A lubricating oil of viscosity 1 poise and specific gravity 0.9 is pumped through a 30mm diameter pipe. If the pressure drop per meter length of pipe is $20 kN/m^2$, determine:

i) The mass flow rate in kg/min,

ii) The shear stress at the pipe wall,

iii) The Reynolds number of flow and,

iv) The power required per 50 m length of the pipe to maintain the flow.

Given,

$μ = 1.0\ poise = 0.1\ Ns/m^2$

$s = 0.9\ \implies ρ = 900\ kg/m^3$

$L = 50m$

$D = 300mm \implies 0.03m$

$R = D/2 = 0.015m$

$Pressure\ Drop\ = 20KN/m^2$

(i) Mass flow rate (m)

Q = ūA

$ū = \frac{(P_1-P_2)D^2}{32ūL}$

$(P_1-P_2) = \frac{32ūμL}{D^2} = \frac{32\times0.1\timesū\times50}{0.03m^2}$

$\implies …