Fluid Statics and Dynamics: P Equation

[vijayramakrishnan]

in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?

 

[Dr. Courtney]

in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?

Look up the Bernoulli equation.

 

[vijayramakrishnan]

Look up the Bernoulli equation.

thank you for replying sir,but it doesn't provide any direction relation between height and pressure?

 

[Chestermiller]

in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?

No. The same equation is not generally valid in fluid dynamics. The fluid dynamics of viscous fluids is described by the much more complicated Navier Stokes equations.

 

[boneh3ad]

thank you for replying sir,but it doesn't provide any direction relation between height and pressure?

If you take a look at it, it's very similar to the equation you provided but also has a velocity term, although it is only valid in a certain subset of fluids problems.

 

[vijayramakrishnan]

No. The same equation is not generally valid in fluid dynamics. The fluid dynamics of viscous fluids is described by the much more complicated Navier Stokes equations.

thank you for replying sir,but we can assume the fluid to be non viscous and flow to be streamline

 

[vijayramakrishnan]

thank you for replying sir,but we can assume the fluid to be non viscous and flow to be streamline

and also incompressible

 

[mfig]

As generally in physics, dynamic problems and static problems are treated differently. You want to look at this link. Study the three terms of the equation at the top of the page. Read the material there and you will have the answer to your question.

 

[boneh3ad]

and also incompressible

Given your criteria you've now laid out, what was wrong with the Bernoulli answer? Take a look at the link provided by @spamanon.

 

[vijayramakrishnan]

Given your criteria you've now laid out, what was wrong with the Bernoulli answer? Take a look at the link provided by @spamanon.

thank you for replying sir,i read that article and it was indeed helpful,and i know what is bernoulli's equation, but all i want to know is can we apply the theorem that pressure = density*g*h in fluid dynamics?for example we have used it in rotating fluids to determine the shape of free surface of liquid but can we do the same if the liquid is moving?or is that equation necessarily not valid in fluid dyanmics?if yes then why so? we use Newton's laws to derive that but if the fluid is moving with uniform velocity it has no acceleration so why can't the same law be applied here?

 

[russ_watters]

I'm not sure how many ways people can say "yes" before you will take it, but yes, given all of those constraints and the constant velocity constraint, yes, Bernoulli's equation basically reduces to the hydrostatic pressure equation.

 

[vijayramakrishnan]

I'm not sure how many ways people can say "yes" before you will take it, but yes, given all of those constraints and the constant velocity constraint, yes, Bernoulli's equation basically reduces to the hydrostatic pressure equation.

sir,i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem.please help.

 

[boneh3ad]

sir,i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem.please help.

You do see that there is a $\rho g z$ term in Bernoulli's equation, right? Bernoulli's equation is essentially an energy balance cast in terms of pressure, where each side of the equation (i.e. each $p + \frac{1}{2}\rho v^2 + \rho g z$ term) constitutes what is commonly called total pressure. One element of that is the hydrostatic pressure.

 

[vijayramakrishnan]

You do see that there is a $\rho g z$ term in Bernoulli's equation, right? Bernoulli's equation is essentially an energy balance cast in terms of pressure, where each side of the equation (i.e. each $p + \frac{1}{2}\rho v^2 + \rho g z$ term) constitutes what is commonly called total pressure. One element of that is the hydrostatic pressure.

sir,so does the third term represent the hydrostatic pressure?

 

[boneh3ad]

sir,so does the third term represent the hydrostatic pressure?

What do you think and why?

 

[russ_watters]

sir,so does the third term represent the hydrostatic pressure?

I don't understand. You were instructed to look up Bernoulli's equation. Did you? Every source describing it should list the meaning of each term. What did your research say?

 

[jtbell]

i worked it out but unable to derive the hydrostatic pressure equation from bernoulli's theorem

Show us what you tried and someone can probably point out where you went wrong,