To determine The inlet area. The throat area. Explanation The following figure represents the nozzle system on T-s diagram with temperature on y axis and entropy at x axis. Figure-(1) Write the expression of inlet area. A y = m ˙ R T y p y V y (I) Here the exit area is A y , temperature at the state y is T y , pressure at the state y is P y and the velocity at state y is V y . Write the expression for the exit velocity. V y = M y k R T y (II) Here, the exit velocity at state y is V y . Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (III) Here, x denotes M y , and y denotes P / P o . Refer table 9.3 “Normal shock function for an ideal gas with k = 1.4 ” to obtain the mach no at state y for mach no 1.2 . M y = 0.8421 Write the formulae for the ratio of pressure at state y and stagnant pressure P o y . r 1 = P y P o y (IV) Write the formulae for the ratio of temperature at state y and stagnant temperature T 2 o y . r 2 = T y T 2 o y (V) Write the formulae for the ratio of area at state y and stagnant area A ∗ . r 3 = A y A ∗ (VI) Conclusion: Refer table 9.2 “isentropic flow function for an ideal gas with k = 1.4 ” to obtain the ratio of pressure at state y and stagnant pressure for M y = 0.8421 ratio number at r = 0.777 bar M y P / P o 0.80 0.656 0.8421 ? 0.90 0.591 Substitute 0.80 for x 1 , 0.8421 for x 2 , 0.90 for x 3 , 0.656 for y 1 , and 0.591 for y 3 in Equation (III). y 2 = { [ ( 0.8421 − 0.80 ) ( 0.591 − 0.656 ) ] ( 0.90 − 0.80 ) + 0.656 } = ( − 2.7 × 10 − 3 ) 0.1 + 0.656 = 0.628 From above calculation the ratio of pressure at state y and stagnant pressure is 0.628 Substitute 100 lbf / in 2 for P o y in Equation (IV). 0.628 = P y 100 lbf / in 2 P y = 62.8 lbf / in 2 Refer table 9.2 “isentropic flow function for an ideal gas with k = 1.4 ” to obtain the ratio T y / T o y at mach number number 0.8421 M y T y / T o y 0.80 0.886 0.8421 ? 0.90 0.860 Substitute 0.80 for x 1 , 0.8421 for x 2 , 0.90 for x 3 , 0.886 for y 1 , and 0.860 for y 3 in Equation (III). y 2 = { [ ( 0.8421 − 0.80 ) ( 0.860 − 0.886 ) ] ( 0.90 − 0.80 ) + 0.886 } = ( − 1.09 × 10 − 3 ) 0.1 + 0.886 = 0.875 From above calculation the the ratio of temperature at state y and stagnant temperature is 0

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 9.14, Problem 140P

To determine

The inlet area.

The throat area.

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Chapter 9.14, Problem 139P

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Fundamentals of Engineering Thermodynamics

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