An oil of relative density `0.9` and viscosity `0.12 kg//ms` flows through a `2.5 cm` diameter pipe with a pressure drop of `38.4 kN//m^(2)` in a length of `30 m`. Determine
Determine the discharge

Options

A. ` 2.16 xx 10 ^(-4) m^3//s `
B. `2.9 xx 10 ^(-3) m^3// s `
C. ` 1 xx 10 ^(-4) m ^ 3 //s `
D. ` 2 xx 10 ^(-4) m ^ 3 // s `

Answer

C

Explanation

Using Poiseuille’s equation, we get
` Q = ((P_1 - P_2) pi D ^ 4 )/(128 eta L ) , P _ 1 - P_2 = 38.4 xx 10 ^3 N//m^ 2 rArr D = 2.5 cm = 2.5 xx 10 ^(-2) m`
` L = 30 m , eta = 0.12 kg//ms rArr Q = ((38.4 xx 10 ^(3) ) (3.14) (2.5 xx 10^(-2) ) ^4 ) / (128 (0.12) (30)) = 1 xx 10 ^(-4) m ^ 3 //s `