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

Determine the transmission angle and the mechanical advantage of the four-bar linkage in the posture shown. What type of four-bar linkage is this?Figure P1.32 RAO2 = 20mm, RBA = 70mm, RBO4 = 90mm,
Determine a suitable set of link lengths for a slider-crank linkage such that the stroke will be 500 mm and the advance-to-return ratio will be 1.8.
The rocker of a crank-rocker four-bar linkage is required to have a length of 6 in and swing through a total angle of 30◦. Also, the advance-to-return ratio of the linkage is required to be 1.75.
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.Figure P1.29
Determine the mechanical advantage of the four-bar linkage in the posture shown.Figure P1.27 O2O4 = 120 mm, O2A = 60 mm, AB = 100 mm, and O4B = 130 mm.
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.Rolling contact+Figure P1.25
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.Rolling contact Figure P1.23
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.Rolling without slip Figure P1.22
Determine the mobility of the mechanism. Number each link and label the lower pairs and the higher pairs. Identify a suitable input, or inputs, for the mechanism.
If the handle of the differential screw in Fig. 1.11 is turned 15 revolutions clockwise, how far and in what direction does the carriage move?
Show how the linkage of Fig. 1.15b can be used to generate a sine wave.
Plot the complete coupler curve of the Roberts’linkage shown in Fig. 1.24b. Use AB = CD =AD = 2.5 in and BC = 1.25 in.
Devise a practical working model of the drag-link linkage.
The mobility of the mechanism is m = 1. Use the Kutzbach criterion to determine the number of lower pairs and the number of higher pairs. Is the wheel rolling without slipping, or rolling and
Does the Kutzbach criterion provide the correct result for this mechanism? Briefly explain why or why not.Figure P1.12
Determine the number of links, the number of lower pairs, and the number of higher pairs. Treat rolling contact to mean rolling with no slipping.Using the Kutzbach criterion, determine the mobility.
Use the Kutzbach criterion to detemine the mobility of the mechanism. Clearly number each link, and label the lower pairs and higher pairs.Figure P1.10
Devise a crank-rocker four-bar linkage, as in Fig. 1.14c, having a rocker angle of 60◦. The rocker length is to be 0.50 m.
6.30 Compressed air is used to accelerate water from a tube.Neglect the velocity in the reservoir and assume the flow in the tube is uniform at any section. At a particular instant, it is known that
6.29 Sketch the energy grade lines (EGL) and hydraulic grade lines(HGL) for the two systems shown in the figure below Turbine P6.29 Pump
6.27 Sketch the energy (EGL) and hydraulic (HGL) grade lines for the system shown in the figure below 5' C B 20 ft D -6 in. d 2 in. d Water A P6.27 12'
6.26 Water flows at low speed through a circular tube with inside diameter of 2 in. A smoothly contoured body of 1.5 in. diameter is held in the end of the tube where the water discharges to
6.25 An air-supported structure is used to enclose a set of tennis courts. It is a semi-cylinder structure with a diameter of 50 ft and a length of 50 ft. The blowers used to inflate the structure
6.24 A horizontal jet of air with 0.4-in.-diameter and a speed of speed 225 ft/s strikes a 7.5 in. diameter stationary vertical disk. A manometer is connected to a hole at the center of the disk.
6.23 Two water reservoirs at a 30 m elevation each have discharge pipes that are connected at a “tee” junction. One pipe has a 200-mm diameter and the other a 150-mm diameter. The outlet pipe
6.22 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 gpm. Calculate the minimum static pressure
6.21 A smoothly contoured nozzle, with outlet diameter d =20 mm, is coupled to a straight pipe by means of flanges. Water flows in the pipe, of diameter D=50 mm, and the nozzle discharges to the
6.31 The velocity field for a two-dimensional flow is V = Ax−By ti− Bx+Ay tj where A = 1 s−2 B = 2 s−2, t is in seconds, and the coordinates are measured in meters. Determine whether this is
6.32 A flow field is characterized by the stream function ψ =Axy, where A=2 s−1 and the coordinates are measured in feet. Verify that the flow is irrotational and determine the velocity potential
6.33 The stream function of a flow field is =Ax3−Bxy2 where A= 1m−1 s−1 and B= 3m−1 s−1, and the coordinates are measured in meters. Find expressions for the velocity field, the velocity
4.40 Transverse thrusters are used to make large ships fully maneuverable at low speeds without tugboat assistance. A transverse thruster consists of a propeller mounted in a duct; the unit is then
4.41 All major harbors are equipped with fire boats for extinguishing ship fires. A 75-mm-diameter hose is attached to the discharge of a 11 kW pump on such a boat. The nozzle attached to the end of
4.42 A pump draws water from a reservoir through a 150-mmdiameter suction pipe and delivers it to a 75-mm-diameter discharge pipe. The end of the suction pipe is 2 m below the free surface of the
6.39 A flow field is formed by combining a uniform flow in the positive x direction with U = 10 m/s, and a counterclockwise vortex with strength K = 16π m2/s located at the origin. Determine the
6.38 The flow in a corner with an angle α can be described in radial coordinates by the stream function as ψ =Arπαsinπθα. Determine the velocity potential for the flow and plot streamlines for
6.37 A source with a strength of q=3π m2 s and a sink with a strength of q=π m2 s are located on the x axis at x = −1 m and x = 1 m, respectively. Determine the stream function and velocity
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

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