Thought experiment about fluid mechanics (reductio ad absurdum) In an interview a philosopher said:
"Suppose I cut the handle off your coffee mug leaving two holes. Would the coffee flow out of one hole faster than the other? If we tried to figure this out by experiment, we would need to carefully measure the flow – and we would ruin your mug. We should instead mentally replace the handle with a tube. If the flow of one hole exceeded the other, we would have a perpetual motion machine. Since that is absurd, we can deduce that the holes have the same rate of flow."
Is this true? Why wouldn't the lower hole have a higher rate of flow? Isn't there a higher pressure?
 A: The argument is wrong. The flow rate that is observed when the hole is freely communicating with the atmosphere is not the same flow rate that will be observed when the two holes are connected with a tube.
The reason is that the flow rate through a hole depends on the pressure differential across the hole - on one side there is a certain height of liquid providing pressure, and on the other side (for the first case) there is just atmospheric pressure. So when you make two holes in your mug, the lower hole will have the faster flow rate. Formally this can be analyzed with Bernoulli's equation, but when you are talking to a philosopher you may want a simpler argument.
Imagine a particle of water starting to "fall" from the top of the surface of the water (since the surface of the water is lowering, you can think of the potential energy lost by the water being equal to energy lost by moving water from the surface to the exit hole - it's not actually the same particle, but as water disappears from the surface it re-appears at the hole). Now that particle (mass $m$) lost potential energy $mgh$. converting that to kinetic energy, it's going to flow at a velocity $v$ such that $\frac12 mv^2 = mgh$, or $v\propto \sqrt{h}$. 
When the two are connected with a tube, there is equal pressure on both sides and no flow at all.
