Dimensions 82434

Water flows into an aquarium with dimensions of 14x26x3m through a tube with a diameter of 5 cm at a speed of 2m/s. How long does it take for the aquarium to fill with water?

Correct answer:

t =  77.2432 h

Step-by-step explanation:

$$\begin{gathered} a=14\text{m} \\ b=26\text{m} \\ c=3\text{m} \\ d=5\text{cm}\to \text{m}=5:100\text{m}=0.05\text{m} \\ v=2\text{m/s} \\ {S}_1=\pi \cdot (d/2{)}^2=3.1416\cdot (0.05/2{)}^2\doteq 0.002{\text{m}}^2 \\ {Q}_1=S_1\cdot v=0.002\cdot 2\doteq 0.0039{\text{m}}^3\text{/s} \\ {Q}_2=3600\cdot Q_1=3600\cdot 0.0039\doteq 14.1372{\text{m}}^3\text{/h} \\ V=a\cdot b\cdot c=14\cdot 26\cdot 3=1092{\text{m}}^3 \\ t=V/Q_2=1092/14.1372=77.2432\text{h} \end{gathered}$$

Try another example