Question

An eletric pump in the ground floor

Answer 1

Answer:

The input power is $44.4\times10^{3}\ kW$

Explanation:

Given that,

Time = 15 min

Volume of water = 30 m³

Height = 40 m

Efficiency = 30%

Density of water = 1000 kg/m³

Suppose, acceleration due to gravity = 10 m/s²

We need to calculate the mass of water pumped

Using formula of mass

$Mass = Volume\times density$

Put the value into the formula

$Mass=30\times1000$

$Mass=3\times10^{4}\ kg$

We need to calculate the output power

Using formula of power

$P_{out}=\dfrac{W}{t}$

$P_{out}=\dfrac{mgh}{t}$

Put the value into the formula

$P_{out}=\dfrac{3\times10^{4}\times10\times40}{15\times60}$

$P_{out}=\dfrac{4}{3}\times10^{4}\ Watt$

We need to calculate the input power

Using formula of efficiency

$\eta=\dfrac{P_{out}}{P_{in}}$

$P_{in}=\dfrac{P_{out}}{\eta}$

Put the value into the formula

$P_{in}=\dfrac{4\times100\times10^{4}}{3\times30}$

$P_{in}=\dfrac{4\times10^{5}}{9}\ Watt$

$P_{in}=44.4\times10^{3}\ kW$

Hence, The input power is $44.4\times10^{3}\ kW$