Thermodynamics ENGR360-MEP112 LECTURE 7
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1 Thermodynamics ENGR360-MEP11 LECTURE 7
2 Thermodynamics ENGR360/MEP11 Objectives: 1. Conservation of mass principle.. Conservation of energy principle applied to control volumes (first law of thermodynamics). 3. Energy balance of common steady-flow devices such as nozzles, diffusers, compressors, turbines, throttling valves, mixing chambers and heat exchangers. of
3 Thermodynamics ENGR360/MEP11 1. CONSERVATION OF MASS Mass and Volume Flow Rates: Mass flow rate, m = ρv n da c m = ρv n A c A c Volume flow rate, V = m ρ = Ac v n da c n: normal unit vector V: Flow velocity V = v n A c V n : normal flow velocity A c : cross sectional area of flow 3 of
4 Thermodynamics ENGR360/MEP11 1. CONSERVATION OF MASS Conservation of Mass Principle: The conservation of mass principle for a control volume can be expressed as: The net mass transfer to or from a control volume during a time interval t is equal to the net change (increase or decrease) in the total mass within the control volume during t. That is, Total mass entering the CV during t Total mass leaving the CV during t = Net change in mass within CV during t In a rate form: m in CS m in CS m out CS = m CV m out CS = dm CV dt 4 of
5 Thermodynamics ENGR360/MEP11 dm CV dt 1. CONSERVATION OF MASS = d ρv CV dt = d dt CV ρdv + Vdρ o The rate of change of the mass within the control volume (CV) is due to the change of its volume dv and the change of the density of the fluid dρ. o dm CV dt density dρ. = 0 if there is no change in volume dv and no change in 5 of
6 Thermodynamics ENGR360/MEP11 1. CONSERVATION OF MASS Mass Balance for Steady-Flow Processes: During a steady-flow process, the total amount of mass contained within a control volume does not change with time (m CV = constant). m in CS = m out CS o For steady-incompressible flow, i.e ρ = constant: V in CS = V out CS 6 of
7 Thermodynamics ENGR360/MEP11. FLOW WORK AND THE ENERGY OF A FLOWING FLUID Unlike closed systems, control volumes involve mass flow across their boundaries, and some work is required to push the mass into or out of the control volume. This work is known as the flow work, or flow energy, and is necessary to maintain a continuous flow through a control volume. W flow = F. L = p. A. L = pv (J) w flow = pv (J/kg) 7 of
8 Thermodynamics ENGR360/MEP11. FLOW WORK AND THE ENERGY OF A FLOWING FLUID For closed system: e = u + ke + pe For open system (control volume): The energy contained in a flowing fluid is θ θ = e + pv = pv + u + ke + pe flow work θ = h + ke + pe Energy Transport by Mass: o Amount of energy transport: E mass = mθ = m h + ke + pe o Rate of energy transport: E mass = mθ = m h + ke + pe 8 of
9 Thermodynamics ENGR360/MEP11 First law of thermodynamics for open-steady flow systems: Q in + 3. ENERGY ANALYSIS OF STEADY-FLOW SYSTEMS W in + CS in Q in + Q in + E in E out = de system dt E in = E out W in + E mass,in = Q out + W out + W in + CS in mθ = m h + v + gz = Zero, for steady-state steady-flow process Q out + Q out + W out + W out + E mass,out CS out mθ CS out m h + v + gz 9 of
10 Thermodynamics ENGR360/MEP11 Special cases: 1. Single stream ( m in = Q in + W in +. Single stream per unit m out = m: m h in + v in + gz in = Q out + W out + m h out + v out + gz out m (single stream per unit mass per unit time): q in + w in + h in + v in + gz in = q out + w out + h out + v out + gz out 3. Single stream per unit m with negligible kinetic and potential energies: q in + w in + h in = q out + w out + h out or 3. ENERGY ANALYSIS OF STEADY-FLOW SYSTEMS q in q out + w in w out = h out h in 10 of
11 Thermodynamics ENGR360/MEP11 Nozzle: Nozzle is a device that increases the velocity of a fluid at the expense of its pressure. Nozzle can be used with compressible or incompressible fluid flow. Energy balance for single stream: Q in + W in + Zero m in h in + v in + gz in = Q out + W out + Zero m out h out + v out Q in Q out = m h h 1 + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out = m h h 1 + v For single stream, neglected change in potential energy and adiabatic nozzle: h h 1 = v 1 v + gz out 11 of
12 Thermodynamics ENGR360/MEP11 Diffuser: Diffuser is a device that increases the pressure of a fluid by slowing it down. Diffuser can be used with compressible or incompressible fluid flow. Energy balance for single stream: Q in + W in + Zero m in h in + v in + gz in = Q out + W out + Zero m out h out + v out Q in Q out = m h h 1 + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out = m h h 1 + v For single stream, neglected change in potential energy and adiabatic diffuser: h h 1 = v 1 v + gz out 1 of
13 Thermodynamics ENGR360/MEP11 Turbine: Turbine is a device that produces power from the fluid. Gas turbine, steam turbine and wind turbine use a compressible fluid flow. Water turbine uses an incompressible fluid flow. Energy balance for single stream fluid flow: Q in + W in + Zero m in h in + v in + gz in = Q out + W out + m out h out + v out Q in Q out W out = m h h 1 + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out W out = m h h 1 + v For single stream, neglected change in potential energy and adiabatic turbine: W out = m h 1 h + v 1 v + gz out 13 of
14 Thermodynamics ENGR360/MEP11 Turbine: Energy balance for single stream-incompressible fluid flow: h = p ρ Q in Q out W out = m p p 1 ρ + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out W out = m p p 1 ρ + v For single stream, neglected change in potential energy and adiabatic turbine: W out = m p 1 p ρ + v 1 v 14 of
15 Thermodynamics ENGR360/MEP11 Q Compressor: Compressor is a device that delivers power to a compressible fluid. Energy balance for single stream-compressible fluid flow: Q in + W in + m in h in + v in + gz in = Q out + W out + m out h out + v out + gz out Zero Q in Q out + W in = m h h 1 + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out + W in = m h h 1 + v For single stream, neglected change in potential energy and adiabatic compressor: W in = m h h 1 + v 15 of
16 Thermodynamics ENGR360/MEP11 Pump: Pump is a device that delivers power to an incompressible fluid. Energy balance for single stream-incompressible fluid flow: Q in + W in + m in h in + v in + gz in = Q out + W out + m out h out + v out Q in Q out + W in = m p Zero p 1 + v + g z ρ z 1 For single stream and neglected change in potential energy: Q in Q out + W in = m p p 1 + v ρ For single stream, neglected change in potential energy and adiabatic pump: W in = m p p 1 + v ρ + gz out 16 of
17 Thermodynamics ENGR360/MEP11 Throttling valve: Throttling valves are any kind of flow-restricting devices that cause a significant pressure drop in the fluid. Throttling valves can be used with compressible or incompressible fluid flow. Energy balance for single stream fluid flow: Q in + W in + m in h in + v in + gz in = Q out + W out + m out h out + v out Zero Zero Q in Q out = m h h 1 + v + g z z 1 For single stream and neglected change in potential energy: Q in Q out = m h h 1 + v For single stream, neglected change in potential energy and adiabatic: h h 1 = v 1 v + gz out 17 of
18 Thermodynamics ENGR360/MEP11 Throttling valve: For single stream, neglected change in potential energy, adiabatic and constant velocity: h = h 1 For single stream, neglected change in potential energy, adiabatic, constant velocity and ideal gas: T = T 1 18 of
19 Thermodynamics ENGR360/MEP11 Mixing chamber: Mixing chamber is a section where the mixing process takes place. Energy balance: Q in + Mass balance: W in + m in h in + v in + gz in = Q out + W out + m out h out + v out + gz out m in = m out For instance, if the mixing chamber has two inlets and one outlet: m 1 + m = m 3 Q in Q out + W in W out = m 3 h 3 + v 3 + gz 3 m 1 h 1 + v 1 + gz 1 For neglected potential and kinetic energy, adiabatic and no work interaction: m 3 h 3 = m 1 h 1 + m h m h + v + gz 19 of
20 Thermodynamics ENGR360/MEP11 Heat exchanger: Heat exchangers are devices where two moving fluid streams exchange heat without mixing. Energy balance: θ in θ out Q in + W in + m in h in + v in + gz in Zero Mass balance: = Q out + W out + m out h out + v out Zero + gz out m in = m out 0 of
21 Thermodynamics ENGR360/MEP11 Heat exchanger: The heat transfer associated with a heat exchanger may be zero or nonzero depending on how the control volume is selected Energy balance: Q in Q out = m B θ + m A θ 4 m B θ 1 m A θ 3 1 of
22 Thermodynamics ENGR360/MEP11 Heat exchanger: For neglected potential and kinetic energy: Q in Q out = m B h + m A h 4 m B h 1 m A h 3 = m A h 4 h 3 Q BA m B h 1 h Q BA For neglected potential and kinetic energy and adiabatic process: m B h + m A h 4 = m B h 1 + m A h 3 m A h 4 h 3 = m B h 1 h = Q BA of
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