Block-shaped 5630

How many hours will a block-shaped pool measuring 24 m, 12 m, and 1.8 m be filled if it flows through a 9 cm diameter pipe at a speed of 2.5 m/s?

Correct answer:

t =  9.0541 h

Step-by-step explanation:

$$\begin{gathered} a=24\text{m} \\ b=12\text{m} \\ c=1.8\text{m} \\ V=a\cdot b\cdot c=24\cdot 12\cdot 1.8=\frac{2592}{5}=518.4{\text{m}}^3 \\ D=9\text{cm}\to \text{m}=9:100\text{m}=0.09\text{m} \\ r=D/2=0.09/2=\frac{9}{200}=0.045\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 0.045^2\doteq 0.0064{\text{m}}^2 \\ {V}_2=S\cdot 2.5\cdot 3600=0.0064\cdot 2.5\cdot 3600\doteq 57.2555{\text{m}}^3\text{/h} \\ t=V/V_2=518.4/57.2555=9.0541\text{h} \end{gathered}$$

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