Sewerage

A heavy rain came onto a football pitch with dimensions 110 m x 70 m and during 15 minutes water fell to a height of 80 mm on each m². The pitch is constructed so that it is drained and water can flow away through 4 channels, each with an internal cross-section of 7.2 dm². How large a volume of water flows away through the sewerage system in one minute, if the speed of water flowing through the sewer pipes is 1.2 m/s?

Final Answer:

Q =  20.736 m³

Step-by-step explanation:

$$\begin{gathered} a=110\text{m} \\ b=70\text{m} \\ S=a\cdot b=110\cdot 70=7700{\text{m}}^2 \\ h=80\text{mm}\to \text{m}=80:1000\text{m}=0.08\text{m} \\ V=a\cdot b\cdot h=110\cdot 70\cdot 0.08=616{\text{m}}^3 \\ t=15\text{min} \\ {Q}_1=V/t=616/15=\frac{616}{15}\doteq 41.0667{\text{m}}^3\text{/min} \\ {S}_1=7.2{\text{dm}}^2\to {\text{m}}^2=7.2:100{\text{m}}^2=0.072{\text{m}}^2 \\ {S}_4=4\cdot S_1=4\cdot 0.072=\frac{36}{125}=0.288{\text{m}}^2 \\ v=1.2\text{m/s} \\ {t}_2=1\text{min}\to \text{s}=1\cdot 60\text{s}=60\text{s} \\ Q=S_4\cdot v\cdot t_2=0.288\cdot 1.2\cdot 60=\frac{2592}{125}=20.736=20.736{\text{m}}^3 \\ Q<Q_1 \end{gathered}$$

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