Question

Fresh water issues from the nozzle with a velocity of $20m/sec$ at the rate of $0.03m^3/sec$ and is split into two equal streams by the fixed vane and deflected through ${60}^{\circ }$ as shown in figure. The force in newtons required to hold the vane in place is
(Assume area of cross section of water in each stream in $A$)

Answer 1

Let $m$ be mass flow rate before the split, then mass flow rate of each stream is $m/2$
here $m=\rho Q$
$Q$ is volume flow rate
$Q=0.03{\text{m}}^3/s$
As Area of cross section is same throughout velocity of water is also same $v=20m/sec$
Rate of change of momentum along X axis is
$\frac{\Delta P}{\Delta t}=mv-2\left(m/2\right)v\cos 60=\frac{mv}{2}=\frac{\rho Qv}{2}$

$=\frac{1}{2}\times 1000\times 0.03\times 20$
$=\frac{1}{2}\times 30\times 20$
$=\frac{1}{2}\times 600N=300N$