Explanation Write the energy rate balance equation. 0 = Q ˙ cv − W ˙ cv + m ˙ [ ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 + g ( z 1 − z 2 ) ] (I) Here, the rate of heat transfer is Q ˙ cv , rate of work transfer is W ˙ cv , rate of mass flow is m ˙ , the enthalpy is h , velocity is V , gravitational acceleration is g , the elevation is z and the suffixes cv, 1 and 2 indicates control volume, initial and final state of the system respectively. Here, the helium operates in steady state. The inlet, exit of the diffuser is at same elevation and the helium flow adiabatically. Hence, neglect the potential energy i.e. g ( z 1 − z 2 ) = 0 , heat transfer i.e. Q ˙ cv = 0 and the work done is also zero in diffuser i.e. W ˙ cv = 0 . Then the Equation (I) becomes as follows to obtain the exit velocity. ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 = 0 h 2 − h 1 = 1 2 ( V 1 2 − V 2 2 ) V 1 2 − V 2 2 = 2 ( h 2 − h 1 ) V 2 2 = V 1 2 − 2 ( h 2 − h 1 ) V 2 = V 1 2 + 2 ( h 1 − h 2 ) (II) Write the formula for change in enthalpy ( h 1 − h 2 ) . h 1 − h 2 = c p ( T 1 − T 2 ) Substitute c p ( T 1 − T 2 ) for h 1 − h 2 in Equation (II). V 2 = V 1 2 + 2 [ c p ( T 1 − T 2 ) ] (III) Write the formula for specific heat at constant pressure. c p = k ( R / M ) k − 1 (IV) Here, the specific heat ratio is k , the molar mass of the helium is M and the universal gas constant is R . Write the formula for exit mass flow rate in terms of ideal gas equation. m ˙ 2 = A 2 V 2 p 2 ( R ¯ / M ) T 2 (V) Here, the exit cross-sectional area is A 2 and the exit velocity is V 2 , the pressure is p , universal gas constant is R ¯ , the molar mass of the helium is M , the temperature is T and the suffix 1 indicates the inlet state. The molar mass ( M ) of helium gas is 4.003 lb/lb ⋅ mol and universal gas ( R ) constant is 1.986 Btu ⋅ lb/mol ⋅ ° R . Conclusion: Substitute 1

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 4.12, Problem 35P

To determine

The mass flow rate of the helium gas through the nozzle, in lb/s.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.12, Problem 34P

Chapter 4.12, Problem 36P

Students have asked these similar questions

Q6/ A helical square section spring is set inside another, the outer spring having a free length of 35 mm greater than the inner spring. The dimensions of each spring are as follows: Mean diameter (mm) Side of square section (mm) Active turns Outer Inner Spring Spring 120 70 8 7 20 15 Determine the (1) Maximum deflection of the two springs and (2) Equivalent spring rate of the two springs after sufficient load has been applied to deflect the outer spring 60 mm. Use G = 83 GN/m².

Q2/ The bumper springs of a railway carriage are to be made of rectangular section wire. The ratio of the longer side of the wire to its shorter side is 1.5, and the ratio of mean diameter of spring to the longer side of wire is nearly equal to 6. Three such springs are required to bring to rest a carriage weighing 25 kN moving with a velocity of 75 m/min with a maximum deflection of 200 mm. Determine the sides of the rectangular section of the wire and the mean diameter of coils when the shorter side is parallel to the axis of the spring. The allowable shear stress is not to exceed 300 MPa and G = 84 kN/mm². Q6/ A belical

11. A load of 2 kN is dropped axially on a close coiled helical spring, from a height of 250 mm. The spring has 20 effective turns, and it is made of 25 mm diameter wire. The spring index is 8. Find the maximum shear stress induced in the spring and the amount of compression produced. The modulus of rigidity for the material of the spring wire is 84 kN/mm². [Ans. 287 MPa; 290 mm]

Chapter 4 Solutions

FUND OF ENGINEERING THERMO W/WILEY PLU

Ch. 4.12 - Prob. 1E Ch. 4.12 - 2. When a drip coffeemaker on-off switch is turned...Ch. 4.12 - Prob. 3E Ch. 4.12 - Prob. 4E Ch. 4.12 - Prob. 5E Ch. 4.12 - Prob. 6E Ch. 4.12 - Prob. 7E Ch. 4.12 - Prob. 8E Ch. 4.12 - Prob. 9E Ch. 4.12 - 10. How does the operator of a pumper-tanker fire...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The mass flow rate of the helium gas through the nozzle, in lb/s .

Videos

The mass flow rate of the helium gas through the nozzle, in lb/s.

Want to see the full answer?

Chapter 4 Solutions