A pump is designed as a horizontal cylinder of area A with a tight fitting piston also having same area and an outlet orifice of area a. 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 ρ.
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Let’s assume the piston is moving with speed vo.
Work done in time t is Fvot
Mass of the liquid flowing out during the time t is M=ρAvot
If v be the velocity of the liquid coming out then the change in Kinetic energy of the liquid during the time t is M(v2-vo2)/2= ρAvot(v2-vo2)/2
Therefore, Fvot= ρAvot(v2-vo2)/2
Or, 2F= ρA(v2-vo2)
Again, Avo=av
Eliminating vo we get
\[v^{2}=\frac{2F}{A\rho }\times \frac{1}{1-\frac{a^{2}}{A^{2}}}\]
If a is very smaller than A then
\[v=\sqrt{\frac{2F}{A\rho }}\]
