A large open tank has two holes in the wall. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The velocity of efflux for a hole at depth $h$ is given by Torricelli's law: $v = \sqrt{2gh}$.The rate of flow of water (volume per second) is giv

Vedclass · Accepted Answer

$\frac{L}{\sqrt{2\pi}}$

Vedclass · Answer

(B) The velocity of efflux for a hole at depth $h$ is given by Torricelli's law: $v = \sqrt{2gh}$.The rate of flow of water (volume per second) is given by $Q = A \cdot v$,where $A$ is the area of the hole.For the square hole at depth $y$:Area $A_1 = L^2$Velocity $v_1 = \sqrt{2gy}$$Q_1 = L^2 \sqrt{2gy}$For the circular hole at depth $4y$:Area $A_2 = \pi R^2$Velocity $v_2 = \sqrt{2g(4y)} = 2\sqrt{2gy}$$Q_2 = \pi R^2 (2\sqrt{2gy})$Given that $Q_1 = Q_2$:$L^2 \sqrt{2gy} = \pi R^2 (2\sqrt{2gy})$$L^2 = 2\pi R^2$$R^2 = \frac{L^2}{2\pi}$$R = \frac{L}{\sqrt{2\pi}}$

Similar Questions

What is the total number of orbitals associated with the principal quantum number $n=3$?

Explain competition in detail.

What is the approximate weight of the flower of $Rafflesia$ $arnoldii$ (in $kg$)?

The condition for the lines $lx + my + n = 0$ and $l_1x + m_1y + n_1 = 0$ to be conjugate with respect to the circle $x^2 + y^2 = r^2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module