In a horizontal pipeline of uniform cross section the pressure falls by `8 N//m^(2)` between two points separated by `1 km`. If oil of density `800 kg//m^(3)` flows through the pipe, find the change in `KE` per kg of oil at these points.

Options

A. `10^(-2)J//kg`
B. `10^(-3)J//kg`
C. `10^(-4)J//kg`
D. `10^(-1)J//kg`

Answer

A

Explanation

According to Bernoull's therorem,
`P_(1)+1/2rhov_(1)^(2)=P_(2)+1/2rhov_(2)^(2)`
`impliesP_(1)-P_(2)=1/2rho(v_(2)^(2)-v_(1)^(2))`
`implies(P_(1)-P_(2))/rho=1/2(v_(2)^(2)-v_(1)^(2))`
Change in kinetic energy per kilogram mass of oil is
`(P_(1)-P_(2))/(rho)`
Substituting the numerical values, change in kinetic energy
`=8/800=10^(-2)J//kg`