Air at 1 MPa and 600°C enters a converging nozzle, shown in...

Air at 1 MPa and 600°C enters a converging nozzle, shown in Fig., with a velocity of 150 m/s. Determine the mass flow rate through the nozzle for a nozzle throat area of 50 cm² when the back pressure is (a) 0.7 MPa and (b) 0.4 MPa. AIR P_i = 1 MPa T_i = 600°C V_i = 150 m/s Converging nozzle P_b A_t = 50 cm² Air at local pressure of 700 kPa and a local temperature of 280 K enters a frictionless, adiabatic convergent-divergent nozzle with a velocity of 152 m/s. The throat area of the nozzle is 3 cm², exit area is 12 cm² and a shock occurs where the nozzle area 6 cm². - Determine the back pressure. - What is the flow velocity on both sides of the shock? - What is the flow rate? - What is the exit Mach number?

Transcript

00:01 In this question, in the first question in part a we have to find the back pressure for so back pressure is given as it is 0 .7 mpa.

00:08 So now to calculate the mass flow rate we have the formula m dot is equal to it is 80 rho 1 so 80 into rho 1 into v1.

00:16 So here we have so first let us calculate the stagnation temperature which is given by ti plus vi square divided by 2 cp which is equal to so it is on substitution we have 873 plus 150 square divided by 2 into 1 .005 which is equal to 884 kelvin.

00:30 Then we have the stagnation pressure is given by it is pi into toi divided by ti whole power gamma divided by gamma minus 1.

00:38 So on substitution we have 1 mpa into 884 divided by 873 divided by 1 .4 divided by 1 .4 minus 1 which is equal to 1 .045 mpa.

00:48 Then we have the critical pressure ratio is given by p star divided by p not is equal to 2 divided by gamma plus 1 power gamma divided by gamma plus so gamma minus 1.

00:58 Therefore we have on substitution so substituting gamma is 1 .4 we have p star by p not is 0 .528.

01:03 Now we have for the first case the back pressure ratio so for case a is given by pb divided by p not is equal to 0 .7 divided by 1 .045 which is equal to so 0 .67.

01:15 So now we have the throat pressure ratio is given by pt by p not is again 0 .670 and mach number is 0 .728.

01:22 So we have tt by t not is equal to 0 .892.

01:25 So from this we have tt is equal to t not is 884.

01:28 So this is 884 t not is 884.

01:31 So we have it is 788 .5 kelvin.

01:34 Now the mass flow rate is given by m dot is equal to rho t into at into pt.

01:38 So which is equal to it is pt divided by r into tt at so into m at root of gamma tt...

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