Answer:
The input power is [tex]44.4\times10^{3}\ kW[/tex]
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
[tex]Mass = Volume\times density[/tex]
Put the value into the formula
[tex]Mass=30\times1000[/tex]
[tex]Mass=3\times10^{4}\ kg[/tex]
We need to calculate the output power
Using formula of power
[tex]P_{out}=\dfrac{W}{t}[/tex]
[tex]P_{out}=\dfrac{mgh}{t}[/tex]
Put the value into the formula
[tex]P_{out}=\dfrac{3\times10^{4}\times10\times40}{15\times60}[/tex]
[tex]P_{out}=\dfrac{4}{3}\times10^{4}\ Watt[/tex]
We need to calculate the input power
Using formula of efficiency
[tex]\eta=\dfrac{P_{out}}{P_{in}}[/tex]
[tex]P_{in}=\dfrac{P_{out}}{\eta}[/tex]
Put the value into the formula
[tex]P_{in}=\dfrac{4\times100\times10^{4}}{3\times30}[/tex]
[tex]P_{in}=\dfrac{4\times10^{5}}{9}\ Watt[/tex]
[tex]P_{in}=44.4\times10^{3}\ kW[/tex]
Hence, The input power is [tex]44.4\times10^{3}\ kW[/tex]
