When a fan is rotating how is the high pressure of air and low pressure of air is formed?
P + pgh + 1/2 mv^2 = constant is bernoullis theorem. For a fan height is constant. So pgh = constant. So eqn is P + 1/2mv^2 = constant. P inversely proportional to v^2 . So when speed increase Pressure decrease.
Now consider the blades of the fan to be rotating. The air column above the fan can be considered to have streamline flow and same elevation. So as the fan blades rotate, they are specially angled to make the air column move and this air column attains a high velocity. So from Bernoulli's Theorem, we can say the pressure of the air column decreases i.e. it has low air pressure.
However the air column below the ceiling fan has high pressure since it is not agitated by the fan blades and has low or no velocity.And we know air moves from high to low pressure. So air from above the fan rushes down and creates winds which increase the rate of evaporation of any liquid on any surface, creating a cooling effect.