Fluid Mechanics-Frank M White Solution Ch6

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Fluid Mechanics-Frank M White Solution Ch6에 대한 보고서 자료입니다.

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P6.1 An engineer claims that flow of SAE 30W oil, at 20°C, through a 5-cm-diameter smooth pipe at 1 million N/h, is laminar. Do you agree? A million newtons is a lot, so this sounds like an awfully high flow rate. Solution: For SAE 30W oil at 20°C (Table A.3), take ρ = 891 kg/m3 and µ = 0.29 kg/m-s. Convert the weight flow rate to volume flow rate in SI units:
Q =  w ρ g = (1E6N/h)(1/3600h/s) (891kg/m3)(9.81m/s2) = 0.0318m3 s = π 4(0.05m)2V , solve V =16.2m s Calculate ReD = ρ VD µ = (891kg/m3)(16.2m/s)(0.05m) 0.29kg/m−s ≈ 2500 (transitional)
This is not high, but not laminar. Ans. With careful inlet design, low disturbances, and a very smooth wall, it might still be laminar, but No, this is transitional, not definitely laminar.

P6.2 Water flows through a 10-cm-diameter pipe at a rate of 10–4 m3/s. Evaluate the Reynolds number when the temperature is (a) 20°C, (b) 40°C, and (c) 60°C. Estimate the temperature at which transition to turbulence occurs. Solution: Reynolds number

Re = Vd V
but

V = 4Q π d2

∴ Re= 4Q π dV
Now d = 0.1 m, Q = 10–4 m3/s Viscosity is a function of temperature.


Temp (°C) V of water (m2 /s) Re 20 1.005 × 10–6 1,267 40 0.662 × 10–6 1,923 60 0.475 × 10–6 2,681
Recrit ~ 2300 happens when V = 0.554 × 10–6 m2/s, which is the kinematic viscosity of water at 50°C.



2

P6.3 The present pumping rate of North Slope crude oil through the Alaska Pipeline (see the chapter-opener photo) is about 600,000 barrels per day (1 barrel = 0.159 m3). What would be the maximum rate if the flow were constrained to be laminar? Assume that Alaskan crude oil fits Fig. A.1 of the Appendix at 60°C.

Solution: From Fig. A.1 for crude at 60°C, ρ = 0.86(1000) = 860 kg/m3 and µ = 0.0040 kg/m-s. From Eq. (6.2), the maximum laminar Reynolds number is about 2300. Convert the pipe diameter from 48 inches to 1.22 m. Solve for velocity:

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