Rain is falling on a poorly designed 150-m² flat roof of a contemporary home. Th

Question

Rain is falling on a poorly designed 150-m² flat roof of a contemporary home. The design flaw requires the water level on the roof to reach approximately 5 cm above the plane of the roof before the water flows into the drains.

(a)Taking the accumulated rain on the roof as the system, can the process before the water level reaches 5 cm be considered batch, semi-batch, or continuous? Is it transient or steady-state? Once the water starts to flow into the drains, how do your answers change?

(b)Before the water starts draining, which of the terms in the general balance equation (Input + generation – output – consumption = accumulation) can be omitted? Why? How do your responses change after water starts draining?

(c)Water begins flowing from the roof after 30 minutes of rainfall. What will the rate of draining (L/s) be if rain continues to fall at the same rate?

Explanation / Answer

(a) Taking the accumulated rain on the roof as a system, the process before the water level reaches 5 cm can be continuous. It is a "steady-state".

(c) If rain continues to fall at the same rate, then it's rate of draining will be given as :

dL / dt = (5 cm) / (30 min)

convert min to sec & cm to m -

dL / dt = (0.05 m) / (1800 s)

dL / dt = 2.77 x 10-5 m/s

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