A cylindrical tank with a large diameter is f | vedclass

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

Question

(D) Applying Bernoulli's principle at the top surface of the water and at the hole:$P_{atm} + \rho g h + \frac{1}{2} \rho v_{top}^2 = P_{atm} + 0 + \f

Vedclass · Accepted Answer

$1.2 	imes 10^{-3}$

Vedclass · Answer

(D) Applying Bernoulli's principle at the top surface of the water and at the hole:$P_{atm} + ho g h + \frac{1}{2} ho v_{top}^2 = P_{atm} + 0 + \frac{1}{2} ho v_{hole}^2$Since the tank has a large diameter, the velocity at the top surface $v_{top} \approx 0$.Thus, the velocity of efflux at the hole is given by Torricelli's Law:$v = \sqrt{2gh}$Given $g = 9.8 \ m/s^2$ (or $9.81 \ m/s^2$) and $h = 0.2 \ m$:$v = \sqrt{2 	imes 9.8 	imes 0.2} = \sqrt{3.92} \approx 1.98 \ m/s$The drainage rate (volume flow rate) $Q = A 	imes v$.Given area $A = 6 \ cm^2 = 6 	imes 10^{-4} \ m^2$.$Q = 6 	imes 10^{-4} 	imes 1.98 \approx 1.188 	imes 10^{-3} \ m^3/s$.Rounding to two significant figures, $Q \approx 1.2 	imes 10^{-3} \ m^3/s$.

$A$ cylindrical tank with a large diameter is filled with water. Water drains out through a hole at the bottom of the tank. If the cross-sectional area of the hole is $6 \ cm^2$, then the drainage rate in $m^3 s^{-1}$ when the depth of the water is $0.2 \ m$ is:

Similar Questions

$A$ container has a hole of cross-sectional area $1 \, cm^2$ at its bottom. If water is poured into the container at a rate of $70 \, cm^3/s$, what is the maximum height (in $cm$) to which the water can be filled?

$A$ rectangular vessel,when full of water,takes $10 \text{ minutes}$ to be emptied through an orifice in its bottom. How many minutes will it take to be emptied when half-filled with water?

There is a hole in the bottom of a tank containing water. If the total pressure at the bottom is $3 \ atm$,then the velocity of water flowing from the hole is $(1 \ atm = 10^5 \ Pa)$ :-

$A$ small hole of area of cross-section $2 \; mm^{2}$ is present near the bottom of a fully filled open tank of height $2 \; m$. Taking $g = 10 \; m/s^{2}$,the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \; m^{3}/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module