Question

A pump is designed as a horizontal cylinder with a piston having an area of $A$ and an outlet orifice having an area of ${}^{\prime }{a}^{\prime }$ arranged near the cylinder axis. Determine the velocity of outflow of a liquid from the pump if the piston moves with a constant velocity under the action of a force $F$. The density of the liquid is $\rho (a<<A)$:

• A. $\sqrt{\frac{F}{2A\rho }}$
• B. $\sqrt{\frac{F}{A\rho }}$
• C. $\sqrt{\frac{2F}{A\rho }}$
• D. $\sqrt{\frac{2F}{3A\rho }}$

Answer 1

The correct option is C $\sqrt{\frac{2F}{A\rho }}$

Applying bernouli's law at the front of the cylinder and at the orifice

$P_1+\frac{1}{2}\rho v_1^2=P_2+\frac{1}{2}\rho v_2^2$

$or,(P_{atm}+\frac{F}{A})+0=P_{atm}+\frac{1}{2}\rho v^2$

$\therefore v=\sqrt{\frac{2F}{A\rho }}$

Answer: $C$