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

In summary, Pascal's Law and Bernoulli's Equation both apply to fluids in motion, but they have different definitions for the parameter z.
  • #1
rudy
45
9
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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  • #2
I'm guessing something else changed that you didnt take into account...velocity?
 
  • #3
Is the rule that Pascal's Law applies to static fluids and Bernoulli's Equation applied to fluids in motion?
 
  • #4
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?
 
  • #5
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.
 
  • #6
So then, Bernoulli's Equation can be used for static or moving fluids, but Pascal's only to static?
 
  • #7
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.
 
  • #8
Thank you!
 

1. When should Pascal's Law be used?

Pascal's Law should be used when studying fluids in a static state, such as when analyzing pressure in a closed container or hydraulic systems.

2. When is Bernoulli's equation applicable?

Bernoulli's equation is used for analyzing fluids in a dynamic state, such as when studying fluid flow or calculating the velocity of a fluid.

3. Can Pascal's Law and Bernoulli's equation be used interchangeably?

No, they cannot be used interchangeably. Pascal's Law applies to static fluids, while Bernoulli's equation applies to dynamic fluids. They are two different principles that cannot be used in place of each other.

4. Are there any real-world applications of Pascal's Law and Bernoulli's equation?

Yes, there are many real-world applications of both principles. Pascal's Law is used in hydraulic systems, such as car brakes and construction equipment. Bernoulli's equation is used in aerodynamics, such as in airplane wings and wind turbines.

5. Is knowledge of both Pascal's Law and Bernoulli's equation necessary for all scientists?

It depends on the field of science one is working in. For those studying fluid mechanics or engineering, knowledge of both principles is essential. However, for other fields, one may only need to have a basic understanding of these principles.

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