Question

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

• A. ${10}^{-2}J/kg$
• B. ${10}^{-3}J/kg$
• C. ${10}^{-4}J/kg$
• D. ${10}^{-1}J/kg$

Answer 1

The correct option is A ${10}^{-2}J/kg$

By Bernouli's equation-

$P+8gh+\frac{1}{2}\rho V^2=constant$

Applying Bernouli's equation at A and B-

$P_1+\rho gh+\frac{1}{2}\rho V_A^2=(P_1-8)+8gh+\frac{1}{2}\rho V_B^2\frac{1}{2}\rho (V_B^2-V_A^2)=\frac{8}{\rho }$

Change in K.E per kg of oil $=\frac{1}{2}\left(1\right)|V_B^2-V_A^2|=\frac{8}{\rho }=\frac{8}{500}={10}^{-2}J/kg$