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mechanical engineering

Questions and Answers of Mechanical Engineering

Knowing that Δp is proportional to L, rescale the data of Example 5.7 to plot dimensionless Δp versus dimensionless diameter. Use this plot to find the diameter required in the first row of
Knowing that Δp is proportional to L, rescale the data of Example 5.7 to plot dimensionless Δp versus dimensionless viscosity. Use this plot to find the viscosity required in the first row
Develop a plot of dimensionless Δp versus dimensionless viscosity, as described in Prob. 5.90. Suppose that L = 200 m, Q = 60 m3/h, and the fluid is kerosene at 20°C. Use your plot to determine
In flow past a sphere, the boundary layer becomes turbulent at about ReD ≈ 2.5E5. To what air speed in mi/h does this correspond to a golf ball whose diameter is 1.6 in? Do the pressure,
Air at approximately 1 atm flows through a horizontal 4-cm-diameter pipe. (a) Find a formula for Qmax, the maximum volume flow for which the flow remains laminar, and plot Qmax versus temperature in
For a thin wing moving parallel to its chord line, transition to a turbulent boundary layer occurs at a “local” Reynolds number Rex, where x is the distance from the leading edge of the wing. The
For flow of SAE 30 oil through a 5-cm-diameter pipe, from Fig A.1, for what flow rate in m3/h would we expect transition to turbulence at (a) 20°C and (b) 100°C?
In flow past a body or wall, early transition to turbulence can be induced by placing a trip wire on the wall across the flow, as in Fig. P6.5. If the trip wire in Fig. P6.5 is placed where the local
A fluid at 20°C flows at 850 cm3/s through an 8-cm-diameter pipe. Determine the entrance length if the fluid is (a) hydrogen; (b) air; (c) gasoline; (d) water; (e) mercury; and (f) glycerin.
Cola, approximated as pure water at 20°C, is to fill an 8-oz container (1 U.S. gal =128 fl oz) through a 5-mm-diameter tube. Estimate the minimum filling time if the tube flow is to remain laminar.
When water at 20°C (ρ = 998 kg/m3, μ = 0.001 kg/m⋅s) flows through an 8-cmdiameter pipe, the wall shear stress is 72 Pa. What is the axial pressure gradient (∂ p/∂ x) if
A light liquid (ρ = 950 kg/m3) flows at an average velocity of 10 m/s through a horizontal smooth tube of diameter 5 cm. The fluid pressure is measured at 1-m intervals along the pipe, as
Water at 20°C (ρ = 998 kg/m3) flows through an inclined 8-cm-diameter pipe. At sections A and B, pA = 186 kPa, VA = 3.2 m/s, zA = 24.5 m, while pB = 260 kPa, VB = 3.2 m/s, and zB = 9.1 m. Which
Water at 20°C flows upward at 4 m/s in a 6-cm-diameter pipe, the pipe length between points 1 and 2 is 5 m, and point 2 is 3 m higher. A mercury manometer, connected between 1 and 2, has a
A 5-mm-diameter capillary tube is used as a viscometer for oils. When the flow rate is 0.071 m3/h the measured pressure drop per unit length, is 375 kPa/m. Estimate the viscosity of the fluid. Is the
A soda straw is 20 cm long and 2 mm in diameter. It delivers cold cola, approximated as water at 10°C, at a rate of 3 cm3/s. (a) What is the head loss through the straw? What is the axial pressure
Water at 20°C is to be siphoned through a tube 1 m long and 2 mm in diameter, as in Fig. P6.14. Is there any height H for which the flow might not be laminar? What is the flow rate if H = 50 cm?
Professor Gordon Holloway and his students at the University of New Brunswick went to a fast-food emporium and tried to drink chocolate shakes (ρ ≈ 1200 kg/m3, μ ≈ 6
Glycerin at 20°C is to be pumped through a horizontal smooth pipe at 3.1 m3/s. It is desired that (1) the flow be laminar and (2) the pressure drop be no more than 100 Pa/m. What is the minimum pipe
A capillary viscometer measures the time required for a specified volume υ of liquid to flow through a small-bore glass tube, as in Fig. P6.17. This transit time is then correlated with fluid
To determine the viscosity of a liquid of specific gravity 0.95, you fill, to a depth of 12 cm, a large container which drains through a 30-cm-long vertical tube attached to the bottom. The tube
An oil (SG = 0.9) issues from the pipe in Fig. P6.19 at Q = 35 ft3/h. What is the kinematic viscosity of the oil in ft3/s? Is the flow laminar?
A high! The rainfall is laminar! The drainpipe in Fig P6.21 is only 2 mm in diameter. (a) When the gutter is full, what is the rate of draining? (b) The gutter is designed for a sudden rainstorm of
In Prob. 6.19 what will the flow rate be, in m3/h, if the fluid is SAE 10 oil at 20°C?
A steady push on the piston in Fig P6.22 causes a flow rate Q = 0.15 cm3/s through the needle. The fluid has ρ = 900 kg/m3 and μ = 0.002 kg/ (m⋅s). What force F is required to maintain
SAE 10 oil at 20°C flows in a vertical pipe of diameter 2.5 cm. It is found that the pressure is constant throughout the fluid. What is the oil flow rate in m3/h? Is the flow up or down?
Two tanks of water at 20ｰC are connected by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2. (a) Estimate the flow rate in
For the configuration shown in Fig P6.25, the fluid is ethyl alcohol at 20°C, and the tanks are very wide. Find the flow rate which occurs in m3/h. Is the flow laminar?
For the system in Fig P6.25, if the fluid has density of 920 kg/m3 and the flow rate is unknown, for what value of viscosity will the capillary Reynolds number exactly equal the critical value of
Let us attack Prob. 6.25 in symbolic fashion, using Fig. P6.27. All parameters are constant except the upper tank depth Z (t). Find an expression for the flow rate Q (t) as a function of Z (t). Set
For straightening and smoothing airflow in a 50-cm-diameter duct, the duct is packed with a €œhoneycomb€ of thin straws of length 30 cm and diameter 4 mm, as in Fig. P6.28. The
Oil, with ρ = 890 kg/m3 and μ = 0.07 kg/m⋅s, flows through a horizontal pipe 15 m long. The power delivered to the flow is 1 hp. (a) What is the appropriate pipe diameter if the flow
SAE 10 oil at 20°C flows through the 4-cm-diameter vertical pipe of Fig.P6.30. For the mercury manometer reading h = 42 cm shown,(a) Calculate the volume flow rate in m3/h, and(b) State the
Light oil, ρ = 880 kg/m3 and μ = 0.015 kg/ (m⋅s), flows down a vertical 6-mmdiameter tube due to gravity only. Estimate the volume flow rate in m3/h if (a) L = 1 m and (b) L = 2 m.
SAE 30 oil at 20°C flows in the 3-cm-diameter pipe in Fig. P6.32, which slopes at 37° for the pressure measurements shown, determine(a) Whether the flow is up or down and(b) The flow rate in
In Problem 6.32, suppose it is desired to add a pump between A and B to drive the oil upward from A to B at a rate of 3 kg/s. At 100% efficiency, what pump power is required?
Derive the time-averaged x-momentum equation (6.21) by direct substitution of Eqs. (6.19) into the momentum equation (6.14), It is convenient to write the convective acceleration as
By analogy with Eq (6.21) write the turbulent mean-momentum differential equation for (a) The y direction and (b) The z direction how many turbulent stress terms appear in each equation? How many
The following turbulent-flow velocity data u(y), for air at 75°F and 1 atm near a smooth flat wall, were taken in the University of Rhode Island wind tunnel: y, in: 0.025 0.035 0.047 0.055
Two infinite plates a distance h apart are parallel to the xz plane with the upper plate moving at speed V, as in Fig. P6.37. There is a fluid of viscosity μ and constant pressure between the
Suppose in Fig. P6.37 that h = 3 cm, the fluid is water at 20°C (ρ = 998 kg/m3, μ = 0.001 kg/m⋅s), and the flow is turbulent, so that the logarithmic law is valid. If the shear
By analogy with laminar shear, τ = μ du/dy. T. V. Bossiness in 1877 postulated that turbulent shear could also be related to the mean-velocity gradient τturb = ε du/dy, where
Theodore von Kármán in 1930 theorized that turbulent shear could be represented by τ turb = ε du/dy where ε = ρκ 2y2du/dy is called the mixing-length eddy
Water at 20°C flows in a 9-cm-diameter pipe under fully developed conditions. The centerline velocity is 10 m/s. Compute (a) Q, (b) V, (c) τw, and (d) Δp for a 100-m pipe length.
It is clear by comparing Figs. 6.12b and 6.13 that the effects of sand roughness and commercial (manufactured) roughness are not quite the same. Take the special case of commercial roughness ratio
Water at 20°C flows for 1 mi through a 3-in-diameter horizontal wrought-iron pipe at 250 gal/min. Estimate the head loss and the pressure drop in this length of pipe.
Mercury at 20°C flows through 4 meters of 7-mm-diameter glass tubing at an average velocity of 5 m/s. Estimate the head loss in meters and the pressure drop in kPa.
Oil, SG = 0.88 and ν = 4E−5 m2/s, flows at 400 gal/min through a 6-inch asphalted cast-iron pipe. The pipe is 0.5 miles long (2640 ft) and slopes upward at 8° in the flow direction.
Kerosene at 20°C is pumped at 0.15 m3/s through 20 km of 16-cm-diameter cast-iron horizontal pipe Compute the input power in kW required if the pumps are 85 percent efficient?
The gutter and smooth drainpipe in Fig P6.47 remove rainwater from the roof of a building. The smooth drainpipe is 7 cm in diameter. (a) When the gutter is full, estimate the rate of draining.
Show that if Eq. (6.33) is accurate, the position in a turbulent pipe flow where local velocity u equals average velocity V occurs exactly at r = 0.777R, independent of the Reynolds number.
The tank-pipe system of Fig P6.49 is to deliver at least 11 m3/h of water at 20°C to the reservoir. What is the maximum roughness height ε allowable for the pipe?
Ethanol at 20°C flows at 125 U.S. gal/min through a horizontal cast-iron pipe with L = 12 m and d = 5 cm. Neglecting entrance effects, estimate (a) the pressure gradient, dp/dx; (b) The wall shear
The viscous sublayer (Fig. 6.10) is normally less than 1 percent of the pipe diameter and therefore very difficult to probe with a finite-sized instrument. In an effort to generate a thick sublayer
The pipe flow in Fig P6.52 is driven by pressurized air in the tank. What gage pressure p1 is needed to provide a 20°C water flow rate Q = 60 m3/h?
In Fig P6.52 suppose p1 = 700 kPa and the fluid specific gravity is 0.68. If the flow rate is 27 m3/h estimate the viscosity of the fluid. What fluid in Table A-5 is the likely suspect?
A swimming pool W by Y by h deep is to be emptied by gravity through the long pipe shown in Fig. P6.54. Assuming an average pipe friction factor fav and neglecting minor losses, derive a formula for
The reservoirs in Fig P6.55 contain water at 20°C. If the pipe is smooth with L = 4500 m and d = 4 cm, what will the flow rate in m3/h be for Δz = 100 m?
Consider a horizontal 4-ft-diameter galvanized-iron pipe simulating the Alaska Pipeline. The oil flow is 70 million U.S. gallons per day, at a density of 910 kg/m3 and viscosity of 0.01 kg/m⋅s
Apply the analysis of Prob. 6.54 to the following data. Let W = 5 m, Y = 8 m, ho =2 m, L = 15 m, D = 5 cm, and ε = 0. (a) By letting h = 1.5 m and 0.5 m as representative depths, estimate the
In Fig P6.55 assume that the pipe is cast iron with L = 550 m, d = 7 cm, and Δz = 100 m. If an 80 percent efficient pump is placed at point B, what input power is required to deliver 160 m3/h
The following data were obtained for flow of 20°C water at 20 m3/hr through a badly corroded 5-cm-diameter pipe which slopes downward at an angle of 8°: p1 = 420 kPa, z1 = 12 m, p2 = 250 kPa, z2 =
J. Nikuradse in 1932 suggested that smooth-wall turbulent pipe flow could be approximated by a Power-law profile
What level h must be maintained in Fig P6.61 to deliver a flow rate of 0.015 ft3/s through the 12 in commercial-steel pipe?
Water at 20°C is to be pumped through 2000 ft of pipe from reservoir 1 to 2 at a rate of 3 ft3/s, as shown in Fig P6.62, if the pipe is cast iron of diameter 6 in and the pump is 75 percent
A tank contains 1 m3 of water at 20°C and has a drawn-capillary outlet tube at the bottom, as in Fig. P6.63. Find the outlet volume flux Q in m3/h at this instant.
Repeat Prob. 6.63 to find the flow rate if the fluid is SAE 10 oil. Is the flow laminar or turbulent?
In Prob. 6.63 the initial flow is turbulent. As the water drains out of the tank, will the flow revert to laminar motion as the tank becomes nearly empty? If so, at what tank depth Estimate the time,
Ethyl alcohol at 20°C flows through a 10-cm horizontal drawn tube 100 m long. The fully developed wall shear stress is 14 Pa. Estimate (a) the pressure drop, (b) the volume flow rate, and (c) the
A straight 10-cm commercial-steel pipe is 1 km long and is laid on a constant slope of 5°. Water at 20°C flows downward, due to gravity only, estimate the flow rate in m3/h. What happens if the
The Moody chart, Fig. 6.13, is best for finding head loss (or Δp) when Q, V, d, and L are known. It is awkward for the “2nd” type of problem, finding Q when hf or Δp are known (see Ex.
For Prob. 6.62 suppose the only pump available can deliver only 80 hp to the fluid. What is the proper pipe size in inches to maintain the 3 ft3/s flow rate?
In Prob. 6.62 suppose the pipe is 6-inch-diameter cast iron and the pump delivers 75 hp to the flow. What flow rate Q in ft3/s results?
It is desired to solve Prob. 6.62 for the most economical pump and cast-iron pipe system. If the pump costs $125 per horsepower delivered to the fluid and the pipe costs $7000 per inch of diameter,
Modify Prob. P6.57 by letting the diameter be unknown. Find the proper pipe diameter for which the pool will drain in about 2 hours flat.
The Moody chart, Fig. 6.13, is best for finding head loss (or Δp) when Q, V, d, and L are known. It is awkward for the €œ3rd€ type of problem, finding d when hf (or
In Fig P6.67 suppose the fluid is gasoline at 20°C and h = 90 ft. What commercial-steel pipe diameter is required for the flow rate to be 0.015 ft3/s?
You wish to water your garden with 100 ft of 5 8 -in-diameter hose whose roughness is 0.011 in. What will be the delivery, in ft3/s, if the gage pressure at the faucet is 60lbf/in2? If there is no
The small turbine in Fig P6.76 extracts 400 W of power from the water flow. Both pipes are wrought iron. Compute the flow rate Q m3/h. Sketch the EGL and HGL accurately.
Modify Prob. 6.76 into an economic analysis, as follows. Let the 40 m of wrought iron pipe have a uniform diameter d. Let the steady water flow available be Q = 30 m3/h. The cost of the turbine is $4
In Fig P6.78 the connecting pipe is commercial steel 6 cm in diameter. Estimate the flow rate, in m3/h, if the fluid is water at 20°C. Which way is the flow?
A garden hose is used as the return line in a waterfall display at the mall. In order to select the proper pump, you need to know the hose wall roughness, which is not supplied by the manufacturer.
The head-versus-flow-rate characteristics of a centrifugal pump are shown in Fig. P6.80. If this pump drives water at 20°C through 120 m of 30-cm-diameter cast-iron pipe, what will be the resulting
The pump in Fig P6.80 is used to deliver gasoline at 20°C through 350 m of 30-cm-diameter galvanized iron pipe. Estimate the resulting flow rate, in m3/s. (Note that the pump head is now in meters
The pump in Fig P6.80 has its maximum efficiency at a head of 45 m. If it is used to pump ethanol at 20°C through 200 m of commercial-steel pipe, what is the proper pipe diameter for maximum pump
For the system of Fig P6.55, let Δz = 80 m and L = 185 m of cast-iron pipe. What is the pipe diameter for which the flow rate will be 7 m3/h?
It is desired to deliver 60 m3/h of water (ρ = 998 kg/m3, μ = 0.001 kg/m⋅s) at 20°C through a horizontal asphalted cast-iron pipe. Estimate the pipe diameter which will cause the
The pump of Fig P6.80 is used to deliver 0.7 m3/s of methanol at 20°C through 95 m of cast-iron pipe. What is the proper pipe diameter?
SAE 10 oil at 20°C flows at an average velocity of 2 m/s between two smooth parallel horizontal plates 3 cm apart. Estimate (a) the centerline velocity, (b) the head loss per meter, and (c) the
A commercial-steel annulus 40 ft long, with a = 1 in and b = 12 in, connects two reservoirs which differ in surface height by 20 ft. Compute the flow rate in ft3/s through the annulus if the fluid is
An oil cooler consists of multiple parallel-plate passages, as shown in Fig. P6.88. The available pressure drop is 6 kPa, and the fluid is SAE 10W oil at 20°C. If the desired total flow rate is 900
An annulus of narrow clearance causes a very large pressure drop and is useful as an accurate measurement of viscosity. If a smooth annulus 1 m long with a = 50 mm and b = 49 mm carries an oil flow
A 90-ft-long sheet-steel duct carries air at approximately 20°C and 1 atm. The duct cross section is an equilateral triangle whose side measures 9 in. If a blower can supply 1 hp to the flow,
Heat exchangers often consist of many triangular passages. Typical is Fig. P6.91, with L = 60 cm and an isosceles triangle cross section of side length a = 2 cm and included angle β = 80°. If
A large room uses a fan to draw in atmospheric air at 20°C through a 30 cm by 30 cm commercial-steel duct 12 m long, as in Fig. P6.92. Estimate (a) The air flow rate in m3/hr if the room pressure
Modify Prob. 6.91 so that the angle β is unknown. For SAE 10 oil at 20°C, if the pressure drop is 120 kPa and the flow rate is 4 m3/h what is the proper value of the angle β, in degrees?
As shown in Fig. P6.94, a multi duct cross section consists of seven 2-cmdiameter smooth thin tubes packed tightly in a hexagonal €œbundle€ within a single 6-cm-diameter tube.
A wind tunnel is made of wood and is 28 m long, with a rectangular section 50 cm by 80 cm. It draws in sea-level standard air with a fan. If the fan delivers 7 kW of power to the air, estimate (a)
Water at 20°C is flowing through a 20-cm-square smooth duct at a (turbulent) Reynolds number of 100,000. For a €œlaminar flow element€ measurement, it is desired to pack the
A heat exchanger consists of multiple parallel-plate passages, as shown in Fig. P6.97 the available pressure drop is 2 kPa, and the fluid is water at 20°C. If the desired total flow rate is

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