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Mass and Energy Analysis of Control Volumes

Mass and Energy Analysis of Control Volumes. A look at some real life devices. Conservation of Mass. Mass, like energy, is a conserved property Given E = mc 2 where c is the speed of light Will find that little mass converts to energy except in nuclear reactions

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Mass and Energy Analysis of Control Volumes

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  1. Mass and Energy Analysis of Control Volumes A look at some real life devices

  2. Conservation of Mass • Mass, like energy, is a conserved property • Given E = mc2 where c is the speed of light • Will find that little mass converts to energy except in nuclear reactions • So in this course will consider mass and energy conserved

  3. Conservation of Mass • For closed systems, no mass transfer so mass is conserved • For open systems, or control volumes, must track the mass entering, leaving and change of mass in the control volume.

  4. Mass and Volume Flow Rates • The amount of mass flowing through a cross section per unit time is called mass flow rate, the dot meaning time rate of change • Across a control surface it is written:

  5. Mass and Volume Flow Rates • Velocity is never uniform over a cross section, define average velocity, Vavg as that average velocity across the cross section, so

  6. Mass and Volume Flow Rates • The volume flow rate

  7. Conservation of Mass Principle • The net mass transfer to or from a control volume during a time interval Δt is equal to the net change (increase or decrease) in the total mass in the control volume during Δt • min – mout = ΔmCV where ΔmCV = mfinal – minital • Can also be done with rate equation • Called mass balance equations

  8. Mass Balance for Steady-Flow Processes

  9. Mass Balance for Steady-Flow Processes • Steady-Flow: total amount of mass contained in the control volume does not change with time (mCV = constant) • Steady-Flow: • Single stream:

  10. Incompressible Flow • For incompressible flow, density is constant, so volume is constant

  11. Flow Work and the Energy of a Flowing Fluid • Some work is required to move the mass into and out of the control volume, this is flow work, or flow energy

  12. Wflow = FL = PAL = PV (kJ) wflow = Pv (kJ/kg) Flow Work and the Energy of a Flowing Fluid

  13. Flow Work and the Energy of a Flowing Fluid

  14. Flow Work and the Energy of a Flowing Fluid • Total energy of a flowing fluid per unit mass is called θ defined as θ = h + ke + pe = h + ½V2 + gz • Only change from energy per unit mass definition is the addition of flow energy, Pv to u to form h

  15. Amount of Energy transport: E = mθ = m(h+½V2+gz) (kJ) Flow Work and the Energy of a Flowing Fluid

  16. Steady-flow: a process during which a fluid flows through a control volume steadily. Steady, no change with time Boundary work = 0, volume is constant Mass balance, energy balance, no changes inside control volume with time Energy Analysis of Steady-Flow Systems

  17. Energy Analysis of Steady-Flow Systems • Energy Balance

  18. Energy Analysis of Steady-Flow Systems

  19. Energy Analysis of Steady-Flow Systems

  20. Nozzles and Diffusers

  21. Nozzles and Diffusers • Nozzles: increase the velocity of fluid at expense of pressure • Diffuser: reduces the velocity of fluid by increasing pressure • Heat transfer rate: small ≈ 0 • Power: small ≈ 0 • Δpe ≈ 0 • Δke ≠ 0

  22. Turbines and Compressors • Turbines convert fluid flow into mechanical work, pressure drop converted to mechanical work • Compressor, pump, fan convert work into increases pressure • Heat transfer rate: ≈ 0 • Δpe ≈ 0 • Δke ≈ 0 (normally not significant)

  23. Throttling Valve • Throttling valve: any flow-restricting device that causes significant pressure drop in the fluid • No work involved • Considered adiabatic: q ≈ 0 • Δpe ≈ 0 • Δke ≈ 0 • h1 ≈ h2

  24. Throttling Valve • For a throttling valve, enthalpy remains constant, isenthalpic device • Internal energy + Flow energy = constant • u1+ P1v1 = u2+ P2v2

  25. Mixing of streams into one output Conservation of mass and energy q ≈ 0 w ≈ 0 Δpe, Δke ≈ 0 Mixing Chambers

  26. Devices where two moving fluids exchange heat without mixing w = 0, Δpe ≈ 0, Δke ≈ 0 No heat lost to outside so all heat moves between two fluids Heat Exchangers

  27. In pipe/duct flow need to consider all factors, situation will decide what is significant Pipe or Duct Flow

  28. Unsteady-flow, changes inside control volume with time Done in finite time period May have boundary work Energy Analysis of Unsteady-Flow Processes

  29. Energy Analysis of Unsteady-Flow Processes • Mass balance: min – mout = Δmsystem (kg) where Δmsystem = mfinal – minitial • Energy balance: Ein– Eout= ΔEsystem (kJ)

  30. Energy Analysis of Unsteady-Flow Processes • Special Case: Uniform-Flow Process • Idealization: the fluid at any inlet or exit is uniform and steady, fluid properties do not change with time or position over the cross section of the inlet or exit. If they do, they are averaged and treated as constants for the process

  31. Uniform-Flow Processes • Energy balance • Simplifies to

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