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

[rudy]

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

 

[russ_watters]

I'm guessing something else changed that you didnt take into account...velocity?

 

[rudy]

Is the rule that Pascal's Law applies to static fluids and Bernoulli's Equation applied to fluids in motion?

 

[Chestermiller]

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?

 

[rudy]

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.

 

[rudy]

So then, Bernoulli's Equation can be used for static or moving fluids, but Pascal's only to static?

 

[Chestermiller]

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.

 

[rudy]

Thank you!