Question

B) A pump is to raise 100 litre of water a height of 1.2 m in 10s. Calculate the power required assuming 1 litre of water has a mass of 1 kg?.

Answer 1

`\color{red}{117.72\ W`

Explanation:

Power (`P`) of the pump that lifts `Q=100` liters of water (density, `rho=1\ \text{kg/Ltr}`) at a vertical height `H=1.2\ m` in time `t=10` sec is given as follows

`P={\rho gQH}/t`

`={1 \cdot 9.81\cdot 100\cdot 1.2}/10`

`=117.72 \ W`

Answer 2

I get `117.6` watts.

Explanation:

The mass of the water here is:

`100color(red)cancelcolor(black)"L"*(1 \ "kg")/(color(red)cancelcolor(black)"L")=100 \ "kg"`

The weight of the water is therefore:

`100 \ "kg"*9.8 \ "m/s"^2=980 \ "kg m/s"^2=980 \ "N" \ (because 1 \ "N"-=1 \ "kg m/s"^2)`

Work done is given by the equation:

`W=F*d`

where:

• `W` is the work done in joules

• `F` is the force exerted in newtons

• `d` is the distance moved in meters

So, we get:

`W=980 \ "N"*1.2 \ "m"`

`=1176 \ "J"`

Power here is given by the equation:

`P=W/t`

where:

• `P` is the power in watts

• `W` is the work done in joules

• `t` is the time taken in seconds

So, we get:

`P=(1176 \ "J")/(10 \ "s")`

`=117.6 \ "W"`