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lect12-13 - Control Volume Analysis Used for flow through...

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Control Volume Analysis Used for flow through systems Use closed system analysis (fixed system mass M) to derive expressions for conservation of mass and energy Time t Time t+ t M S (t) = M CV (t) + m i M S (t+ t) = M CV (t+ t) + m e Note: m i doesn’t have to be equal to m e since M CV (t) doesn’t have to be equal to M CV (t+ t) 74 HEAT WORK CONTROL VOLUME
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For a closed system M S (t) = M S (t+ t), so M CV (t) + m i = M CV (t+ t) + m e M CV (t+ t) - M CV (t) = m i - m e Divide through by t to get time rate quantities t m t m t (t) M t (t M e i CV CV - = - 29 + Taking limit as t 0, closed system and control volume boundaries coincide e i CV CV Δt m m t (t) M t (t M - = - 29 + 0 lim Note: m is called the mass flow rate with units kg/s, subscript i is for inlet and e is for exits e i CV m m dt dM - = Time rate of change of mass contained within the control volume equals the net mass flow rate m into the control volume 75
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For multiple inlets and outlets - = e e i i CV m m dt dM For steady-state (dM
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