A civil engineer is designing a pipe to transport 178 m^3/s of water a distance

Question

A civil engineer is designing a pipe to transport 178 m^3/s of water a distance of 4.35 X 10^4 m. To save capital costs, he would like the pipe diameter to be as small as possible, but to save pumping sosts, he would like the flow to stay laminar and not becom turbulent.  What is the smallest diameter that allows the flow to stay laminar?  The actual pipe diameter will be 20% larger than this minimum diameter in order to provide a margin of safety.  What delta P must be generated by the pump?  Comment of the practicality of the engineer's desire for the flow to be laminar?

Explanation / Answer

For laminar flow, Re < 2300.

Re = V*d / neu

For water, kin.viscosity neu = 0.8*10^-6 m^2/s

V = Q / A

V = 178 / (pi/4 *d^2)

Thus, 2300 = [178 / (3.14/4 *d^2)] * d / (0.8*10^-6)

Solving, d = 123234 m

Actual pipe dia = 1.2*123234 = 147881 m

Friction factor f = 64 / Re = 64 / 2300 = 0.0278

V = Q / A = 178 / (3.14/4 * 147881^2) = 1.0378*10^-8 m/s

delta P = rho*g*[f*(L/d)*V^2 / (2g)]

= 1000*9.81* 0.0278 *(4.35*10^4 / 147881) *(1.0378*10^-8)^2 / (2*9.81)

= 4.395*10^-16 Pa

This dia is unrealistically high.!!

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