Efficiency 35023

The cellar, which has a floor area of ​​50 m² and is 3 m below ambient level, was flooded with water to a height of 80 cm. How long does it take for a pump with a power input of 1 kW and an efficiency of 75% (η = 0.75) to drain the water?

Correct answer:

t =  0.4444 h

Step-by-step explanation:

$$\begin{gathered} S=50{\text{m}}^2 \\ c=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ h=3\text{m} \\ V=S\cdot c=50\cdot 0.8=40{\text{m}}^3 \\ \rho =1000{\text{kg/m}}^3 \\ m=\rho \cdot V=1000\cdot 40=40000\text{kg} \\ g=10{\text{m/s}}^2 \\ W=m\cdot g\cdot h=40000\cdot 10\cdot 3=1200000\text{J} \\ {P}_1=1\text{kW}\to \text{W}=1\cdot 1000\text{W}=1000\text{W} \\ \eta =0.75 \\ {P}_2=\eta \cdot P_1=0.75\cdot 1000=750\text{W} \\ P=W/t \\ {t}_1=W/P_2=1200000/750=1600\text{s} \\ t=t_1\to \text{h}=t_1:3600\text{h}=1600:3600\text{h}=0.444\text{h}=0.4444\text{h} \end{gathered}$$

Try another example