Fluids (Fluid Flow Concept and Basic Equation)Online version
Final Examination
1
Three pipes steadily deliver water at 20°C to a large exit pipe in Fig. P3.8. The velocity V2 = 5 m/s, and the exit flow rate Q4 = 120 m3/h. Find (a) V1;
2
Three pipes steadily deliver water at 20°C to a large exit pipe in Fig. P3.8. The velocity V2 = 5 m/s, and the exit flow rate Q4 = 120 m3/h. Find (b) V3;
3
Three pipes steadily deliver water at 20°C to a large exit pipe in Fig. P3.8. The velocity V2 = 5 m/s, and the exit flow rate Q4 = 120 m3/h. Find (c) V4 if it is known that increasing Q3 by 20% would increase Q4 by 10%.
4
Water flowing through an 8-cm-diameter pipe enters a porous section, as in Fig. P3.10, which allows a uniform radial velocity vw through the wall surfaces for a distance of 1.2 m. If the entrance average velocity V1 is 12 m/s, find the exit velocity V2 if (a) vw = 15 cm/s out of the pipe walls;
5
Water flowing through an 8-cm-diameter pipe enters a porous section, as in Fig. P3.10, which allows a uniform radial velocity vw through the wall surfaces for a distance of 1.2 m. If the entrance average velocity V1 is 12 m/s, find the exit velocity V2 if (b) vw = 10 cm/s into the pipe.
6
Water flowing through an 8-cm-diameter pipe enters a porous section, as in Fig. P3.10, which allows a uniform radial velocity vw through the wall surfaces for a distance of 1.2 m. If the entrance average velocity V1 is 12 m/s, find the exit velocity V2 if (c) What value of vw will make V2 = 9 m/s?
7
The pipe flow in Fig. P3.12 fills a cylindrical tank as shown. At time t = 0, the water depth in the tank is 30 cm. Estimate the time required to fill the remainder of the tank.
8
Water at 20°C flows steadily at 40 kg/s through the nozzle in Fig. P3.13. If D1 = 18 cm and D2 = 5 cm, compute the average velocity, in m/s, at (a) section 1
9
Water at 20°C flows steadily at 40 kg/s through the nozzle in Fig. P3.13. If D1 = 18 cm and D2 = 5 cm, compute the average velocity, in m/s, at (b) section 2.
10
The open tank in the figure contains water at 20°C. For incompressible flow, (b) If h is constant, determine V2 for the given data if V1 = 3 m/s and Q3 = 0.01 m3/s.
11
Water flows steadily through the round pipe in the figure. The entrance velocity is Vo. The exit velocity approximates turbulent flow, u = umax(1 − r/R)1/7. Determine the ratio Uo/umax for this incompressible flow.
12
Incompressible steady flow in the inlet between parallel plates in Fig. P3.17 is uniform, u = Uo = 8 cm/s, while downstream the flow develops into the parabolic laminar profile u = az(zo − z), where a is a constant. If zo = 4 cm and the fluid is SAE 30 oil at 20°C, what is the value of umax in cm/s?
13
An incompressible fluid flows steadily through the rectangular duct in the figure. The exit velocity profile is given by u ≈ umax(1 – y2/b2)(1 – z2/h2). (a) Does this profile satisfy the correct boundary conditions for viscous fluid flow? (b) Find an analytical expression for the volume flow Q at the exit. (c) If the inlet flow is 300 ft3/min, estimate umax in m/s.
14
Water from a storm drain flows over an outfall onto a porous bed which absorbs the water at a uniform vertical velocity of 8 mm/s, as shown in Fig. P3.19. The system is 5 m deep into the paper. Find the length L of bed which will completely absorb the storm water.
15
Oil (SG-0.91) enters the thrust bearing at 250 N/hr and exits radially through the narrow clearance between thrust plates. Compute (a) the outlet volume flow in mL/s,
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Oil (SG-0.91) enters the thrust bearing at 250 N/hr and exits radially through the narrow clearance between thrust plates. Compute (b) the average outlet velocity in cm/s.
17
A dehumidifier brings in saturated wet air (100 percent relative humidity) at 30°C and 1 atm, through an inlet of 8-cm diameter and average velocity 3 m/s. After some of the water vapor condenses and is drained off at the bottom, the somewhat drier air leaves at approximately 30°C, 1 atm, and 50 percent relative humidity. For steady operation, estimate the amount of water drained off in kg/h. (This problem is idealized from a real dehumidifier.)
18
The converging-diverging nozzle shown in Fig. P3.22 expands and accelerates dry air to supersonic speeds at the exit, where p2 = 8 kPa and T2 = 240 K. At the throat, p1 = 284 kPa, T1 = 665 K, and V1 = 517 m/s. For steady compressible flow of an ideal gas, estimate (a) the mass flow in kg/h,
19
The converging-diverging nozzle shown in Fig. P3.22 expands and accelerates dry air to supersonic speeds at the exit, where p2 = 8 kPa and T2 = 240 K. At the throat, p1 = 284 kPa, T1 = 665 K, and V1 = 517 m/s. For steady compressible flow of an ideal gas, estimate (b) the velocity V2,
20
The converging-diverging nozzle shown in Fig. P3.22 expands and accelerates dry air to supersonic speeds at the exit, where p2 = 8 kPa and T2 = 240 K. At the throat, p1 = 284 kPa, T1 = 665 K, and V1 = 517 m/s. For steady compressible flow of an ideal gas, estimate (c) the Mach number Ma2.
21
The hypodermic needle in the figure contains a liquid (SG = 1.05). If the serum is to be injected steadily at 6 cm3/s, how fast should the plunger be advanced (a) if leakage in the plunger clearance is neglected;
22
The hypodermic needle in the figure contains a liquid (SG = 1.05). If the serum is to be injected steadily at 6 cm3/s, how fast should the plunger be advanced (b) if leakage is 10 percent of the needle flow?
23
A thin layer of liquid, draining from an inclined plane, as in the figure, will have a laminar velocity profile u = Uo(2y/h − y2/h2), where Uo is the surface velocity. If the plane has width b into the paper, (a) deter-
mine the volume rate of flow of the film.
24
A thin layer of liquid, draining from an inclined plane, as in the figure, will have a laminar velocity profile u = Uo(2y/h − y2/h2), where Uo is the surface velocity. If the plane has width b into the paper, (b) Suppose that h = 0.5 in and the flow rate per foot of channel width is 1.25 gal/min. Estimate Uo in ft/s.
25
A wedge splits a sheet of 20°C water, as shown in Fig. P3.30. Both wedge and sheet are very long into the paper. If the force required to hold the wedge stationary is F = 124 N per
meter of depth into the paper, what is the angle θ of the wedge?
26
Water at 20°C flows through the piping junction in the figure, entering section 1 at 20 gal/min. The average velocity at section 2 is 2.5 m/s. A portion of the flow is diverted through the showerhead, which contains 100 holes of 1-mm diameter. Assuming uniform shower flow, estimate the exit velocity from the showerhead jets.
27
In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig. P3.33 contains 1200 holes of 5-mm diameter each per square meter of wall area. The suction velocity through each hole is Vr = 8 m/s, and the test-section entrance velocity is V1 = 35 m/s. Assuming incompressible steady flow of air at 20°C, compute (a) Vo,
28
In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig. P3.33 contains 1200 holes of 5-mm diameter each per square meter of wall area. The suction velocity through each hole is Vr = 8 m/s, and the test-section entrance velocity is V1 = 35 m/s. Assuming incompressible steady flow of air at 20°C, compute (b) V2,
29
In some wind tunnels the test section is perforated to suck out fluid and provide a thin viscous boundary layer. The test section wall in Fig. P3.33 contains 1200 holes of 5-mm diameter each per square meter of wall area. The suction velocity through each hole is Vr = 8 m/s, and the test-section entrance velocity is V1 = 35 m/s. Assuming incompressible steady flow of air at 20°C, compute (c) Vf, in m/s.
30
A rocket motor is operating steadily, as shown in Fig. P3.34. The products of combustion flowing out the exhaust nozzle approximate a perfect gas with a molecular the given conditions calculate V2 in ft/s.
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