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Lecture 4

Lecture 4. Conservation and Balance Concepts. The Balance Concept.

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Lecture 4

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  1. Lecture 4 Conservation and Balance Concepts

  2. The Balance Concept Consider the system shown. X flows in and out of the system over a specified time period, dt. The quantity X is either transported, produced, destroyed, or stored. Therefore,

  3. The Balance Concept Simplifying the balance … Net transport of Xinto the system Net production of Xin the system Therefore …

  4. The Balance Concept In shorthand form, This equation was developed for a specified time period. At an instant in time, the balance becomes, This is known as the rate form of the balance equation.

  5. Another Way to Think about Balances Total form – What happens over a finite time interval Recording a movie to watch what happens over time

  6. Another Way to Think about Balances Rate form – What happens at an instant in time Taking a picture to see what is happening at that instant in time

  7. The Conservation Concept Conserved quantities cannot be created or destroyed. Therefore, for a conserved quantity, For a conserved quantity, the balance equation becomes, This form (total or rate) is known as the conservation law, or the conservation equation.

  8. What Quantities are Conserved? • Mass (in non-nuclear reactions) • Conservation of Mass (Continuity Equation) • Momentum (linear and angular) • Conservation of Momentum • Energy • Conservation of Energy(1st Law of Thermodynamics) • Electrical Charge • Conservation of Charge

  9. Conservation Laws Conservation laws allow us to solve what seem to be very complex problems without relying on ‘formulas’. Consider the following problem from physics ... Given: A baseball is thrown vertically from the ground with a speed of 80 ft/s. Find: Neglecting friction, how high will the ball go?

  10. The Conservation Solution The energy of the ball is made up of kinetic energy and potential energy. Since energy is a conserved quantity, There is no net gain of energy in the ball (it is at the same temperature always), This means that the net energy transported to/from the ball must be zero. Another way of stating this is that the energy of the ball at state 1 must be equal to the energy of the ball at state 2.

  11. The Conservation Solution Therefore, Substituting the expressions for kinetic and potential energy, Applying the conditions at state 1 and state 2,

  12. Conservation of Mass (Continuity) Total mass form (making a movie)

  13. Conservation of Mass (Continuity) Rate form (taking a picture)

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