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Consider a tank with a drain pipe in its bottom opening into an
identical tank directly below the first:
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|____ ____|
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|__________|
The drain pipe is below the water level in the lower tank.
Let point 1 be on the free air-water surface of the upper tank and
let point 2 be on the free air-water surface of the lower tank.
How does the speed v1 compare to v2?
Answer 1. Use the equation of continuity. Both tanks have the same
cross-sectional area A. Hence v1 = v2. In Torricelli problems, this
speed is taken to be nearly zero if A is big enough.
Answer 2. Use Bernoulli's equation where P1 = P2 = P_atm. Therefore
v2^2 - v1^2 = 2gh, where h is the difference in heights of water in
the two tanks.
Obviously both answers cannot be right.
I suspect the second is wrong
and that there is *necessarily* some kind of turbulent or viscous
loss of speed.
I am worried about typical end-of-chapter problems involving siphons,
Torricelli tanks, etc where clearly one is supposed to ignore such
losses.