Problem 22P

Applying Conservation of Mass

Figure P4.22 shows a cylindrical tank being drained through a duct whose cross-sectional area is 3 × 10−4 m2. The velocity of the water at the exit varies according to (2gz)1/2, where z is the water level, in m, and g is the acceleration of gravity, 9.81 m/s2. The tank initially contains 2500 kg of liquid water. Taking the density of the water as 103 kg/m3, determine the time, in minutes, when the tank contains 900 kg of water.

Fig. P4.22

Step 1 of 2

We have to determine the time when the tank contains 900 kg of water initially it contains 2500 kg of liquid water.

The mass rate balance for control volume is given by the expression

where ,is the mass flow rate at the exit

Now,

cross sectional area = 3m2

= velocity of water at the exit in m/s

density of liquid at the exit

So,

But

Hence,