Fluids - variation of velocity for free jets

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SUMMARY

The discussion centers on the variation of water velocity as it exits holes in a tin can, specifically addressing the effects of hole geometry and pressure gradients. The user assumes that the holes are uniform in size and possess sharp corners, leading to the vena contracta effect, which influences fluid velocity. The user concludes that the velocity is a function of hole size and pressure gradient, suggesting that the velocity vectors should resemble those in option C, which depicts an increase in velocity with depth. However, there is uncertainty, and option B is also considered a possibility.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically Bernoulli's equation.
  • Knowledge of vena contracta effect in fluid flow.
  • Familiarity with steady, incompressible, and inviscid flow assumptions.
  • Ability to interpret velocity vector diagrams in fluid dynamics.
NEXT STEPS
  • Study Bernoulli's equation and its applications in fluid mechanics.
  • Research the vena contracta effect and its implications on fluid velocity.
  • Learn about the impact of hole geometry on fluid flow characteristics.
  • Explore velocity vector analysis in various fluid flow scenarios.
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Students and professionals in fluid mechanics, engineers designing fluid systems, and anyone interested in understanding fluid flow behavior through orifices.

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hey guys, only my second post here, hope these boards are helpful!

I have a problem for my fluid mechanics class and was wondering if anyone could help me out. i will post the question and the figures and what assumptions i have made due to the lack of information.

Several holes are punched into a tin can as shown in Fig. P3.17. Which of the figures represents the variation of the water velocity as it leaves the holes? Justify your choice.
The figures are attached below.

I have assumed that all of the holes are the same size and are not smooth/curved as i would suspect a drill would leave them upon pushing the material inwards towards its vertical z-axis of symmetry. if the holes aren't smooth/curved, they have 90 degree corners which gives the exiting fluid the vena contracta effect...

I know velocity is a direct function of the size of the holes and the pressure gradient (dp/dr). the pressure is dependent upon the depth of each hole, so this means that the velocity vectors should be like those in C which increase more over depth in a fashion that we would expect them to, right? if the answer isn't C, then it would have to be B, but I'm so confused now that it could be either one of them.

hope someone knows more about fluids than myself!
 

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oh, of course i have assumed steady, incompressible, inviscid flow!
 

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