Explanation Here, the air flows at steady state through the diffuser. Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 (I) Write the formula for inlet mass flow rate in terms of ideal gas equation. m ˙ 1 = A 1 V 1 p 1 ( R ¯ / M ) T 1 (II) 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 (III) Here, the cross sectional area is A , the velocity is V , the pressure is p , universal gas constant is R ¯ , the molar mass of the air is M , the temperature is T and the suffixes 1 and 2 indicates the inlet and exit states. Substitute A 1 V 1 p 1 ( R ¯ / M ) T 1 for m ˙ 1 and A 2 V 2 p 2 ( R ¯ / M ) T 2 for m ˙ 2 in Equation (I). A 1 V 1 p 1 ( R ¯ / M ) T 1 = A 2 V 2 p 2 ( R ¯ / M ) T 2 (IV) Rearrange the equation (IV) to obtain the exit pressure ( p 2 ) . A 1 V 1 p 1 T 1 = A 2 V 2 p 2 T 2 p 2 = p 1 ( A 1 A 2 ) ( V 1 V 2 ) ( T 2 T 1 ) (V) 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 ) ] (VI) 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 air operates in steady state. The inlet, exit of the diffuser is at same elevation and the ignoring the heat transfer (given). Hence, neglect the potential energy i.e. g ( z 1 − z 2 ) = 0 , heat transfer i.e. Q ˙ cv = 0 and the work done i.e. W ˙ cv = 0 . Then the Equation (VI) becomes as follows to obtain the exit enthalpy ( h 2 ) of diffuser. 0 = m ˙ [ ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 ] 0 = ( h 1 − h 2 ) + ( V 1 2 − V 2 2 ) 2 h 2 = h 1 + ( V 1 2 − V 2 2 ) 2 (VII) At inlet: Refer Table A-22E, “Ideal Gas Properties of Air”

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

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

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 4.12, Problem 38P

To determine

The exit temperature of air from the diffuser, in °R and the pressure in lbf/in.2.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.12, Problem 37P

Chapter 4.12, Problem 39P

Students have asked these similar questions

Spur gears Note : Exam is open notes &tables / Answer all questions. Q.1. The press shown for Figure.1 has a rated load of 22 kN. The twin screws have double start Acme threads, a diameter of 50 mm, and a pitch of 6 mm. Coefficients of friction are 0.05 for the threads and 0.08 for the collar bearings. Collar diameters are 90 mm. The gears have an efficiency of 95 percent and a speed ratio of 60:1. A slip clutch, on the motor shaft, prevents overloading. The full-load motor speed is 1720 rev/min. (a) When the motor is turned on, how fast will the press head move? (Vm= , Vser. = ) (5M) (b) What should be the horsepower rating of the motor? (TR=, Tc= Pser. = " Bronze bushings Foot Motor Bearings watt, Pm= watt, Pm= h.p.) (20M) 2['s Fig.1 Worm Collar bearing

Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.

An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.

Chapter 4 Solutions

Fundamentals of Engineering Thermodynamics

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 exit temperature of air from the diffuser, in ° R and the pressure in lbf/in . 2 .

Videos

The exit temperature of air from the diffuser, in °R and the pressure in lbf/in.2.

Want to see the full answer?

Chapter 4 Solutions