A fan is to accelerate quiescent air to a velocity of 12.5 m/s at a rate of 9 m3/s. Determine the minimum power that must be supplied to the fan. Take the density of air to be 1.18 kg/m3.

= 829.69 Watt

≅ 830 Watt

Explanation:

Given that,

Velocity of air flow = 12.5m/s

Rate of flow of air = 9m³/s

Density of air = 1.18kg/m³

power by kinetic energy = 1/2 (mv²)

mass = density * volume

m = 1.18 * 9

= 10.62 kg/s

power = 1/2 mV²

= 1/2 (10.62 * 12.5²)

= 829.69 Watt

≅ 830 Watt

Flow rate

u

=

9

m

3

/

s

Velocity of the air

V

=

8

m/s

Density of the air

ρ

=

1.18

kg

/

m

3