Answer
(a) $0.53N$
(b) $20.4m/s$
Work Step by Step
(a) The required force can be determined as follows:
$F=pd^2_{plunger}\frac{\pi}{4}$
We plug in the known values to obtain:
$F=140mm.\rho Hg.g.(0.6cm)^2\frac{\pi}{4}$
$\implies F=0.53N$
(b) We can find the required flow speed as follows:
$v=\frac{V}{At}$
$\implies v=\frac{4V}{d^2_{needle}\pi t}$
We plug in the known values to obtian:
$v=\frac{4(2)}{(0.25)^2\pi (2)}$
This simplifies to:
$v=20.4m/s$
