A pump draws water from a tank which is 2.5; | vedclass

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

Question

(B) The power $P$ required by the pump is given by the rate of change of mechanical energy: $P = \left(gh + \frac{v^{2}}{2}\right) \frac{dm}{dt}$.Firs

Vedclass · Accepted Answer

$185$

Vedclass · Answer

(B) The power $P$ required by the pump is given by the rate of change of mechanical energy: $P = \left(gh + \frac{v^{2}}{2}ight) \frac{dm}{dt}$.First,calculate the mass flow rate $\frac{dm}{dt} = ho A v$.Given $ho = 1000\; kg/m^{3}$,$A = 10\; cm^{2} = 10 	imes 10^{-4}\; m^{2}$,and $v = 5\; m/s$:$\frac{dm}{dt} = 1000 	imes 10 	imes 10^{-4} 	imes 5 = 5\; kg/s$.Now,substitute the values into the power equation using $g = 10\; m/s^{2}$,$h = 2.5\; m$,and $v = 5\; m/s$:$P = \left(10 	imes 2.5 + \frac{5^{2}}{2}ight) 	imes 5$.$P = (25 + 12.5) 	imes 5$.$P = 37.5 	imes 5 = 187.5\; W$.Rounding to the nearest provided option,the correct value is $185\; W$.

Similar Questions

$A$ $60\; HP$ electric motor lifts an elevator having a maximum total load capacity of $2000\; kg$. If the frictional force on the elevator is $4000\; N$,the speed of the elevator at full load is close to .............. $m/s$.
$(1\; HP = 746\; W, g = 10\; ms^{-2})$

An electric motor exerts a force of $40 N$ on a cable and pulls it by a distance of $30 m$ in one minute. The power supplied by the motor (in Watts) is

The machine gun fires $240$ bullets per minute. If the mass of each bullet is $10 \ g$ and the velocity of the bullets is $600 \ ms^{-1}$, the power (in $kW$) of the gun is

The power of a pump,which can pump $500 \,kg$ of water to a height of $100 \,m$ in $10 \,s$,is .......... $kW$. (Take $g = 10 \,m/s^2$)

$A$ body of mass $1 \ kg$ starts from rest and moves with uniform acceleration. In $2 \ s$,its velocity is $10 \ m/s$. The power exerted on the body in $1 \ s$ is (in $W$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module