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EGR 334 Thermodynamics Chapter 4: Section 1-3

EGR 334 Thermodynamics Chapter 4: Section 1-3. Lecture 12: Control Volumes and Conservation of Mass. Quiz Today?. Today’s main concepts:. Be able to explain what a control volume is Be able to write mass balance and mass rate balance equations for a control volume.

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EGR 334 Thermodynamics Chapter 4: Section 1-3

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  1. EGR 334 ThermodynamicsChapter 4: Section 1-3 Lecture 12: Control Volumes and Conservation of Mass Quiz Today?

  2. Today’s main concepts: • Be able to explain what a control volume is • Be able to write mass balance and mass rate balance equations for a control volume. • Be able to explain the continuity of mass flow equation. • Explain the difference between mass flow rate and volumetric flow rate. • Be able to set up problems involving mass balance Reading Assignment: • Read Chap 4: Sections 4-5 Homework Assignment: From Chap 4: 1, 6, 11, 22

  3. Sec 4.1: Conservation of Mass Q and W Now move to open system, mass can also pass the boundary. add the mass balance. Mass So far we have looked at closed systems Only Q and W pass the boundary Energy Balance From Chapter 2: Energy Balance • [ ] E within the system net Qinput • net W • output • [ ] • [ ] + = MassBalance • [ ] m within the system • [ ] • [ ] net minput • net m output + =

  4. Sec 4.1: Conservation of Mass MassBalance • [ ] m within the system • [ ] • [ ] net minput • net m output + = CV = control volume i = inlet, e = exit General form for multiple inlets/exits

  5. Sec 4.1.2: Mass Flow Rate Continuity Principle: mass flow is steady and continuous where ρ = density Vn = normal velocity component A = cross sectional area V = volume Mass flow rate: for constant Area for variable Area MassFlux

  6. Sec 4.2 Mass Rate Balance One-Dimensional Flow (Continuity Equation) • Flow is normal to the boundary • The fluid is homogeneous (intensive properties are uniform with position). where: = mass flow rate ρ = density = volumetric flow rate V = velocity v = specific volume A = area General form for multiple inlets/exits At steady State, and

  7. Sec 4.3 : Applications of the Mass Rate Balance Example: (4.16) Ammonia enters a control volume operating at steady state at pA= 14 bar, TA= 28oC, with a mass flow rate of 0.5 kg/s. Saturated vapor at pB = 4 bar leaves through one exit, with a volumetric flow rate of 1.036 m3/min and saturated liquid at pC=4 bar leaves through a second exit. Determine (a) the minimum diameter of the inlet pipe, in cm, so the ammonia velocity does not exceed 20 m/s (b) the volumetric flow rate of the second exit stream in m3/min. • Saturated vapor • pB= 4 bar, • 1.036 m3/min • pA= 14 bar, TA= 28oC • 0.5 kg/s • pC= 4 bar • Saturated liquid

  8. Sec 4.3 : Applications of the Mass Rate Balance • pA= 14 bar • TA= 28oC • mA=0.5 kg/s • Saturated vapor • pB= 4 bar, • 1.036 m3/min • pC= 4 bar • Saturated liquid Ammonia What else can you determine about the states? State 1: from table A-14 (state A is compressed liquid… let vA≈ vf @28oC = 1.6714x10-3 m3/kg) State 2: from table A-14 ( vB = vg @4bar) = 0.3094 m3/kg and TB=Tsat = -1.9oC) State 3: from table A-14 ( vC = vf @4bar)= 0.0015597 m3/kg and TC=Tsat = -1.9oC)

  9. Sec 4.3 : Applications of the Mass Rate Balance • Ammonia • Saturated vapor • Liquid • Saturated • liquid Consider mass flows: State A: already known… State B: can be found from volumetric flow rate State C: can be found from mass rate balance

  10. Sec 4.3 : Applications of the Mass Rate Balance • Ammonia • Saturated vapor • Liquid • Saturated • liquid What can we learn from the continuity equation: State A: State B: (already known) State C:

  11. Sec 4.3 : Applications of the Mass Rate Balance • Ammonia • Liquid • Saturated • vapor • Saturated • liquid Determine the size of the inlet pipe so that the velocity does not exceed VA = 20 m/s from the continuity equation: Area of a circular cross section: therefore:

  12. Sec 4.3 : Applications of the Mass Rate Balance Example 2: ( fromProb4.16) Liquid water at 70 oF enters a pump through an inlet pipe having a diameter of 6 in. The pump operates at steady state and supplies water to two exit pipes having diameters of 3 in and 4 in. The velocity of the 3 in pipe is 1.31 ft/s. At the exit of the 4 in pipe the velocity is 0.74 ft/s. The temperature of the water in each exit is 72 deg F. Determine a) the mass flow rate in lb/s in the inlet and each of the exit pipes. b) the volumetric flow rate at the inlet in ft3/min. Exit B Exit C Inlet A Identify what you know:

  13. Sec 4.3 : Applications of the Mass Rate Balance Use continuity to find volumetric flow rates Volumetric Flow Rate: Area: Exit B Exit C

  14. Sec 4.3 : Applications of the Mass Rate Balance Next find the mass flow rates Specific Volumes may be found on Table A-2E: vA= vf@ 70 oF =0.01605 ft3/lbm vB= vC = vf@ 72 oF = 0.01606 ft3/lbm Exit B Exit C Inlet A: (apply mass balance)

  15. Sec 4.3 : Applications of the Mass Rate Balance Finally, the volumetric flow rate of the inlet may be found: Summary:

  16. End of slides for Lecture 12

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