Department of Mechanical Engineering ME 322 – Mechanical Engineering Thermodynamics Lecture 4 Conservation and Balance Concepts

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

3 Simplifying the balance … Net transport of X into the system Net production of X in the system Therefore …

The Balance Concept 4 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.

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

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 6

The Conservation Concept 7 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.

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 (1 st Law of Thermodynamics) Electrical Charge –Conservation of Charge 8

Conservation Laws 9 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?

The Conservation Solution 10 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.

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

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

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