The surface of water in a water tank of cross | vedclass

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

Question

(D) According to the equation of continuity,the volume flow rate at the tank surface must equal the volume flow rate at the tap.$A_1 v_1 = A_2 v_2$Her

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) According to the equation of continuity,the volume flow rate at the tank surface must equal the volume flow rate at the tap.$A_1 v_1 = A_2 v_2$Here,$A_1 = 750 \, cm^2 = 750 	imes 10^{-4} \, m^2$ and $A_2 = 500 \, mm^2 = 500 	imes 10^{-6} \, m^2$.The velocity of water at the tap is $v_2 = 30 \, cm/s = 0.3 \, m/s$.The velocity of the water surface $v_1$ is equal to $|\frac{dh}{dt}|$.Substituting the values: $750 	imes 10^{-4} 	imes |\frac{dh}{dt}| = 500 	imes 10^{-6} 	imes 0.3$.$|\frac{dh}{dt}| = \frac{500 	imes 0.3 	imes 10^{-6}}{750 	imes 10^{-4}} = \frac{150 	imes 10^{-6}}{750 	imes 10^{-4}} = 0.2 	imes 10^{-2} \, m/s = 2 	imes 10^{-3} \, m/s$.Since the height $h$ is decreasing,$\frac{dh}{dt} = -2 	imes 10^{-3} \, m/s$.Comparing with $x 	imes 10^{-3} \, m/s$,we get $x = 2$ (taking the magnitude as per standard convention for such problems).

Similar Questions

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

Which of the following electronic configurations is not possible according to Hund's rule?

Which of the following logic gates is a universal gate?

$A$ uniform chain of length $L$ is lying on a horizontal table. If the coefficient of friction between the chain and the table top is $\mu$, what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?

What is absent in yeast?

Vedclass Test Series

Exam Paper Generator

Online Exam Module