Question

Calculate the power of an electric pump in horsepower with can lift $2000m^3$ of water from a depth of $20m$ in $25min$.($1m^3$ of water=${10}^{3}kg$, g=$10m/s^2$)

[$1HP=750watts$]

Answer 1

Step 1: Given data,
The volume of water = $2000m^3$

Depth = $20m$

Time = $25min$

Acceleration due to gravity g=$10m/s^2$
Step 2: Conversion of units,

To convert the volume of water into the mass of water,

$1m^3$ = ${10}^{3}kg$

$\Rightarrow 2000m^3$ = $2000\times {10}^{3}kg$

$\Rightarrow 2000m^3$=$2\times {10}^{6}kg$

To convert minutes into seconds,

$25min$ =$25\times 60=1500s$.

Step 3: To find the force of water,

The force of water= Weight of water

$F=mg$$=2\times {10}^6\times 10=2\times {10}^{7}N$

Step 4: To find work done by water:

Formula used: $work=force\times displacement$

W$=2\times {10}^7\times 20=4\times {10}^{8}J$

Step 5: To find power:

Formula used: $power=\frac{work}{time}$

$P=\frac{4\times {10}^8}{1500}$

$P=0.266\times {10}^{6}watts$
Converting from watt to HP:

$1HP=750watts$

$1watt=\frac{1}{750}HP$

$0.266\times {10}^{6}watts=\frac{0.266\times {10}^6}{750}HP$

$=355.55HP$

Thus, the power of the electric pump in the given case is $355.55HP$.