Power

• Definition of power
• Unit of power
• Relation between power and velocity

Power

• Power is defined as the time rate at which work is done or energy is transferred.

Average Power:
Ratio of work done(W) in a total time interval of t.
`P_(av)`= `W/t`

Instantaneous Power:
When the time interval t, approaches zero the limiting value of average power becomes instantaneous power.
`P = (dW)/dt`

• We can write `W = F. dr,`
  `P = F . (dr)/dt`
  `P = F.v` , where v is instantaneous velocity.

• Power is a scalar quantity

• SI unit of power – Watt (W)

• Its dimensions are [ML²T^–3].

• 1 hp = 746 W

• We encounter the unit watt when we buy electrical goods such as bulbs, heaters and refrigerators. A 100 watt bulb which is on for 10 hours uses 1 kilowatt hour (kWh) of energy.

  100 (watt) × 10 (hour) = 1000 watt hour

  = 1 kilowatt hour (kWh)

  = 103 (W) × 3600 (s)

  = 3.6 × 106 J

• Our electricity bills carry the energy consumption in units of kWh. Note that kWh is a unit of energy and not of power.

Example: A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m³ in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?
Solution: `P = W/t = (mgh)/t`
mass of water to be moved = ρV = 30000 kg
g = 9.8
h = 40 m
t = 15 x 60 = 900 s
P = 13066.67 W = 13.067 kW
Now `η = P/(P_(ACTUAL)) => P_(ACTUAL) = 13.067/0.3 = 43.6 kW`