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An engineer came to me with the following problem.

I'm not convinced the problem is correct - but I've probably just overlooked something, since I haven't done any vaguely practical problems in years.

Anyway, here it is.

[PLAIN]http://img526.imageshack.us/img526/1911/54308613.png [Broken]

Volume of a cone, I'm guessing trivial applications of chain rule in 1D. Some integration (integrating factor at worst? Probably separable.)

Putting pi*7.5^2*30/3 (should be the volume of that cone) into google gives 1,700 or so.

So suppose the cone is almost full - then the out-flow greatly dwarfs the in-flow.

So the cone can never fill up, surely?

Indeed, the liquid level should just sit at a stable equilibrium at 400 units of liquid.

What have I missed?

The ridiculous non-SI units don't help as well.

Is the answer complex? (even pure imaginary?)

I'm not convinced the problem is correct - but I've probably just overlooked something, since I haven't done any vaguely practical problems in years.

Anyway, here it is.

## Homework Statement

[PLAIN]http://img526.imageshack.us/img526/1911/54308613.png [Broken]

## Homework Equations

Volume of a cone, I'm guessing trivial applications of chain rule in 1D. Some integration (integrating factor at worst? Probably separable.)

## The Attempt at a Solution

Putting pi*7.5^2*30/3 (should be the volume of that cone) into google gives 1,700 or so.

So suppose the cone is almost full - then the out-flow greatly dwarfs the in-flow.

So the cone can never fill up, surely?

Indeed, the liquid level should just sit at a stable equilibrium at 400 units of liquid.

What have I missed?

The ridiculous non-SI units don't help as well.

Is the answer complex? (even pure imaginary?)

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