- #1

WhiteWolf98

- 86

- 5

- Homework Statement
- A surface water drain causes your basement to flood at the steady rate of ##2.5~cm/hour##. The basement floor area is ##121~m^2##. At what flow rate (in ##m^3/s## should a pump operate to keep the water accumulated in your basement at a constant level? (give your answer in ##m^3/hour##).

- Relevant Equations
- -

Some thoughts that I've had on the question are saying the volume flow rate (##Q##) in, must equal the volume flow rate out. If that's the case, then:

##Q_{in} = Q_{out}##

##A_1V_1=A_2V_2##

But... no areas have been given. And height doesn't enter this equation at all.

Then I thought it could have something to do with Torricelli's Law.

##\Delta t = \frac {2A} {a \sqrt {2g}} (\sqrt {h_1} - \sqrt {h_2} ##

But again, still, no areas are given. Also, if the height is constant, then:

##\sqrt {h_1} - \sqrt {h_2} = 0##

So the whole equation becomes zero. Besides of which, velocity isn't in that equation at all.

Finally, I thought Bernoulli; that's just out of the question though. There's no streamline.

I know I need to link the height with velocity and somehow area, but I can't find a relationship.

##Q_{in} = Q_{out}##

##A_1V_1=A_2V_2##

But... no areas have been given. And height doesn't enter this equation at all.

Then I thought it could have something to do with Torricelli's Law.

##\Delta t = \frac {2A} {a \sqrt {2g}} (\sqrt {h_1} - \sqrt {h_2} ##

But again, still, no areas are given. Also, if the height is constant, then:

##\sqrt {h_1} - \sqrt {h_2} = 0##

So the whole equation becomes zero. Besides of which, velocity isn't in that equation at all.

Finally, I thought Bernoulli; that's just out of the question though. There's no streamline.

I know I need to link the height with velocity and somehow area, but I can't find a relationship.