Question

Water stands at a depth H in a large open tank whose side walls are vertical. A hole is made in one of the walls at a depth d below the water surface.

At what distance R from the foot of the wall of the tank does the emergent stream strike the floor?

How far above the bottom of the tank could the second hole be cut so that the stream emerging from it could have the same range as for the first hole?

Answer 1

A).

R = velocity of efflux of water*time of fall

velocity of efflux of water = sqrt(2gh)

Time of fall of water (from s = ut +1/2 at^2 in vertical direction))

= sqrt[2g(H - h)/g]

Therefore,

R = sqrt(2gh)*sqrt[2g(H - h)/g]

= sqrt[4(H-h)h]

B.

It is at height h from the bottom.