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In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N, E, and S are equal. The flow rate in the pipe connecting W and J is Q. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements: I: The flow rate in pipe connecting J and E is Q/21. II: The pressure difference between J and N is equal to the pressure difference between J and E. Which of the following options is CORRECT?

1. I is True and II is False
2. I is False and II is True
3. Both I and II are True
4. Both I and II are False

Correct answer: Both I and II are True

Solution

Both statements are true because the flow rate in the longer pipe connecting J and E is reduced due to the longer length and equal friction factor, resulting in a flow rate of Q/21. Additionally, since the pressures at points N, E, and S are equal, the pressure difference between J and N must match the pressure difference between J and E, confirming the second statement.

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