An engine pumps water through a hose pipe. Wa | vedclass

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

Question

(B) The power $P$ required to pump water is given by the rate of change of kinetic energy.$P = \frac{d}{dt} (\frac{1}{2} m v^2) = \frac{1}{2} v^2 \fra

Vedclass · Accepted Answer

$400$

Vedclass · Answer

(B) The power $P$ required to pump water is given by the rate of change of kinetic energy.$P = \frac{d}{dt} (\frac{1}{2} m v^2) = \frac{1}{2} v^2 \frac{dm}{dt}$.Here,$\frac{dm}{dt}$ is the mass flow rate,which can be expressed as $\frac{dm}{dt} = \lambda v$,where $\lambda$ is the mass per unit length $(100\, kg/m)$ and $v$ is the velocity $(2\, m/s)$.Thus,$\frac{dm}{dt} = 100\, kg/m 	imes 2\, m/s = 200\, kg/s$.Substituting this into the power formula:$P = \frac{1}{2} 	imes (200\, kg/s) 	imes (2\, m/s)^2$.$P = \frac{1}{2} 	imes 200 	imes 4 = 400\, W$.

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2\, m/s$. The mass per unit length of water in the pipe is $100\, kg/m$. Calculate the power $W$ of the engine. (in $, W$)

Similar Questions

$A$ car of mass $1250 \ kg$ is moving with a velocity of $30 \ m/s$. If the engine delivers $30 \ kW$ of power and the resistive force acting on the car is $750 \ N$,find the maximum acceleration of the car.

$A$ motor can pump $7560 \text{ kg}$ of water per hour from a well of depth $100 \text{ m}$. If the efficiency of the pump is $70 \%$, then the power of the pump is (Acceleration due to gravity $= 10 \text{ m s}^{-2}$) (in $\text{ kW}$)

An object of mass $m$ is projected with an initial velocity $u$ at an angle $\theta$ with the horizontal. What is the average power delivered by gravity in reaching the highest point?

$A$ body of mass $2 \ kg$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $P$. Its displacement in $4 \ s$ is $\frac{1}{3} \alpha^2 \sqrt{P} \ m$. The value of $\alpha$ will be $.............$

$A$ man is riding a cycle with a velocity of $7.2 \text{ km/hr}$ up a hill having a slope of $1$ in $20$. The total mass of the man and the cycle is $100 \text{ kg}$. The power of the man is ............ $\text{W}$. (in $\text{ W}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module