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mechanical engineering

Questions and Answers of Mechanical Engineering

A rectangular heat exchanger is to be divided into smaller sections using sheets of commercial steel 0.4 mm thick, as sketched in Fig. P6.98. The flow rate is 20 kg/s of water at 20°C. Basic
Air, approximately at sea-level standard conditions, is to be delivered at 3 m3/s through a horizontal square commercial-steel duct, what are the appropriate duct dimensions if the pressure drop is
Repeat Prob. 6.92 by including minor losses due to a sharp-edged entrance, the exit into the room, and an open gate valve. If the room pressure is 10 Pa (vacuum), by what percentage is the flow rate
In Fig P6.101 a thick filter is being tested for losses. The flow rate in the pipe is 7 m3/min and the upstream pressure is 120 kPa. The fluid is air at 20°C. Using the water manometer reading,
A 70 percent efficient pump delivers water at 20°C from one reservoir to another 20 ft higher, as in Fig. P6.102. The piping system consists of 60 ft of galvanized iron 2-in pipe, a reentrant
The reservoirs in Fig P6.103 are connected by cast-iron pipes joined abruptly, with sharp-edged entrance and exit. Including minor losses, estimate the flow of water at 20°C if the surface of
Reconsider the air hockey table of Problem 3.162, but with inclusion of minor losses. The table is 3 ft by 6 ft in area, with 1/16-in-diameter holes spaced every inch in a rectangular grid (2592
The system in Fig P6.105 consists of 1200 m of 5 cm cast-iron pipe, two 45° and four 90° flanged long-radius elbows, a fully open flanged globe valve, and a sharp exit into a reservoir. If
The water pipe in Fig. 6.106 slopes upward at 30°. The pipe is 1-inch diameter and smooth. The flanged globe valve is fully open. If the mercury manometer shows a 7-inch deflection, what is the
In Fig P6.107 the pipe is galvanized iron. Estimate the percentage increase in the flow rate (a) if the pipe entrance is cut off flush with the wall and (b) if the butterfly valve is opened wide.
The water pump in Fig P6.108 maintains a pressure of 6.5 psig at point 1. There is a filter, a half-open disk valve, and two regular screwed elbows. There are 80 ft of 4-inch diameter commercial
In Fig P6.109 there are 125 ft of 2-in pipe, 75 ft of 6-in pipe, and 150 ft of 3-in pipe, all cast iron. There are three 90° elbows and an open globe valve, all flanged. If the exit elevation is
In Fig P6.110 the pipe entrance is sharp-edged. If the flow rate is 0.004 m3/s, what power, in W, is extracted by the turbine?
For the parallel-pipe system of Fig P6.111, each pipe is cast iron, and the pressure drop p1 − p2 = 3 lbf/in2. Compute the total flow rate between 1 and 2 if the fluid is SAE 10 oil at 20°C.
If the two pipes in Fig P6.111 are instead laid in series with the same total pressure drop of 3 psi, what will the flow rate be? The fluid is SAE 10 oil at 20°C.
The parallel galvanized-iron pipe system of Fig P6.113 delivers water at 20°C with a total flow rate of 0.036 m3/s. If the pump is wide open and not running, with a loss coefficient K = 1.5,
Modify Prob. 6.113 as follows: Let the pump be running and delivering 45 kW to the flow in pipe 2. The fluid is gasoline at 20°C. Determine (a) the flow rate in each pipe, and (b) the overall
In Fig P6.115 all pipes are 8-cm-diameter cast iron. Determine the flow rate from reservoir (1) if valve C is (a) closed; and (b) open, with Kvalve = 0.5.
For the series-parallel system of Fig P6.116, all pipes are 8-cm-diameter asphalted cast iron. If the total pressure drop p1 − p2 = 750 kPa, find the resulting flow rate Q m3/h for water at
A blower delivers air at 3000 m3/h to the duct circuit in Fig. P6.117. Each duct is commercial steel and of square cross-section, with side lengths a1 = a3 = 20 cm and a2 = a4 = 12 cm. Assuming
For the piping system of Fig P6.118, all pipes are concrete with a roughness of 0.04 inch. Neglecting minor losses, compute the overall pressure drop p1 − p2 in lbf/in2. The flow rate is 20
Modify Prob. 6.118 as follows. Let the pressure drop (p1 − p2) be 98 lbf/in2. Neglecting minor losses, determine the flow rate in ft3/s.
Three cast-iron pipes are laid in parallel with these dimensions: Pipe 1: L1 = 800 m d1 = 12 cm Pipe 2: L2 = 600 m d2 = 8 cm Pipe 3: L3 = 900 m d3 = 10 cm The total flow rate is 200 m3/h of water
Consider the three-reservoir system of Fig. P6.121 with the following data: L1 = 95 m L2 = 125 m L3 = 160 m z1 = 25 m z2 = 115 m z3 = 85 m All pipes are 28-cm-diameter unfinished concrete (ε
Modify Prob. 6.121 by reducing the diameter to 15 cm, with ε = 1 mm. Compute the flow rate in each pipe. They all reduce, compared to Prob. 6.121, by a factor of about 5.2. Can you explain this?
Modify Prob. 6.121 on the previous page as follows. Let z3 be unknown and find its value such that the flow rate in pipe 3 is 0.2 m3/s toward the junction (This problem is best suited for computer
The three-reservoir system in Fig P6.124 delivers water at 20°C. The system data are as follows:D1 = 8 in D2 = 6 in D3 = 9 inL1 = 1800 ft L2 = 1200 ft L3 = 1600 ftAll pipes are galvanized iron.
Suppose that the three cast-iron pipes in Prob. 6.120 are instead connected to meet smoothly at a point B, as shown in Fig. P6.125. The inlet pressures in each pipe are: p1 = 200 kPa; p2 = 160 kPa;
Modify Prob. 6.124 as follows. Let all data be the same except that pipe 1 is fitted with a butterfly valve (Fig. 6.19b). Estimate the proper valve opening angle (in degrees) for the flow rate
In the five-pipe horizontal network of Fig. P6.127, assume that all pipes have a friction factor f = 0.025. For the given inlet and exit flow rate of 2 ft3/s of water at 20°C, determine the flow
Modify Prob. 6.127 above as follows: Let the inlet flow at A and the exit flow at D be unknown. Let pA − pB = 100 psi. Compute the flow rate in all five pipes.
In Fig P6.129 all four horizontal cast-iron pipes are 45 m long and 8 cm in diameter and meet at junction delivering water at 20°C. The pressures are known at four points as shown: p1 = 950 kPa
In Fig P6.130 lengths AB and BD are 2000 and 1500 ft, respectively. The friction factor is 0.022 everywhere, and pA 90 lbf/in2 gage. All pipes have a diameter of 6 in. For water at
A water-tunnel test section has a 1-m diameter and flow properties V = 20 m/s, p =100 kPa, and T = 20°C. The boundary-layer blockage at the end of the section is 9 percent. If a conical diffuser is
For Prob. 6.131, suppose we are limited by space to a total diffuser length of 10 meters. What should be the diffuser angle, exit diameter, and exit pressure for maximum recovery?
A wind-tunnel test section is 3 ft square with flow properties V = 150 ft/s, p = 15 lbf/in2 absolute, and T = 68°F. Boundary-layer blockage at the end of the test section is 8 percent. Find the
For Prob. 6.133 above, suppose we are limited by space to a total diffuser length of 30 ft. What should the diffuser angle, exit height, and exit pressure be for maximum recovery?
An airplane uses a pitot-static tube as a velocimeter. The measurements, with their uncertainties, are a static temperature of (−11 ± 3)°C, a static pressure of 60 ± 2 kPa, and a pressure
For the pitot-static pressure arrangement of Fig P6.136, the manometer fluid is (colored) water at 20°C. Estimate (a) the centerline velocity, (b) the pipe volume flow, and (c) the (smooth) wall
For the 20°C water flow of Fig. P6.137, use the pitot-static arrangement to estimate (a) the centerline velocity and (b) the volume flow in the 5-indiameter smooth pipe. (c) What error in flow
An engineer who took college fluid mechanics on a pass-fail basis has placed the static pressure hole far upstream of the stagnation probe, as in Fig. P6.138, thus contaminating the pitot measurement
Professor Walter Tunnel must measure velocity in a water tunnel. Due to budgetary restrictions, he cannot afford a pitot-static tube, so he inserts a total-head probe and a static-head probe, as
Kerosene at 20°C flows at 18 m3/h in a 5-cm-diameter pipe. If a 2-cm-diameter thin-plate orifice with corner taps is installed, what will the measured pressure drop be, in Pa?
Gasoline at 20°C flows at 105 m3/h in a 10-cm-diameter pipe. We wish to meter the flow with a thin-plate orifice and a differential pressure transducer which reads best at about 55 kPa. What is the
The shower head in Fig P6.142 delivers water at 50°C. An orifice-type flow reducer is to be installed. The upstream pressure is constant at 400 kPa. What flow rate, in gal/min, results without
A 10-cm-diameter smooth pipe contains an orifice plate with D: 12 D taps and β = 0.5. The measured orifice pressure drop is 75 kPa for water flow at 20°C. Estimate the flow rate, in m3/h. What
Accurate solution of Prob. 6.143, using Fig. 6.41, requires iteration because both the ordinate and the abscissa of this figure contain the unknown flow rate Q. In the spirit of Example 5.8, rescale
The 1-m-diameter tank in Fig P6.145 is initially filled with gasoline at 20°C. There is a 2-cm-diameter orifice in the bottom. If the orifice is suddenly opened, estimate the time for the fluid
A pipe connecting two reservoirs, as in Fig P6.146, contains a thin-plate orifice. For water flow at 20°C, estimate (a) the volume flow through the pipe and (b) the pressure drop across the
Air flows through a 6-cm-diameter smooth pipe which has a 2 m-long perforated section containing 500 holes (diameter 1 mm), as in Fig. P6.147. Pressure outside the pipe is sea-level standard air. If
A smooth pipe containing ethanol at 20°C flows at 7 m3/h through a Bernoulli obstruction, as in Fig. P6.148. Three piezometer tubes are installed, as shown. If the obstruction is a thin-plate
In a laboratory experiment, air at 20°C flows from a large tank through a 2- cm-diameter smooth pipe into a sea-level atmosphere, as in Fig. P6.149. The flow is metered by a long-radius nozzle of
Gasoline at 20°C flows at 0.06 m3/s through a 15-cm pipe and is metered by a 9-cm-diameter long-radius flow nozzle (Fig. 6.40a). What is the expected pressure drop across the nozzle?
Ethyl alcohol at 20°C, flowing in a 6-cm-diameter pipe, is metered through a 3-cm-diameter long-radius flow nozzle. If the measured pressure drop is 45 kPa, what is the estimated flow rate in m3/h?
Kerosene at 20°C flows at 20 m3/h in an 8-cm-diameter pipe. The flow is to be metered by an ISA 1932 flow nozzle so that the pressure drop is 7 kPa. What is the proper nozzle diameter?
Two water tanks, each with base area of 1 ft2, are connected by a 0.5-indiameter long-radius nozzle as in Fig. P6.153 If h = 1 ft as shown for t = 0, estimate the time for h(t) to drop to 0.25 ft.
Water at 20°C flows through the orifice in the figure, which is monitored by a mercury manometer, If d = 3 cm, (a) what is h when the flow is 20 m3/h; and (b) what is Q when h = 58 cm?
It is desired to meter a flow of 20°C gasoline in a 12-cm-diameter pipe, using a modern venturi nozzle. In order for international standards to be valid (Fig. 6.40), what is the permissible range of
Ethanol at 20°C flows down through a modern venturi nozzle as in Fig. P6.156 if the mercury manometer reading is 4 in, as shown, estimate the flow rate, in gal/min.
Modify Prob. 6.156 if the fluid is air at 20°C, entering the venturi at a pressure of 18 psia. Should a compressibility correction be used?
Water at 20°C flows in a long horizontal commercial-steel 6-cm-diameter pipe which contains a classical Herschel venturi with a 4-cm throat, the venturi is connected to a mercury manometer whose
A modern venturi nozzle is tested in a laboratory flow with water at 20°C. The pipe diameter is 5.5 cm, and the venturi throat diameter is 3.5 cm. The flow rate is measured by a weigh tank and the
The butterfly-valve losses in Fig. 6.19b may be viewed as a type of Bernoulli obstruction device, as in Fig. 6.39, the €œthroat area€ At in Eq. (6.104) can be interpreted as the
Air flows at high speed through a Herschel venturi monitored by a mercury manometer, as shown in Fig. P6.161. The upstream conditions are 150 kPa and 80°C. If h = 37 cm, estimate the mass flow in
Modify Prob. 6.161 as follows. Find the manometer reading h for which the mass flow through the venturi is approximately 0.4 kg/s, [HINT: The flow is compressible.]
For flow at 20 m/s past a thin flat plate, estimate the distances x from the leading edge at which the boundary layer thickness will be either 1 mm or 10 cm, for a) Air; and (b) Water at 20°C and
Air, equivalent to a Standard Altitude of 4000 m, flows at 450 mi/h past a wing which has a thickness of 18 cm, a chord length of 1.5 m, and a wingspan of 12 m. What is the appropriate value of the
Equation (7.1b) assumes that the boundary layer on the plate is turbulent from the leading edge onward. Devise a scheme for determining the boundary-layer thickness more accurately when the flow is
A smooth ceramic sphere (SG = 2.6) is immersed in a flow of water at 20°C and 25 cm/s. What is the sphere diameter if it is encountering (a) creeping motion, Red = 1; or (b) transition to
SAE 30 oil at 20°C flows at 1.8 ft3/s from a reservoir into a 6-in-diameter pipe. Use flat-plate theory to estimate the position x where the pipe-wall boundary layers meet in the center. Compare
For the laminar parabolic boundary-layer profile of Eq. (7.6), compute the shape factor “H” and compare with the exact Blasius-theory result, Eq. (7.31).
Air at 20°C and 1 atm enters a 40-cmsquare duct as in Fig. P7.7. Using the €œdisplacement thickness€ concept of Fig. 7.4, estimate(a) The mean velocity and(b) The mean
Air, ρ =1.2 kg/m3 and μ = 1.8E−5 kg/m⋅s, flows at 10 m/s past a flat plate. At the trailing edge of the plate, the following velocity profile data are measured: y, mm: 0
Repeat the flat-plate momentum analysis of Sec. 7.2 by replacing the parabolic profile, Eq. (7.6), with the more accurate sinusoidal profile: Compute momentum-integral estimates of Cf,
Repeat Prob. 7.9, using the polynomial profile suggested by K. Pohlhausen in 1921: Does this profile satisfy the boundary conditions of laminar flat-plate flow?
Air at 20°C and 1 atm flows at 2 m/s past a sharp flat plate, Assuming that the Kármán parabolic-profile analysis, Eqs. (7.6−7.10), is accurate, estimate (a) the local velocity u; and (b)
The velocity profile shape u/U ≈ 1 − exp (−4.605y/δ) is a smooth curve with u = 0 at y = 0 and u = 0.99U at y = δ and thus would seem to be a reasonable substitute for the
Show that the two-dimensional laminar-flow pattern with dp/dx = 0 Cy u=Uo (1−e) υ=υ0
Derive modified forms of the laminar boundary-layer equations for flow along the outside of a circular cylinder of constant R, as in Fig. P7.13. Consider the two cases (a) δ R; and (b) δ
Discuss whether fully developed laminar incompressible flow between parallel plates, Eq. (4.143) and Fig. 4.16b, represents an exact solution to the boundary-layer equations (7.19) and the boundary
A thin flat plate 55 by 110 cm is immersed in a 6-m/s stream of SAE 10 oil at 20°C. Compute the total friction drag if the stream is parallel to (a) the long side and (b) the short side.
Helium at 20°C and low pressure flows past a thin flat plate 1 m long and 2 m wide. It is desired that the total friction drag of the plate be 0.5 N. What is the appropriate absolute pressure of the
The approximate answers to Prob. 7.11 are u ≈ 1.44 m/s and τ ≈ 0.0036 Pa at x = 50 cm and y = 5 mm. [Do not reveal this to your friends who are working on Prob. 7.11.] Repeat that
Program a method of numerical solution of the Blasius flat-plate relation, Eq. (7.22), subject to the conditions in (7.23). You will find that you cannot get started without knowing the initial
Air at 20°C and 1 atm flows at 20 m/s past the flat plate in Fig P7.20, A pitot stagnation tube, placed 2 mm from the wall, develops a manometer head h = 16 mm of Merriam red oil, SG = 0.827. Use
For the experimental set-up of Fig P7.20, suppose the stream velocity is unknown and the pitot stagnation tube is traversed across the boundary layer of air at 1 atm and 20°C. The manometer fluid is
For the Blasius flat-plate problem Eqs, (7.21) to (7.23), does a two-dimensional stream function ψ(x, y) exist? If so, determine the correct dimensionless form for ψ, assuming that ψ =
Suppose you buy a 4 Ã— 8-ft sheet of plywood and put it on your roof rack, as in the figure. You drive home at 35 mi/h.(a) If the board is perfectly aligned with the airflow, how thick is
Air at 20°C and 1 atm flows past the flat plate in Fig P7.24, the two pitot tubes are each 2 mm from the wall. The manometer fluid is water at 20°C. If U = 15 m/s and L =50 cm, determine the
Consider the smooth square 10 by 10 cm duct in Fig. P7.25, the fluid is air at 20°C and 1 atm, flowing at Vavg = 24 m/s. It is desired to increase the pressure drop over the 1-m length by adding
Consider laminar flow past the square-plate arrangements in the figure below. Compared to the drag of a single plate (1), how much larger is the drag of four plates together as in configurations (a)
A thin smooth disk of diameter D is immersed parallel to a uniform stream of velocity U. Assuming laminar flow and using flat-plate theory as a guide, develop an approximate formula for the drag of
Flow straighteners are arrays of narrow ducts placed in wind tunnels to remove swirl and other in-plane secondary velocities. They can be idealized as square boxes constructed by vertical and
Let the flow straighteners in Fig. P7.28 form an array of 20 × 20 boxes of size a = 4 cm and L = 25 cm. If the approach velocity is Uo = 12 m/s and the fluid is sea-level standard air, estimate (a)
Repeat Prob. 7.16 if the fluid is water at 20°C and the plate is smooth.
The centerboard on a sailboat is 3 ft long parallel to the flow and protrudes 7 ft down below the hull into seawater at 20°C. Using flat-plate theory for a smooth surface estimate its drag if the
A flat plate of length L and height δ is placed at a wall and is parallel to an approaching boundary layer, as in Fig. P7.32. Assume that the flow over the plate is fully turbulent and that the
An alternate analysis of turbulent flat-plate flow was given by Prandtl in 1927, using a wall shear-stress formula from pipe flow Show that this formula can be combined with Eqs. (7.32) and (7.40) to
A thin equilateral-triangle plate is immersed parallel to a 12 m/s stream of water 20°C, as in Fig. P7.34. Assuming Retr = 5 Ã— 105, estimate the drag of this plate.
Repeat Problem 7.26 for turbulent flow. Explain your results.

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