Discussion

Water flows through a pipe of diameter 86 mm at a rate of 5 m/s. The volume of water discharged per minute is

Answer: D

The water leaving in one minute forms a cylinder whose cross-section is the pipe's and whose length is the distance the flow covers in that minute.

\[ d = 86 \text{ mm} = 0.086 \text{ m} \quad\Longrightarrow\quad r = 0.043 \text{ m} \]

\[ \text{length per minute} = 5 \times 60 = 300 \text{ m} \]

\[ V = \pi r^{2} \times 300 = 3.1416 \times (0.043)^{2} \times 300 \]

\[ = 3.1416 \times 0.001849 \times 300 = 1.7429 \text{ m}^{3} \]

Since \( 1 \text{ m}^{3} = 1000 \) litres:

\[ V \approx 1742.87 \text{ litres} \]

The two conversions - millimetres to metres and seconds to minutes - are what set the scale of the answer.

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