Question

prove velocity of efflux of a liquid is equal to the velocity of a body falling freely from surface to orifice ​

Answer 1

Here,

H = Height of container

h = Height from the surface of the container to the orifice made

Let atmospheric pressure be P , density of liquid in tank be ρand velocity of liquid at efflux be v

Applying Bernoulli's equation at the surface of container and at the orifice we get

P+ρgH=P+12ρv2+ρg(H−h)⇒0=12ρv2−ρgh⇒12ρv2=ρgh⇒v=2gh−−−√

Thus the velocity of efflux is v=2gh−−−√

And velocity of a body falling freely has same velocity as by third equation of motion v2=0+2ghv=2gh−−−√and for range time to reach ground t=2(H−h)g−−−−−−√and range R=vt=2gh−−−√×2(H−h)g−−−−−−√=2h(H−h)−−−−−−−−√

Hope it helps!