A tank of height 15 m and cross-section area | vedclass

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

Question

(A) Let the pressure applied by the piston be $P$ and the atmospheric pressure be $P_a$. The excess pressure is $\Delta P = P - P_a$. The height of th

Vedclass · Accepted Answer

$233$

Vedclass · Answer

(A) Let the pressure applied by the piston be $P$ and the atmospheric pressure be $P_a$. The excess pressure is $\Delta P = P - P_a$. The height of the water column above the hole is $h = 15 \ m - 12 \ m = 3 \ m$. The height of the hole from the ground is $H = 12 \ m$.Using Bernoulli's equation at the top surface and the hole,the velocity of efflux $v$ is given by $v = \sqrt{2gh + \frac{2\Delta P}{ho}}$.The time taken for the water to reach the ground is $t = \sqrt{\frac{2H}{g}}$.The horizontal range $R$ is given by $R = v 	imes t = \sqrt{2gh + \frac{2\Delta P}{ho}} 	imes \sqrt{\frac{2H}{g}}$.Given $R = 16 \ m$,$H = 12 \ m$,$h = 3 \ m$,$ho = 1000 \ kg/m^3$,and $g = 10 \ m/s^2$:$16 = \sqrt{2(10)(3) + \frac{2\Delta P}{1000}} 	imes \sqrt{\frac{2(12)}{10}}$$16 = \sqrt{60 + \frac{\Delta P}{500}} 	imes \sqrt{2.4}$$256 = (60 + \frac{\Delta P}{500}) 	imes 2.4$$106.67 = 60 + \frac{\Delta P}{500}$$46.67 = \frac{\Delta P}{500} \Rightarrow \Delta P = 23335 \ Pa \approx 23.3 \ kPa$.Wait,re-calculating: $256 / 2.4 = 106.666...$,so $106.666 - 60 = 46.666$. $\Delta P = 46.666 	imes 500 = 23333 \ Pa$.Force $F = \Delta P 	imes A = 23333 	imes 10 = 233330 \ N = 233.3 \ kN \approx 233 \ kN$.

Similar Questions

The reading of a pressure meter attached to a closed pipe is $4.5 \times 10^4 \ N/m^2$. On opening the valve,water starts flowing and the reading of the pressure meter falls to $2.0 \times 10^4 \ N/m^2$. The velocity of water is found to be $\sqrt{V} \ m/s$. The value of $V$ is . . . . . .

Explain the upward force (dynamic lift) acting on an airplane wing.

$Assertion :$ The velocity of flow of a liquid is smaller when pressure is larger and vice-versa.
$Reason :$ According to Bernoulli's theorem,for the stream line flow of an ideal liquid,the total energy per unit mass remains constant.

The weight of an aeroplane flying in the air is balanced by:

Write the limitations of Bernoulli's equation.

Vedclass Test Series

Exam Paper Generator

Online Exam Module