Question 13: Which is the type of process occurring here? Molten sodium is used as a coolant in a nuclear reactor. The cylindrical containment vessel has a cross-sectional area of 10 ft2 and safe operation is assured if the liquid metal level is at least 10 ft. But there has been a loss of coolant flow accident and the plant has temporarily lost coolant feed. Nevertheless, the exiting stream continues to flow. It is known that the volumetric outflow rate Fo, (ft3 /h) is directly proportional to the liquid coolant height: Fo = 0.75h (note: h is in feet). Alarms have already sounded and if the coolant level drops to 75% of its original value a serious situation is near.

i) Derive a differential equation to describe the variation of liquid height h with time t (show all steps).

ii) Solve the differential equation for h(t), using an appropriate initial condition.

iii) How long do the operators have to fix the problem and prevent activation of the core shutdown sequence, or worse, some catastrophic accident?