W@ter is pumped from the b0tt0m t0 the t0p of a 61- meter , vert1cal pipe of a d
ID: 2994899 • Letter: W
Question
W@ter is pumped from the b0tt0m t0 the t0p of a 61-meter, vert1cal pipe of a d1ameter of 0.02664 meters.
-Find the ReynoId's number
-St@te whether the fIow is lam1nar or not (not lam1nar is Re > 4000).
-What is the pump1ng power requ1red for a Q of 0.0017 meters cubed per second if the pressures at the inIet and outIet are equaI?
Dynamic viscosity of water (SI units): 0.001002
DISCLAIMER: Use any information from anywhere in the problem at any time during the problem. You don't have to solve in order. Our dumb teacher made up this problem and it's all over the place. The answer should be around one point 38 kilowatts or one point 8 5 3 horsepower.
Explanation / Answer
reynolds number Re = density*velocity*characterisitic lenght / visocity
density of water = 1000 kg/m3
velocity = Q/ area = 0.0017 / (pi*0.01332^2) = 3.0515 m/s
area is area of cross section = area of circle
characterisitic length = length = 61 m
viscosity = 0.001002
hence
Re = 1000*3.0515*61/0.001002 = 185768869 = 1.86 x 10^8
this flow is clearly not laminar...
for turbulent flow
head loss = h = fL/D * v^2/2g = 0.017*61/0.02664 * (3.0515^2) / 2*9.8 = 21.76 m
where f is friction factor due to trublulence
f = 0.017 for Re = 1.86 x 10^8
hence new height for power formula h = 61 + 21.76 = 82.76
power = density*Q*9.8*h = 1000*0.0017*9.8*82.76 = 1378.7816 = 1.38 kilowatt
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