(a) Explanation Assume the nozzle to be control volume. Write the energy work equation for the nozzle. ∫ 1 2 v ⋅ d p + V 2 2 − V 1 2 2 + g ( z 2 − z 1 ) = 0 (I) Here, the specific volume is v , the velocity at inlet is V 1 , the velocity at exit is V 2 , the acceleration due to gravity is g , the datum head at inlet is z 1 and the datum head at exit is z 2 . The potential energy changes are negligible hence the initial and final datum head must be equal, that is z 1 = z 2 . Write the polytropic expansion work in the nozzle. ∫ 1 2 v ⋅ d p = − n R n − 1 [ T 2 − T 1 ] Here, the temperature at inlet is T 1 , the temperature at exit is T 2 , the gas constant is R and the polytropic index is n . Substitute − n R n − 1 [ T 2 − T 1 ] for ∫ 1 2 v ⋅ d p and z 2 for z 1 in Equation (I). − n R n − 1 [ T 2 − T 1 ] + V 2 2 − V 1 2 2 + g ( z 2 − z 2 ) = 0 − n R n − 1 [ T 2 − T 1 ] + V 2 2 − V 1 2 2 = 0 V 2 2 = V 1 2 + 2 n R n − 1 [ T 1 − T 2 ] V 2 = V 1 2 + 2 n R n − 1 [ T 1 − T 2 ] (II) Write the final temperature for a polytropic process. T 2 = T 1 ( p 2 p 1 ) ( n − 1 n ) (III) Here, the pressure at inlet is p 1 and the pressure at exit is p 2 . Write the gas constant for the gas. R = R ¯ M (IV) Here, the universal gas constant is R ¯ and the molar mass of the gas is M . Conclusion: The universal gas constant is 8.314 kJ / K ⋅ kmol and the molar mass of Nitrogen is 28.01 kg / kmol . Substitute 8.314 kJ / K ⋅ kmol for R ¯ and 28.01 kg / kmol for M in Equation (IV) (b) To determine The rate of heat transfer in kJ / kg , of gas flowing.

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ISBN: 2818440116926

Author: MORAN

Publisher: WILEY CONS

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Chapter 6.13, Problem 185P

(a)

To determine

The exit velocity of the Nitrogen gas.

(b)

To determine

The rate of heat transfer in kJ/kg, of gas flowing.

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Chapter 6.13, Problem 184P

Chapter 6.13, Problem 186P

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