Explanation Here, the system (air compressor) operates in steady state with one inlet and one exit. Hence, the inlet mass flow rate of the air is equal to the exit flow rate of air. m ˙ 1 = m ˙ 2 (I) Write the formula for inlet mass flow rate. m ˙ 1 = A 1 V 1 v 1 (II) Write the formula for exit mass flow rate. m ˙ 2 = A 2 V 2 v 2 (III) Here, the cross sectional area is A , the velocity is V and the specific volume is v ; the suffixes 1 and 2 indicate the inlet and exit stages respectively. Write the formula to calculate the area of the pipe at exit. A 2 = π d 2 2 4 (IV) Substitute A 1 V 1 v 1 for m ˙ 1 and A 2 V 2 v 2 for m ˙ 2 in Equation (I). A 1 V 1 v 1 = A 2 V 2 v 2 Substitute π d 2 2 4 for A 2 and solve for exit pipe diameter ( d 2 ) . A 1 V 1 v 1 = ( π d 2 2 4 ) V 2 v 2 A 1 V 1 v 1 = π d 2 2 V 2 4 v 2 d 2 2 = A 1 V 1 ( 4 v 2 ) v 1 ( π V 2 ) d 2 = [ 4 A 1 V 1 π V 2 ( v 2 v 1 ) ] 1 / 2 (V) Here, the process is described by p v 1.3 = c o n s tan t . It is the polytropic process. The polytropic relationships between the inlet and exit stages are as follows. p 1 v 1 1.3 = p 2 v 2 1.3 p 1 p 2 = v 2 1

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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The word 'thermodynamics' can be divided into two words, 'thermo' and 'dynamics'. The word thermo deals with the heat and thermal phenomenon, whereas dynamics deals with forces or external agent that drives the heat flow or aids in the motion of heat.

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Chapter 4.12, Problem 21P

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The diameter of the exit pipe, in inches.

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Chapter 4.12, Problem 20P

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