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# More on finding fluid speed from hole

Clarification of, and more thoughts on, the Bernoulli's equation example problem where liquid exits a hole in a container. Created by Sal Khan.

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• Does this hold true for vessels NOT in a vacuum? I'm guessing on the surface of earth, P_in would equal 1 atmosphere. And P_out would be almost the same. So both pressures would cancel each other out.
• I think it is important to specify here that if both ends are open or in a vacuum Pi = Po however if one end is in a vacuum and the other is open to the atmosphere that atmospheric pressure is acting on that (hole or opening) so Po becomes 1atm .

just to be extra clear
• If there is vacuum everywhere around the canister, shouldn't the liquid be boiling?
• yes it would but we just pretend it doesn't. The reason Sal made it a vacuum is to simplify the calculations.
• Sal says that the external pressure P2 = 0 , since it's vacuum all around. I don't get it.. Shouldn't P2 be the pressure with which the fluid comes out and not the external pressure acting at that point? Please help.
• Remember, we are interested in finding the flow velocity (v at point 2), which is just out side of the hole. Therefore the pressure just outside of the hole is what we are interested in. P2 = Patm (in this case it is 0, because it is a vacuum)
• So is the pressure output always the pressure exerted on the outgoing fluid and not the pressure by the outgoing fluid?.. In the previous video explaining Bernoulli equation it was given the direction of P2 pressure to be along the direction of the flow of the fluid.. I am confused.. Thanks for replying in advance..
• if P1=P2=0 then why is the fluid moving out of the hole?
(1 vote)
• P1 and P2 are the pressures outside the canister. And P1=P2.

But inside the canister, there'll be some pressure and it'll be (Rho)gh. And since fluids move from high pressure to low pressure, the fluid will move outside to P2.
• Why isn't the pressure from outside = 1atm??
(1 vote)
• It depends on the frame of reference. If I'm out in space looking at the earth. I see all the gasses of the atmosphere being pulled toward earth. The combined weight of the gasses at sea level translates to 1 atm of pressure. This is sometimes referred to as "absolute pressure."

Now, If I'm sitting at sea level, and measuring the ambient pressure with a bicycle pump pressure gauge, I see zero pressure. That's because when we measure pressure at sea level, we are really comparing it to the 1 atm that is already around us. We are seeing how much greater than 1 atm the pressure in the bicycle tire (or any other object that can hold compressed air) is. This is sometimes referred to as the "gauge pressure."
• hi, I am not sure this is the right place to ask the following qsn...sorry in advance,
Here goes,
' Does surface tension of a fluid depend on g(9.8ms^-2) and is it affected by gravity ? '
So if i take a spoonful of fruit juice and try to form a bubble on eart it eill not happen,but would the same be possible on a zero gravity situation like moon ? ---thanks !
• At the end of the video, the equation can be rearranged to solve for v=sqrt(2*g*h), which is the standard potential to kinetic energy result. Is this affected by the diameter of the hole/ pipe attached to the reservoir?
• as long as area_top/area_hole is large enough (=1000 in this case), v_hole is independent from the size and shape of the hole alone

cause on the right side, we get 1000/1000 - 1/1000 = 999/1000 as a coefficient at the end of the day, which is close to 1

thus the larger the ratio of areas, the closer the coefficient would be to 1, so the smaller effect on the final equation
(1 vote)
• Why is there no pressure at P2 given there is some type of velocity and flux across the P2 hole? Could height #2 be a negative number since it is below the surface given the mass or weight of the water above? It seems that P2 should have more pressure than P1 due to the divergence field within the fluid. Just a thought...