Question

Helium gas enters an adiabatic nozzle at 35 psia and 820 degrees R with an initial velocity of 10 ft/s. The helium leaves the nozzle at 782 degrees R and 29 psia.

(a) What is the velocity of the helium at the nozzle's exit? (ft/s)

(b) What is the isentropic efficiency of the nozzle? (%)

(c) What is the rate of entropy generation for this process? (Btu/lbm R)

Answer 1

P₁=820^oR

T₁=35 psia

P₂=782^oR

T₂ = 29psia

V₁ =10ft/s

for given temperature & p conditions you can find data for h₁ , s₁ & h₂,s₂

a)we can take nozzle as system,which is control volume .Energy balance for steady state flow system can be expressed in rate form as:

as steady state

then exit velocity become

(b) isentropic efficiency of nozzle

first we need to calculate exit velocity at isentropic condition that can be calculated as

where h2s can be found from given P₂ data at s_2s=s₁ ( from P₂ & s₁ find corresponding h_2s)

thus,

(c)rate of entropy generated from process

entropy generated can be calculated by taking energy balance at actual nozzle

net entropy transfer by heat & mass + entropy generated =change in system entropy (i.e zero for steady state)

so

s_gen =s₂-s₁

energy desructed = T₀S_gen=T₀(s₂-s₁)