A rectangular opening on the side of a tank has a width ℓ . The top of the opening is at a depth h 1 below the surface of the water and the bottom is at a depth h 2 (Figure). The volume of water t

Question

A rectangular opening on the side of a tank has a width $ℓ$ . The top of the opening is at a depth $h_{1}$ below the surface of the water and the bottom is at a depth $h_{2}$ (Figure). The volume of water that emerges from the opening in a unit time is given by $α 2 g m^{3} / s (g =$ acceleration due to gravity). Find the value of $α$ . Assume $ℓ$ is very small compared to radius of tank.

TestHub · Accepted Answer

Assuming a strip of thickness dx at a distance x above the top surface of water. $v = 2 gx ∴$ Volume of water coming out in unit time $=$

$(ℓ d x)_{v} = ℓ d x 2 gx ∴ v_{total} = \int_{h_{1}}^{h_{2}} ℓ 2 gx d x = \frac{2}{3} ℓ 2 g [h_{2}^{3/2} - h_{1}^{3/2}]$

Physics - Fluid Question with Solution | TestHub

Doubts & Discussion

JEE Main 2027 (Class 12)