In a machine, a fluid from a compressor, which is at high pressure, is allowed to pass through a nozzle. Cross section of the nozzle is shown in the fiuge. The nozzle consists of two sections of radii `r_(1)` and `r_(2)`. The nozzle is fixed on a stand with the help of a clamp. the clamp is a circular ring of radius `r_(1)` and width b. The fluid from the compressor is at a presssure of n times the atmospheric pressure `p_(0)`. assume that the entrie system is horizontal the fluid is ideal and the flow is steady.

(a) what should be the volume flow rate so that pressure of the fluid at end B reduces to half of its value at end A?
(b) If the entire system is kept in gravity free space and the net force on the nozzle due to the fluid flow is F then determine the minimum radial pressure that should be applied on the clamp. so the nozzle remains in place. Coefficient of friction betwwen clamp and nozzle is `mu`.
(c) If a small hole is punched anywhere on the thinner part of the nozzle (close to end B) what should be the volume flow rate of the fluid so that it does not gush out?

Answer

(a) `Q=pir_(1)^(2)r_(1)^(2)sqrt((nP_(0))/(rho(r_(1)^(4)-r_(2)^(4))))`
(b) `(F)/(2pimur_(1)b)`
(c) `Q=pi r_(1)^(2)r_(2)^(2)sqrt((2(n-1)P_(0))/(rho(r_(1)^(4)-r_(2)^(4))))`