(a) Explanation Write the expression for mass flow rate at inlet 1. m 1 = P 1 ( A V ) 1 R T 1 (I) Here, the mass flow rate at inlet 1 is m 1 , pressure at inlet 1 is P 1 , the product of area and velocity at inlet 1 is ( A V ) 1 . the gas constant is R and temperature at inlet 1 is T 1 . Write the expression for cross-sectional area at inlet 2. A 2 = ( π D 2 2 4 ) (II) Here, the cross-sectional area at inlet 2 is A 2 and the diameter of inlet 2 is D 2 . Write the expression for mass flow rate at inlet 2. m 2 = P 2 A 2 V 2 R T 2 (III) Here, the mass flow rate at inlet 2 is m 2 , pressure at inlet 2 is P 2 , the velocity at inlet 2 is V 2 . and temperature at inlet 2 is T 2 . Write the expression for energy rate balance. m 1 ( C p ) ( T 1 − T 3 ) + m 2 ( C p ) ( T 3 − T 2 ) = 0 m 1 ( T 1 − T 3 ) + m 2 ( T 3 − T 2 ) = 0 (IV) Here, the specific heat is C p , the temperature at inlet 1 is T 1 , the temperature at inlet 2 is T 2 and the temperature of mixed air at state 3 is T 3 . Conclusion: Substitute 1 atm for P 2 , 2000 ft 3 / min for ( A V ) 1 , 53.3533 ft ⋅ lbf / lb ⋅ °R for R and 90 ° F for T 1 in Equation (I). m 1 = ( 1 atm ) ( 2000 ft 3 / min ) ( 53.3533 ft ⋅ lbf / lb ⋅ °R ) ( 90 ° F ) = ( 1 atm ) ( 14 .7 × 144 lbf 1 atm ⋅ ft 2 ) ( 2000 ft 3 / min ) ( 53.3533 ft ⋅ lbf / lb ⋅ °R ) ( 90 + 460 ) ° R = 144 (b) To determine The diameter of the mixed air duct.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832318

Author: MORAN

Publisher: WILEY

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Chapter 4.12, Problem 84P

(a)

To determine

The temperature of mixed air.

(b)

To determine

The diameter of the mixed air duct.

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Chapter 4.12, Problem 83P

Chapter 4.12, Problem 85P

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