Question

Air enters a diffuser witha velocity of 400 m/s, a pressure of 1 bar and temperature of 25 C. It exits with a temperature of 100 C. What is the exit velocity of the air? Assume there are no heat losses or change in potential energy Data:= 0.718 kJ/kg.°C. MW = 28.9 g/mol

Answer 1

Answer:

Exit velocity of air is 96.43 m/s.

Explanation:

Given that

$V_1=400\ m/s$

$T_1=25C$

$T_2=100C$

For air

$C_p=1.005\ KJ/kg.K$

Now from first law of thermodynamics for open system at steady state

$h_1+\dfrac{V_1^2}{2000}+Q=h_2+\dfrac{V_2^2}{2000}+w$

For diffuser

$h_1+\dfrac{V_1^2}{2000}=h_2+\dfrac{V_2^2}{2000}$

We know that

$h=C_pT$

$h_1+\dfrac{V_1^2}{2}=h_2+\dfrac{V_2^2}{2000}$

$1.005\times 25+\dfrac{400^2}{2000}=1.005\times 100+\dfrac{V_2^2}{2}$

$V_2=96.43\ m/s$

So the exit velocity of air is 96.43 m/s.