Converging and diverging nozzles

[tsukuba]

Homework Statement

air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 400° C, and the velocy is 570 m/s.
Determine the static pressure and temperature of the air at this state.

Homework Equations

T_t=T + V² / 2 C_p where C_p is 1.005 Kj/ Kg* ° K

The Attempt at a Solution

what I did was Isolate for T since that is what I am looking for. [/B]

2 C_p x T_t - v² = T
somewhere in here I know I have to throw in 1000m²/s²/ Kj/kg °k
when I do that I get -323.5 ° K

the answer is 518.6 ° K

Someone please let me know where I have gone wrong. Thank you

 

[SteamKing]

Homework Statement

air flows through a device such that the stagnation pressure is 0.6 MPa, the stagnation temperature is 400° C, and the velocy is 570 m/s.
Determine the static pressure and temperature of the air at this state.

Homework Equations

T_t=T + V² / 2 C_p where C_p is 1.005 Kj/ Kg* ° K

The Attempt at a Solution

what I did was Isolate for T since that is what I am looking for. [/B]

2 C_p x T_t - v² = T
somewhere in here I know I have to throw in 1000m²/s²/ Kj/kg °k
when I do that I get -323.5 ° K

the answer is 518.6 ° K

Someone please let me know where I have gone wrong. Thank you

Your algebra is a little dodgy in solving for T.

The correct equation is:
T_t = T + [V² / (2 C_p)]

which means your equation for T is incorrect.

 

[tsukuba]

brackets or no brakets, wouldn't T stay the same when isolating it?

 

[SteamKing]

brackets or no brakets, wouldn't T stay the same when isolating it?

Tt = T + [V² / (2 Cp)]

T = Tt - [V² / (2 Cp)]

But you had

2 Cp x Tt - V² = T

which is not the same. Apparently, you multiplied only one side of the equation by (2 C_p).

 

[tsukuba]

hmm, not sure how you get that equation but I'm still not getting the right answer. I will have to ask the professor tomorrow