Question

Air flows through a device such that the stagnation pressure is 0.4 MPa, the stagnation temperature is 400°C, and the velocity is 528 m/s. Determine the static pressure and temperature of the air at this state. The properties of air at an anticipated average temperature of 600 K are cp = 1.051 kJ/kg·K and k = 1.376.

Answer 1

To solve this problem it is necessary to apply the concepts related to temperature stagnation and adiabatic pressure in a system.

The stagnation temperature can be defined as

`T_0 = T+(V^2)/(2c_p)`

Where

T = Static temperature

V = Velocity of Fluid

`c_p =` Specific Heat

Re-arrange to find the static temperature we have that

`T = T_0 - (V^2)/(2c_p)`

`T = 673.15-((528)/(2*1.005))((1)/(1000))`

`T = 672.88K`

Now the pressure of helium by using the Adiabatic pressure temperature is

`P = P_0 ((T)/(T_0))^(k/(k-1))`

Where,

`P_0`= Stagnation pressure of the fluid

k = Specific heat ratio

Replacing we have that

`P = 0.4 ((672.88)/(673.15))^(1.4/(1.4-1))`

`P = 0.399Mpa`

Therefore the static temperature of air at given conditions is 72.88K and the static pressure is 0.399Mpa

Note: I took the exactly temperature of 400 ° C the equivalent of 673.15K. The approach given in the 600K statement could be inaccurate.