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Bml
Bml
10:02
@JohnRennie Hi :-)
John Rennie
John Rennie
Hi :-)
Bml
Bml
Could I ask you a question?
John Rennie
John Rennie
Yes, go ahead :-)
Bml
Bml
I have a problem. There is an open container filled with a fluid, with a hole at depth h. That container is located on the Moon. Given that the acceleration of gravity on the moon is 1/6 of that on Earth, find the ratio of the efflux velocity of the container on the moon to that of the same container if it were on earth.

According to my prof the right answer is that you cannot calculate it, since the efflux velocity on the moon is 0, since there is no atmospheric pressure on the moon. Do you think it is right?
John Rennie
John Rennie
I disagree.
Bml
Bml
10:10
@JohnRennie Could you explain? Thank you very much, as usual...
John Rennie
John Rennie
All that matters is the pressure difference in the fluid. It doesn't matter if the ambient pressure is 1 atm 100000 atm or 0 atm. The pressure difference is still ΔP = ρah, where 𝑎 is the gravitational acceleration.
In any case, the pressure on the Moon is not zero. It's just very low.
Bml
Bml
@JohnRennie So, is the velocity v = \sqrt{2gh}?
John Rennie
John Rennie
v = √2ah
where a = g/6
Bml
Bml
Could we go through Bernoulli to see if my understanding is correct?
John Rennie
John Rennie
Bernoulli's equation is:
P₁ + ¹⁄₂ρv₁² + ρgh₁ = P₂ + ¹⁄₂ρv₂² + ρgh₂
Yes?
Bml
Bml
10:17
Yes
John Rennie
John Rennie
There are no restrictions on what the pressures are. One or both of P₁ and P₂ can be zero.
Bml
Bml
OK
John Rennie
John Rennie
On Earth P₁ = P₂ so the pressures cancel on both sides anyway.
We are left with:
¹⁄₂ρv₁² + ρgh₁ = ¹⁄₂ρv₂² + ρgh₂
and that doesn't even mention the external pressure.
So why would it be different on the Moon?
Bml
Bml
So is the ratio 1/\sqrt{6}?
John Rennie
John Rennie
Yes
Bml
Bml
10:26
@JohnRennie Thanks
John Rennie
John Rennie
You're welcome :-)
Bml
Bml
I have other questions...
John Rennie
John Rennie
Go ahead :-)
Bml
Bml
11:06
From the very beginning, I was taught in school that: The electron can be in an area described by the wave function, and the square modulus of the wave function (always greater than or equal to zero) returns the probability that the electron is at a given point, which, however, cannot be known because of Heisenberg's Undeterminacy Principle. But is this correct?

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