1. The Balance Equation and the Mass Balance

2. Outline The Balance Equation The Mass Balance Rate Equation Steady-State Balances The Steady-State One-Dimensional Balance Unsteady-State Mass Balances

3. Outline (Continued) Comparison between Steady-State and Unsteady-State Processes Mass Balances for Mixtures Multidimensional Flows

4. Objectives Introduce the balance equation. Apply the overall and component mass balances to formulate, and solve engineering problems which involve steady and unsteady one-dimensional fluid flow problems.

5. Objectives (Continued) Compare steady-state and unsteady-state processes. Introduce multidimensional flows.

6. Summary Define the system first. The balance equation (between t1 and t2) (Accumulation)=(Generation)-(Destruction)+(Flow In)-(Flow Out) Rate equation (at time t) (Rate of Accumulation)=(Rate of Generation)-(Rate of Destruction)+(Flow Rate In)- (Flow Rate Out) Accumulation = (rate of accumulation) dt

7. Summary (Continued) The Mass Balance (Accumulation of Mass)=(Flow of Mass In)-(Flow of Mass Out) Rate equation (Rate of Accumulation of Mass)=(Flow Rate of Mass In)-(Flow Rate of Mass Out) Steady state means nothing is changing with respect to time (x,y, and z being fixed). For one-dimensional flows at steady-state mass flow rate=

8. Summary (Continued) The capital cost per unit produced is low for steady-state large production and unsteady-state small production. For multicomponent systems, use the general balance equation. The generation and consumption terms are not zero if the component is a product, reactant, or both. Multidimensional flows