Answer to Question #295547 in Molecular Physics | Thermodynamics for Losifer

Question #295547

A blower handles 1kg/s of air at 20^(@)C and consumes a power of 15kW.The inlet and outlet velocities of air are 100m/s and 150m/s respectively.Find the exit air temperature assuming adiabatic conditions.Take c_(p) of air is 1.005kJ/kg-K.

1
Expert's answer
2022-02-09T08:03:51-0500

Solution;

Given;

m˙=1kg/s\dot{m}=1kg/s

T1=20oc=293T_1=20^oc=293

W=15kWW=15kW

V1=100m/sV_1=100m/s

V2=150m/sV_2=150m/s

cp=1.00kJ/kgKc_p=1.00kJ/kgK

The process is adiabatic;

Q=0Q=0

Apply steady flow energy equation;

m˙(h1+V122000)+W=m˙(h2+V222000)\dot{m}(h_1+\frac{V_1^2}{2000})+W=\dot{m}(h_2+\frac{V_2^2}{2000})

where;

h=cpTh=c_pT

By direct substitution;

1[(1.005×293)+10022000]+15=1[(1.005×T2)+15022000)1[(1.005 \times 293)+\frac{100^2}{2000}]+15=1[(1.005\times T_2)+\frac{150^2}{2000})

314.465=1.005T2+11.25314.465=1.005T_2+11.25

T2=301.7064KT_2=301.7064K or 28.71oc28.71^oc


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