Fluid in a tank

[G1SG2]

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Imagine we have a tank of fluid with a hole at the bottom. Now, as per Bernoulli's equation, we'd end up with v=sqrt2gh. Then according to the formula, the velocity of the fluid would decrease as its moving down the tank toward the hole because delta h decreases (comparing the surface to the hole, where the surface level would be decreasing since the fluid level is decreasing as its being drained through the hole). However, doesn't this go against the whole concept of something gaining KE as its losing PE??? Aren't we to think that the fluid velocity is increasing as the fluid in the tank drops to the level of the hole?? Or am I approaching this the wrong way?

 

[kobe200LATE]

The h represents the depth of the fluid or the amount of fluid above the hole at the bottom, not the position of the fluid. As a fluid moves down the tank, the velocity of the fluid in the tank is negligible because the area of the tank compared to the area of the hole is so big that you can assume the velocity is negligible. Once the fluid reaches the hole, the velocity increases dramatically due to the much smaller area of the hole compared to the tank.

So basically if the fluid hasn't reached the hole yet and is still in the tank, its velocity is 0 due to the huge area of the tank. At this point, its pretty much all potential energy.

Once it reaches the hole, the area decreases so much that it dramatically increases in velocity, converting all of that potential energy into kinetic energy.

 

[neil100]

The h represents the depth of the fluid or the amount of fluid above the hole at the bottom, not the position of the fluid. As a fluid moves down the tank, the velocity of the fluid in the tank is negligible because the area of the tank compared to the area of the hole is so big that you can assume the velocity is negligible. Once the fluid reaches the hole, the velocity increases dramatically due to the much smaller area of the hole compared to the tank.

So basically if the fluid hasn't reached the hole yet and is still in the tank, its velocity is 0 due to the huge area of the tank. At this point, its pretty much all potential energy.

Once it reaches the hole, the area decreases so much that it dramatically increases in velocity, converting all of that potential energy into kinetic energy.

👍

The second concept about area and velocity of the container is called the continuity expression.