When to apply Pascal's Law vs Bernoulli's equation

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SUMMARY

This discussion centers on the application of Pascal's Law and Bernoulli's Equation in fluid dynamics, particularly in scenarios involving pressure changes at different elevations. Pascal's Law is applicable only to static fluids, while Bernoulli's Equation can be used for both static and moving fluids. The user, DR, initially misapplied the equations due to a misunderstanding of the parameters involved, specifically the definitions of height (h) and elevation (z). The conversation clarifies that discrepancies in results can arise from sign errors and the flow velocity of the fluid.

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  • Understanding of Pascal's Law (p = p(initial) + rho*g*h)
  • Familiarity with Bernoulli's Equation (p + rho*g*h + 1/2rho*v^2)
  • Basic knowledge of fluid dynamics concepts
  • Ability to interpret parameters in hydrostatic and dynamic fluid equations
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  • Research the conditions under which to apply Pascal's Law versus Bernoulli's Equation
  • Study the implications of fluid velocity on pressure calculations
  • Explore the significance of parameter definitions in fluid equations
  • Learn about hydrostatic pressure and its applications in real-world scenarios
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Students and professionals in engineering, particularly those focused on fluid dynamics, hydraulic systems, and anyone needing to understand the principles governing pressure in static and moving fluids.

rudy
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Hello,

I was solving a problem regarding pressure at different elevations. The question regarded water flowing through a pipe which travels up 5 meters.

I used Pascal's Law (p = p(initial) + rho*g*h : rho is density of fluid, g is gravity and h is the height) and came up with an answer slightly higher than the answer key.

The answer key used Bernoulli's equation (p + rho*g*h + 1/2rho*v^2) ad got an answer slightly lower than mine.

At first I thought the difference was just due to the textbook usually rounding more than I do, but did I actually choose the wrong equation? What situations would you know to apply one equation and not the other?

Thanks in advance,

-DR
 
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I'm guessing something else changed that you didnt take into account...velocity?
 
Is the rule that Pascal's Law applies to static fluids and Bernoulli's Equation applied to fluids in motion?
 
rudy said:
Is the rule that Pascal's Law applies to static fluids and Bernoulli's Equation applied to fluids in motion?
No. The two equations should be consistent if the flow velocity is zero. If the results are not consistent, you must have a sign error. What is your definition of the parameter h in the hydrostatic equation and what is your definition of the parameter z in the Bernoulli equation?
 
Hello,

The flow velocity was not zero. It regarded water flowing into a house through a pipe and then up to the second story.

I defined h to be the number of meters below the initial position. I do not have a parameter z, can you specify?

I can post a picture if you like, but I have been having problems getting images to show up on here.
 
So then, Bernoulli's Equation can be used for static or moving fluids, but Pascal's only to static?
 
rudy said:
So then, Bernoulli's Equation can be used for static or moving fluids, but Pascal's only to static?
Yes. In the Bernoulli equation, h is measured upward, and in the hydrostatic equation (the version you have written), h is measured downward. So, they're opposite in sign.
 
Thank you!
 

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