Question

As shown in the figure, a pump is designed as a horizontal cylinder with a piston having area A and an outer orifice having an area 'a'. The piston moves with a constant velocity under the action of force F. If the density of the liquid is ρ, then the speed of liquid emerging from the orifice is(assume A>>a)

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

Answer 1

Answer: (C)

$\sqrt{\frac{2F}{\rho A}}$

Answer 2

The equation P 1​+12​ ρv 12​=P 2​+12​ ρv 22​ can be simplified as P 0​+AF +0=P 0​+1/2​ ρv 2​, which further simplifies to 1/2​ ρv 2​. Therefore, the expression for v can be derived as 2 F/ρA ​.

The correct answer is option (C): $\sqrt{\frac{2F}{\rho A}}$