Guage Pressure and Velocity

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September24

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So Princeton Review is kind of confusing me with something.

There is a problem in which there is a tank of water with three holes in it of same size. The holes are at different heights (hole 1 is above hole 2 which is above hole 3). They also list bernoullis equation.

They ask a random question but it leads to this conclusion. The speed of the water at hole 3(lowest one) is the highest (highest horizontal velocity) since water is at the highest gauge pressure (so it is moved out most forcefully).


It makes sense intuitively since more pressure should force it out faster. However, according to bernoulli's, Pressure and velocity are inversely related. If pressure is high, how it velocity also high in this case?

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http://forums.studentdoctor.net/threads/tprh-science-workbook-passage-15-1.903700/#post-12376174

That post is a good summary but basically the Bernoulli pressure is due to random molecular movement, so when you begin moving fluid in a uniform direction, it has less 'random' movement and thus lower pressure. Simply put, if all the molecules were moving in the same direction they would impact each other (and the container walls) less often resulting in lower pressure.

In your example hole 3 has the greatest pressure difference and therefore the greatest force/area, so the fluid is 'forced' out the fastest.
 
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Hi, to also comment on this issue, remember that Bernoulli's law is created as a fluid analogy to the conservation of energy. Thus, if you are decreasing the potential energy (at hole 3 you have the lowest potential due to having the lowest height), you will need to make that up with kinetic energy. The pressure in this equation is not the gauge pressure but the pressure of the system outside of the hole--which is exposed to air, so at 1 atm. Remember to keep the concepts of gauge pressure and the pressure in Bernoulli's equation separate.
 
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