Air at 1 MPa and 600 K enters a converging nozzle with a vel

Air at 1 MPa and 600 K enters a converging nozzle, with a velocity of 200 m/s. The nozzle area at throat is 100cm^2 and the back pressure is 0.8 MPa

a. What is the stagnation pressure?

b. What’s the mass flow rate?

c. What’s the mass flow rate if the back pressure is 0.35 MPa?

Step 1:

The pressure a fluid attains when brought to rest isentropically is called the stagnation pressure Po:

For ideal gases with constant specific heats Po is related to the the static pressure of the fluid by

Po/P = (To/T)^K/k-1

The nominal values used for air at 300 K are CP = 1.005 kJ/kg,

k =1.4

^{To = T+ V^2/ 2cp} ^{= 600 + 200^2/ 2*1005 = 600+40000/2 =620k}

Po/1 = (600/620)^1.4/(1.4-1)

^{= 3.36 mpa}

^{Po = 3.36 mpa}

^{Step 2:}

^{Ws = cp(To-T1)=}^{1.005(620-600)= 20* 1.005 =20.1 kg/sec}

^{e= density of air =} 1.225 kg/m^3,

^{a= throat area = 100 cm^2 =100/10000 = 0.01 m^2}

^{m = eav}^{= 1.225*0.01* 200 = 2.45 kg/ sec}

^{step 3:}

^{m = A*po squre root (k/RTo)*(2/k+1)^ (k+1)/ 2(k-1) =}

^{0.01 * 0.35* squre root (1.4/0.287*620)*(2/2.4)^(2.4)/2(0.4)= 2.1 kg/sec}