The vertical side of a large tank is pierced by a small hole at a height above the ground

PHYSICS · Subjective · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

The vertical side of a large tank is pierced by a small hole at a height

h

above the ground. The free surface of water in the tank is maintained at a constant height

H

above the ground where

H>h

. Water exits the hole horizontally and strikes the ground at a horizontal distance

R

from the foot of the tank. (i) Show that

R = 2\sqrt{h\,(H-h)}

. (ii) Determine the value of

h

(in terms of

H

) for which

R

is maximum and obtain the corresponding maximum range

R_{\max}

. (iii) If the water surface is

3.2\,\text{m}

above the ground, calculate numerically the optimum height of the hole and the maximum horizontal distance reached by the jet.