Equation of Continuity. differential control volume:

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Presentation transcript:

Equation of Continuity

differential control volume:

Differential Mass Balance mass balance:

Differential Equation of Continuity divergence of mass velocity vector (  v) Partial differentiation:

Differential Equation of Continuity Rearranging: substantial time derivative If fluid is incompressible:

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Equation of Continuity

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Equation of Continuity

Dividing both sides by MW A

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Equation of Continuity

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Equation of Continuity Example 1. Estimate the effect of chemical reaction on the rate of gas absorption in an agitated tank. Consider a system in which the dissolved gas A undergoes an irreversible first order reaction with the liquid B; that is A disappears within the liquid phase at a rate proportional to the local concentration of A. What assumptions can be made?

Equation of Continuity 1.Gas A dissolves in liquid B and diffuses into the liquid phase 2.An irreversible 1 st order homogeneous reaction takes place A + B  AB Assumption: AB is negligible in the solution (pseudobinary assumption)

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Equation of Continuity A hollow sphere with permeable solid walls has its inner and outer surfaces maintained at a constant concentration C A1 and C A0 respectively. Develop the expression for the concentration profile for a component A in the wall at steady-state conditions. What is the flux at each surface? Example 2.