Question

A flat plate moves normally towards a discharging jet of water at the rate of $3m/s$. The jet discharges the water at the rate of $0.1m^3/s$ and at the speed of 18 m/s. The force exerted on the plate due to the jet is

• A. $1800N$
• B. $2100N$
• C. $2450N$
• D. $1560N$

Answer 1

Answer: (C)

$2450N$

Relative velocity of the water jet with respect to the moving plate $=(18+3)=21m/s$.

The mass of water hitting the plate per second $=a\rho \left(21\right)$, where a is the cross-sectional area of the jet.
$F=$ Force normal to the plate
$=$ Rate of change of momentum along the direction of the water jet
$=\left(Mass\right)\times \left(Velocity\right)=\left[a\rho \right(21\left)\right]21=441a\rho$
$=441\times \rho \times \left(\frac{0.1}{18}\right)$
$=\frac{441\times 0.1\times 1000}{18}N=2450N$