In a pipe of 300mm dia and 800m length oil of specific gravity 0.8 is flowing at the rate of 0.45 m3 /s. find Head lost due to friction, and Power required to maintain the flow. Take kinematic viscosity of oil as 0.3 stokes.

 In a pipe of 300mm dia and 800m length oil of specific gravity 0.8 is flowing at the rate of 0.45 m3 /s. find Head lost due to friction, and Power required to maintain the flow. Take kinematic viscosity of oil as 0.3 stokes. 

Solution: 

dia of the pipe, D=0.3m 

Length of the pipe, L=800m

Specific gravity of oil =0.8 

Kinematic viscosity of oil ν=0.3 stokes=0.3*10-4 m 2 /s 

 Discharge Q=0.45 m3 /s

 Head lost due to friction, hf 

Velocity, v= Q/area =0.45/(π*0.32 /4) =6.366m 

Reynolds number, Re=v*D/ν =6.366*0.3/0.3*10-4 =6.366*104 

 Coefficient of friction, f = 0.0791/(Re)0.25 = 0.0791/(6.366*104 ) 0.25 

                                                                       = 0.00498 

 hf = 4fLv2 /2gD=4* 0.00498*800*6.3662 /(0.3*2*9.81) = 109.72 m 

Power required ‘P’ =wQhf 

 w=0.8*9.81=7.848kN/m3

 hf=109.72m and Q=0.43 m3 /s 

P=7.848*0.45*109.72

 P = 387.48kW