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

If $\lambda_0$ is the de-Broglie wavelength for a proton accelerated through a potential difference of $100 \ V$,the de-Broglie wavelength for an $\alpha$-particle accelerated through the same potential difference is

Which one has the maximum oxidation number of phosphorus?

$A$ person in an elevator accelerating upwards with an acceleration of $2\,m s^{-2}$ tosses a coin vertically upwards with a speed of $20\,m s^{-1}$. After how much time will the coin fall back into his hand? $(g = 10\,m s^{-2})$

One litre of oxygen at a pressure of $1 ~atm$ and two litres of nitrogen at a pressure of $0.5 ~atm$ are introduced into a vessel of volume $1 ~L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

$\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module