to capillary action of water exposed to air in a circular tube of diameter D=0 5 mm with that between two infinite vertical parallel plates of gap a=0 5 mm.
3.20 The elevation of Tucson, AZ, is about 500 m, and Mt. Lemmon is about 2000 m higher. Assuming standard atmospheric conditions in Tucson, determine the pressure at the top of Mt. Lemmon
3.10 A water tank filled to a depth of 16 ft has a 1 in. × 1 in. inspection cover at the base. The cover is held in place by a plastic bracket that can withstand a load of 9 lbf. Determine whether
3.9 The compressibility of sea water has a significant effect on the variation of density and pressure with depth. The density at sea level is 1020 kg/m3 and the pressure is atmospheric. Determine
3.8 An open tank contains water to a depth of 6 ft and a layer of oil on top of the water that is 3 ft deep. Determine the pressure at the bottom of the tank.
3.7 Calculate the absolute and gage pressure in an open tank of crude oil 2.4 m below the liquid surface. If the tank is closed and pressurized to 130 kPa, what are the absolute and gage pressures at
3.4 For a car parked at an altitude of 7000 ft, the tire is at atmospheric temperature and the tire pressure is indicated as 31 psi. Determine the absolute and gage pressures for the tire when the
3.3 Ear “popping” occurs as air leaves the inner ear rapidly to accommodate a sudden change in the outside pressure. Determine the change in pressure if your ears “pop” when you are in a car
3.2 Atmospheric pressure decreases with altitude, which affects the boiling point of water and, consequently, the cooking times for some foods. Determine and plot the boiling temperature of water
3.1 At standard atmospheric conditions, a gage measures the pressure in a tank as −2.1 psi. Determine the absolute pressure in psia and kPa.
Create a graph showing the capillary rise or fall of a column of water or mercury, respectively, as a function of tube diameter D.Find the minimum diameter of each column required so that the height

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