Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

9.7 Conservation of Mass 243

Example 9.3 How much water is stored after 5 minutes in each of the tanks shown in Figure 9.5? How long

will it take to fill the tanks completely provided that the volume of each tank is 12 m

3

? Assume

the density of water is 1000 kg /m

3

.

2 kg/s

(a)

2 kg/s

1 kg/s

(b)

■Figure 9.5

The tanks of Example 9.3.

We will use the conservation of mass statement to solve this problem.

Realizing that no water leaves tank (a) we have

After 5 minutes,

To determine how long it will take to fill the tank, first we will make use of the relation-

ship among mass, density, and volume — mass (density)(volume)— to compute how much

mass each tank can hold.

By rearranging terms in the conservation of mass equation we can now solve for the time that

is required to fill the tank.

Water enters tank (b) at 2 kg /s and leaves the tank at 1 kg /s. Applying conservation of mass to

tank (b) we have

1 2 kg/s 2  1 1 kg/s 2 

changes of mass inside the control volume

change in time

time required to fill the tank

12,000 kg

1 2 kg/s 2

 1 6000 s 2 100 min

mass 1 1000 kg/m

3

21 12 m

3

2 12,000 kg

change of mass inside the control volume 1 2 kg/s 21 5 min2a

60 s

1 min

b600 kg

1 2 kg/s 2  102 

changes of mass inside the control volume

change in time

(the rate of accumulation

or depletion of the mass

of fluid within the given

control volume)



(the rate at which the fluid

leaves the control volume)

(the rate at which fluid

enters a control volume)

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