A fan is to be selected to ventilate a bathroom whose dimensions are 2 m × 3 m × 3 m. The air velocity is not to exceed 8 m/s to minimize vibration noise. The combined efficiency of the fan-motor unit to be used can be taken to be 50 percent. If the fan is to replace the entire volume of air in 10 min, determine (a) the wattage the fan-motor unit to be purchased, (b) the diameter of the

FIGURE P12-56

fan casing, and (c) the pressure difference across the fan. Take the air density to be 1.25 kg/m3 and disregard the effect of the kinetic energy correction factors.

Step 1 of 6</p>

In bathroom, a fan is replacing the entire volume of air for every 10 minutes where air speed remains below as shown in figure below. Here we need to calculate the fan motor wattage , the fan casing diameter and the pressure difference across the fan.

The effect of kinetic energy correction factors is negligible (), the density of air is given as . Also we are assuming that the flow is steady and incompressible.

Step 2 of 6</p>To determine the wattage of the fan motor,

Given data,

Density of air, Volume of air ,Time interval ,

Using 1 min = 60 sec

Speed of air, The volume flow rate through the casing is given by,

Substituting and

Similarly the mass flow rate through the casing is,

Substituting ,

Step 3 of 6</p>

Let us consider the points 1 and 2 at the inlet and outlets of the fan as shown in the figure above. This two points are far from the fan so that and the flow velocity is negligible .

The energy equation for this control volume between points 1 and 2 is given by,

Using , , , and

We get,

Substituting , and

Using

Therefore, the wattage of the fan motor should be 1.2 W.