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

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Discussion Overview

The discussion revolves around the appropriate application of Pascal's Law and Bernoulli's equation in fluid dynamics, particularly in the context of pressure calculations for water flowing through a pipe that ascends 5 meters. Participants explore the conditions under which each equation should be applied, considering factors such as fluid motion and elevation changes.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant, DR, questions whether they chose the wrong equation after finding a discrepancy between their result using Pascal's Law and the answer key using Bernoulli's equation.
  • Another participant suggests that the difference in results might be due to an unaccounted change in velocity.
  • There is a proposal that Pascal's Law applies to static fluids while Bernoulli's equation applies to fluids in motion.
  • A later reply challenges this by stating that both equations should yield consistent results if the flow velocity is zero, indicating a potential sign error in the application of the equations.
  • DR clarifies that the flow velocity was not zero and defines 'h' as the number of meters below the initial position, seeking clarification on the parameter 'z' in Bernoulli's equation.
  • Another participant confirms that Bernoulli's equation can be used for both static and moving fluids, while Pascal's Law is limited to static fluids, noting the difference in how 'h' is measured in each equation.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Pascal's Law versus Bernoulli's equation, with some asserting clear distinctions based on fluid motion and others questioning the consistency of results. The discussion remains unresolved regarding the specific conditions under which each equation should be applied.

Contextual Notes

Participants have not fully defined the parameters used in their equations, leading to potential misunderstandings. The discussion also highlights the importance of sign conventions in the application of the equations.

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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