Water is filled in a cylindrical container to | vedclass

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

Question

(A) Let $A$ be the cross-sectional area of the tank and $a$ be the cross-sectional area of the orifice.Let $V$ be the velocity with which the water le

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(A) Let $A$ be the cross-sectional area of the tank and $a$ be the cross-sectional area of the orifice.Let $V$ be the velocity with which the water level decreases in the tank and $v$ be the velocity of efflux from the orifice.From the equation of continuity,$av = AV$,so $V = \frac{av}{A}$.Applying Bernoulli's theorem between the top surface of the water (point $1$) and the orifice (point $2$):$P_0 + ho g h_1 + \frac{1}{2} ho V^2 = P_0 + ho g h_2 + \frac{1}{2} ho v^2$Here,$h_1 = 3 \ m$ and $h_2 = 0.525 \ m$. The effective height of the water column above the orifice is $h = h_1 - h_2 = 3 - 0.525 = 2.475 \ m$.Rearranging the equation: $\frac{1}{2} ho v^2 - \frac{1}{2} ho V^2 = ho g h$$v^2 - V^2 = 2gh$Substituting $V = \frac{a}{A}v$:$v^2 - (\frac{a}{A})^2 v^2 = 2gh$$v^2 [1 - (\frac{a}{A})^2] = 2gh$Given $\frac{a}{A} = 0.1$,$g = 10 \ m/s^2$,and $h = 2.475 \ m$:$v^2 [1 - (0.1)^2] = 2 	imes 10 	imes 2.475$$v^2 [1 - 0.01] = 49.5$$v^2 [0.99] = 49.5$$v^2 = \frac{49.5}{0.99} = 50 \ m^2/s^2$.

Water is filled in a cylindrical container to a height of $3 \ m$. The ratio of the cross-sectional area of the orifice and the beaker is $0.1$. The square of the speed of the liquid coming out from the orifice is ....... $m^2/s^2$ $(g = 10 \ m/s^2)$.

Similar Questions

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

Explain why the roof of a building flies off during a stormy wind.

$A$ horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity $1 \ m/s$ when the pressure is $50 \ kPa$ at a point. If the velocity of flow has to be $2 \ m/s$ at some other point, the pressure at that point should be: (in $kPa$)

Why does an airplane run a certain length on the runway first before taking off?

The Bernoulli's equation is given by $p + \frac{1}{2} \rho v^{2} + h \rho g = k$,where $p =$ pressure,$\rho =$ density,$v =$ speed,$h =$ height of the liquid column,$g =$ acceleration due to gravity,and $k$ is a constant. The dimensional formula for $k$ is the same as that for:

Vedclass Test Series

Exam Paper Generator

Online Exam Module