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

8.54 An air flow of 3.65 m3/s at atmospheric pressure flows in a 0.5 m diameter duct. A 0.35 m diameter ASME long radius nozzle and a water manometer is used to measure the flow rate. Determine the
8.53 An 8 in. diameter water pipe has a 5.2 in. diameter ASME longradius nozzle installed for flow metering. The mercury-water manometer used to measure the pressure difference reads 3.2 in.mercury.
8.52 A 12 in. × 6 in. Venturi meter is installed in a horizontal waterline.The pressure gages read 30 and 20 psi. Calculate the flow rate for a water temperature of 68 F and the head loss between
8.51 A 75-mm-diameter orifice with D and D/2 taps is used to measure the flow rate of 65 C water in a 150-mm-ID pipe. Determine the pressure difference for a flow rate of 20 L/s.
8.48 A new pump is required for the water supply system of a highrise office building. The system requires 0.06 m3/s of water pumped to a reservoir at the top of the tower 340 mabove the street. City
8.46 Determine the diameter of a 175 m long pipe with a roughness of 2.5 mm that will provide a flow of 0.075 m3 s with a 500 kPa pressure drop.
8.45 Determine the minimum size smooth rectangular duct with an aspect ratio of 3 that will pass 1 m3 s of 10 C air with a head loss of 25 mm of water per 100 m of duct.
8.43 An industrial plant requires a water flow rate of 5.7 m3/min.The gage pressure in the water main, located in the street 50 m from the plant, is 800 kPa and the gage pressure required in the
8.42 A 4-ft-diameter cast iron pipeline 4 miles long connects two reservoirs with surface elevations of 500 and 300 ft. It is proposed to increase the flow rate through the line by installing a
8.41 Determine the diameter of a smooth steel pipe that will carry 50 cfs of water between a reservoir with a surface at an elevation of 250 ft and one at 100 ft that are located 2 miles apart
8.40 Two water tanks are connected by a horizontal pipeline. The first tank has a square-edged outlet 3 m below the surface that is connected to a 50-mm-diameter PVC pipe. At 15 m from the tank the
8.39 Hydraulic mining is to be done using water from a lake located 300 m above the mine site. A 900 m long fire hose with an inside diameter of 75 mm and a relative roughness of 0.01 will be
8.38 Water flows steadily in a 125-mm-diameter cast-iron pipe 150 m long. The pressure drop between sections and is 150 kPa, and section is located 15 m above section . Find the volume flow rate.
8.37 Determine the flow rate (gpm) of 0 C water that will be produced in a 75-mm-diameter pipe that is 200 m long for a pressure drop of 425 kPa. The pipe roughness element size is 2.5 mm.
8.36 A fire hose and nozzle assembly is being designed to deliver 0.75 ft3/s of water. The hose is 3 in. in diameter with a relative roughness of 0.004. The fire hose is made up of four 60 ft
8.34 The exhaust duct for a clean room test chamber is 150-mm in diameter and 7 m long. The duct originally had a square-edge entrance, but it was replaced by a well-rounded entrance. The pressure in
8.32 Air at standard conditions flows through a 75 mm diameter circular duct that has a sudden expansion to 225 mmdiameter. The pressure downstream is 5 mm of water higher than that
8.31 Water flows through a 2-in.-diameter tube that suddenly contracts to 1 in. diameter. The pressure drop across the contraction is 0.5 psi. Determine the volume flow rate.
8.30 A 150-mm-diameter horizontal pipe discharges a 0.05 m3/s flow of water to the atmosphere through a smooth nozzle with a tip diameter of 75 mm diameter. The nozzle loss coefficient is
8.29 Two reservoirs are connected by three clean cast-iron pipes in series, L1 = 600 m, D1 = 0.3 m, L2 = 900 m, D2 = 0.4 m, L3 = 1500 m, and D3 = 0.45 m. The flow rate is 0.11 m3/s of water at 15
8.28 Water flows in a smooth 0.2 m diameter pipeline that is 65 m long. The Reynolds number is 106. Determine the flow rate and pressure drop. After many years of use, minerals deposited on the pipe
8.27 A reservoir at 300 ft elevation has a 6-in.-diameter discharge pipe located 50 ft below the surface. The pipe is 600 ft long and drops in elevation to 150 ft where the flow discharges to the
8.26 A smooth copper tube 50 ft long and 2 1/2 in.-diameter carries a water flow at 60 F of 120 gpm. Determine the pressure drop and head loss for a 50 ft length of tube.
8.25 Water flows in a horizontal 75 mm diameter pipe at an average speed of 5 m/s. The pressure at the pipe inlet is 275 kPa gage and the outlet is at atmospheric pressure. (a) Determine the head
8.24 A pipe runs for an elevation of 45 m to an elevation of 115 m.The inlet pressure is 8.5 MPa and the head loss is 6.9 kJ/kg. Calculate the outlet pressure for (a) the inlet at the 45 m elevation
8.23 Using Eqs. 8.24 and 8.27, evaluate the kinetic energy coefficientα for turbulent power law velocity profiles with n = 1/7 and 1/10.
8.22 Determine the kinetic energy coefficient α for fully developed laminar flow in a circular tube.
8.20 For a turbulent flow of a fluid in 0.6 m diameter pipe, the velocity 0.15 m from the wall is 2.7 m/s. Estimate the wall shear stress using the 1/7th expression for the velocity profile.
8.19 A fully developed turbulent flow of a fluid in a 3 in. diameter horizontal pipe has a static pressure difference measured between two sections 15 ft apart of 750 psi. Calculate the wall shear
8.17 A fluid of specific gravity 0.90 flows at a Reynolds number of 1500 in a 0.3-m-diameter pipeline. The velocity 50 mm from the wall is 3 m s. Calculate the flow rate and the velocity gradient at
8.16 Determine the largest diameter of pipeline that may be used to carry 100 gpm of jet fuel (JP-4) at 59 F if the flow is to be laminar.
8.15 Oil with a viscosity 1.2 Pa-s and a density of 820 kg/m3 flows in a 0.3 mdiameter pipe. The flow is fully established and the velocity at the center of is 4.5 m/s. Verify that the flow is
8.14 Carbon dioxide flows in a 50-mm-diameter pipe at a velocity of 1 5m s, temperature 66 C, and absolute pressure 50 kPa. Determine whether the flow is laminar or turbulent. If the temperature is
8.13 Determine the maximum flow rate (kg/s) and corresponding pressure gradient (Pa/m) for which laminar flow would occur for water, SAE 10W oil, and glycerin. The fluids are at 20 C. Draw some
8.12 Water at 20 C flows in a 1.3 cm diameter pipe that is 30 m long and discharges to the atmosphere. The pressure at the entrance to the pipe is 0.82 kPa gage. Determine the mass flow rate and
8.10 There is a fully developed laminar flow of air between parallel plates. The upper plate moves at 5 ft/s and the spacing between the plates is a = 0.1 in. (a) Assume that the air is
8.8 Two immiscible fluids are of equal thickness are contained between infinite parallel plates separated by a distance 2 h. The lower plate is stationary and the upper plate moves at constant speed
8.7 A sealed journal bearing is formed from concentric cylinders.The inner and outer radii are 25 and 26 mm, the journal length is 100 mm, and it turns at 2800 rpm. The gap is filled with oil in
8.6 A fully developed and laminar flow of oil occurs between parallel plates. The pressure gradient creating the flow is 1.25 kPa/m of length and the channel half-width is 1.5 mm. Calculate the
8.5 A horizontal laminar flow occurs between two infinite parallel plates that are 0.3 m apart. The velocity at the centerline is 2.7 m/s.Determine the flow rate through a section 0.9 m wide, the
8.3 An incompressible fluid flows between two infinite stationary parallel plates. The velocity profile is given by u=umax Ay2 +By+C , where A, B, and C are constants and y is measured upward from
8.2 Determine the maximum flow rate of air at laminar conditions in a 4-in.-diameter pipe at an absolute pressure of 30 psia and 100 F?Determine the maximum flow rate when (a) the pressure is raised
8.1 For incompressible flow in a circular tube, derive expressions for Reynolds number in terms of (a) volume flow rate and tube diameter and (b) mass flow rate and tube diameter.
A centrifugal pump has an efficiency of 80 percent at its design-point specific speed of 2000 (units of rpm, gpm, and feet). The impeller diameter is 8 in. At design-point flow conditions, the volume
The drag of a sonar transducer is to be predicted, based on wind tunnel test data. The prototype, a 1-ft diameter sphere, is to be towed at 5 knots (nautical miles per hour) in seawater at 40 F. The
When a small tube is dipped into a pool of liquid, surface tension causes a meniscus to form at the free surface, which is elevated or depressed depending on the contact angle at the
The pressure drop, Δρ, for steady, incompressible viscous flow through a straight horizontal pipe depends on the pipe length, l, the average velocity, V, the fluid viscosity, μ, the pipe diameter,
Use the Kutzbach criterion to determine the mobility of the mechanism.Figure P1.6
Find the mobility of each mechanism.
Plot the complete path of coupler point C.Figure P1.4
A crank-rocker linkage has a 100-mm frame, a 25-mm crank, a 90-mm coupler, and a 75-mm rocker. Draw the linkage and find the maximum and minimum values of the transmission angle. Locate both toggle
The link lengths of a planar four-bar linkage are 1 in, 3 in, 5 in, and 5 in. Assemble the links in all possible combinations and sketch the four inversions of each. Do these linkages satisfy
Sketch at least six different examples of the use of a planar four-bar linkage in practice. These can be found in the workshop, in domestic appliances, on vehicles, on agricultural machines, and so
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 P1.21
Find the advance-to-return ratio of the linkage of Prob. 1.3.
Sketch a planar linkage with only revolute joints and a mobility of m = 1 that contains a quaternary link. How many distinct variations of this linkage can you find?
Use the Kutzbach criterion to detemine the mobility of the mechanism. Clearly number each link, and label the lower pairs (j1 joints) and higher pairs (j2 joints).1 1Figure P1.8
Determine the number of links, the number of lower pairs, and the number of higher pairs. Use the Kutzbach criterion to determine the mobility of the mechanism. Is the answer correct? Briefly
A crank-rocker four-bar linkage is required to have an advance-to-return ratio Q = 1.2. The rocker is to have a length of 2.5 in and oscillate through a total angle of 60◦. Determine a suitable set
Determine the advance-to-return ratio for the slider-crank linkage with the offsete. Also, determine in which direction the crank should rotate to provide quick return.
Find θ2 and θ4 corresponding to a dead-center posture. Is there a toggle posture?
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 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

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