Heat Transfer

Principle of Conservation of Energy 39

Example 3.7

Write the mass balance equation for the control volume of Figure 3.9.

Solution

The mass balance equation is

  

mmmm m

2314 5

+=++.

or, in terms of density, cross section area, and velocity at every inlet and exhaust

ρρρρ ρAV AV AV AV AV

(

)

+

(

)

=

(

)

+

(

)

+

(

)

2314 5

.

A procedure similar to that used to develop the mass balance equation for a con-

trol volume is used to derive an appropriate form of the energy balance equation for

a control volume. Figure 3.10 shows the same control mass at times t and t + dt. In

1

2

3

4

5

FIGURE 3.9 A control volume with multiple inlets and multiple exhausts.

C

A

B

Inlet

V

i

A

i

ρ

i

P