As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice having an area ' a '. The piston moves with a constant velocity under the

Question

As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet 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 the liquid emerging from the orifice is, (assume $A >> a$ )

TestHub · Accepted Answer

Hint: by principle of continuity AV = av by Bernoulis principle ​ P + 2 1 ​ ρ V 2 = P 0 ​ + 2 1 ​ ρ v 2 [ A F ​ + P 0 ​ ] + 2 1 ​ ρ V 2 = P 0 ​ + 2 1 ​ ρ v 2 A F ​ + 2 1 ​ ρ [ A a v ​ ] 2 = 2 1 ​ ρ v 2 A F ​ = 2 1 ​ ρ v 2 [ 1 − A 2 a 2 ​ ] ​ ​ v = ρ A [ 1 − A 2 a 2 ​ ] 2 F ​ ​ a 2 ≪ A 2 v = ρ A 2 F ​ ​ ​

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