Question

a spherical tank, of diameter 35 cm, is leaking air through a 5-mm-diameter hole in its side. the air exits the hole at 360 m/s and a density of 2.5 kg/m3. assuming uniform mixing, (a) find a formula for the rate of change of average density in the tank and (b) calculate a numerical value for (dr/dt) in the tank for the given data.

Answer 1

From continuity equation,





Here,  is the volume of the tank,  is the density of fluid in tank,  is the velocity of flow through the hole, and is the area of the hole.

Therefore, the formula for the rate of change of density is