A fire hydrant delivers water of density rho | vedclass

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

Question

(D) The rate of change of momentum of the water is equal to the force exerted by the pipe on the water. Let the initial velocity be $\vec{v}_i = V \ha

Vedclass · Accepted Answer

$\sqrt{2} \rho VL$

Vedclass · Answer

(D) The rate of change of momentum of the water is equal to the force exerted by the pipe on the water. Let the initial velocity be $\vec{v}_i = V \hat{j}$ and the final velocity be $\vec{v}_f = V \hat{i}$. The mass flow rate is $\frac{dm}{dt} = \rho \frac{dV}{dt} = \rho L$. The force exerted by the pipe on the water is $\vec{F}_{pw} = \frac{d\vec{p}}{dt} = \frac{dm}{dt} (\vec{v}_f - \vec{v}_i) = \rho L (V \hat{i} - V \hat{j}) = \rho VL \hat{i} - \rho VL \hat{j}$. The magnitude of this force is $|\vec{F}_{pw}| = \sqrt{(\rho VL)^2 + (-\rho VL)^2} = \sqrt{2} \rho VL$. By Newton's third law,the force exerted by the water on the pipe corner is equal in magnitude and opposite in direction to the force exerted by the pipe on the water. Therefore,the magnitude of the force exerted by the water on the corner is $\sqrt{2} \rho VL$.

Similar Questions

The energy of an electromagnetic radiation is $19.875 \times 10^{-13} \ erg$. What is its wave number in $cm^{-1}$? $(h = 6.625 \times 10^{-27} \ erg \ sec, c = 3 \times 10^{10} \ cm \ sec^{-1})$

Name the ion responsible for unmasking of active sites for myosin for cross-bridge activity during muscle contraction.

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}$,$4 \hat{i}$,$3 \hat{i}+3 \hat{j}$ and $-3 \hat{i}+2 \hat{j}$ respectively. Then the quadrilateral $PQRS$ must be a

The chemical reaction that involves the roasting process is

Ethanol,when reacted with $PCl_5$,gives $A$,$POCl_3$,and $HCl$. $A$ reacts with silver nitrite to form $B$ (major product) and $AgCl$. $A$ and $B$ are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module