Question

What work should be done in order to squeeze all water from a horizontally located cylinder (Fig. 1.85) during the time t by means of a constant force acting on the piston? The volume of water in the cylinder is equal to V, the cross-sectional area of the orifice to s, with s being considerably less than the piston area. The friction and viscosity are negligibly small.

Answer 1

Let the force acting on the piston he F and foe length of the cylinder be l. Then, work done = FI       (1)

Applying Bernoulli's theorem for points A and B, p= 1/2 ρv² where ρ is density and v is the velocity at point B. Now, force on the piston,

where A is the cross section area of piston. Also, discharge through the orifice during time interval t = Svt and this is equal to the volume of the cylinder, i.e.,