Question

A water pump lifts water from a level $10m$ below the ground. Water is pumped at a rate of $30kg/\min$ with negligible velocity. Calculate the minimum horsepower the engine should have to do this.

Answer 1

Hint
Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. Since the flow rate of the pump is given. So by applying a power formula we will calculate the power and then putting the values for the required minimum horsepower.
Power, $P = \dfrac{{mgh}}{t}$ ; Where ‘P’ is the power, ‘m’ is the mass, ‘g’ is the acceleration due to gravity and t is the time.
Horsepower, $Horsepower = \dfrac{P}{{786}}$ ; Where P is the power.

Complete step by step answer
Since height and the flow rate of the pump is given. So firstly we will calculate the power at which the water is following.
Flow rate $= 30kg/{\text{ minute}}$
$\Rightarrow \dfrac{{30}}{{60}}kg/{\text{ second}}$
$\Rightarrow 0.5kg/{\text{ second}}$
Now, we put the values in the below formula of power,
$P = \dfrac{{mgh}}{t}$
On substituting the values, we get
$\Rightarrow \dfrac{{0.5 \times 9.8 \times 10}}{1}watt$
$\Rightarrow 49{\text{ }}watt$
So after this now we will calculate the minimum horsepower,
For this we will put all the required values in the below formula.
On substituting the values, we get
$Horsepower = \dfrac{P}{{746}}hp$
$\Rightarrow \dfrac{{49}}{{746}}hp$
$\Rightarrow 0.065{\text{ hp}}$
Hence the minimum horsepower the engine should have to do this is $0.065{\text{ hp}}$.

Note
Horsepower is the associated imperial unit of power of an engine. It’s defined as the work done per unit time. The term HP was made-up by James Watt. It’s a unit power that compares the facility of a machine to the horse muscle power. Later it had been swollen to differing kinds of piston engines, electrical motors, turbines and alternative machinery.