Question

A cylindrical vessel contains a liquid of density r upto a height h. The liquid is closed by a piston of mass m and area of cross-section a. There is a small hole at the bottom of the vessel. The speed v with which the liquid comes out of the hole is: (neglect presence of atmosphere)

Answer 1

The speed v with which liquid comes out is v = √2(gh+mg/ρA).

Density of the vessel = r (Given)

Height of the vessel = h (Given)

According to the bernoulli equation -

1/2ρv²1 + ρgh1 + P1 = 1/2ρv²2 + ρgh2 + P2

Now P1 = P0 + mg/A and

P2=P0  where P0  is the atomspheric pressure

According to the question , h1 = h h2 = 0 v1 = 0 and v2 = v then

ρgh+P0+mg/A=1/2ρv²+P0

v = √2(gh+mg/ρA)

Therefore, the speed v with which liquid comes out is v = √2(gh+mg/ρA).

Answer 2

Answer:

The vessels are filled with the liquid upto same level. Which vessel will have highest pressure at the bottom? yes the 4th one is the answer but why? All vessels will have same pressure Because :-) (Pressure = dgh) and pressure depends on the height.