Fluid Statics and Dynamics: P Equation

In summary: I tried to find the equation for p=patm+density*g*h in terms of pressure, but I wasn't able to find it. I think I might have been looking in the wrong place. I'll try to look for it again and get back to you.
  • #1
vijayramakrishnan
90
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in fluid statics we have learned that p =patm+density*g*h.
is the same equation valid in fluid dynamics?
 
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  • #2
vijayramakrishnan said:
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.
 
  • #3
Dr. Courtney said:
Look up the Bernoulli equation.
thank you for replying sir,but it doesn't provide any direction relation between height and pressure?
 
  • #4
vijayramakrishnan said:
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.
 
  • #5
vijayramakrishnan said:
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.
 
  • #6
Chestermiller said:
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
 
  • #7
vijayramakrishnan said:
thank you for replying sir,but we can assume the fluid to be non viscous and flow to be streamline
and also incompressible
 
  • #8
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.
 
  • #9
vijayramakrishnan said:
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.
 
  • #10
boneh3ad said:
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?
 
  • #11
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.
 
  • #12
russ_watters said:
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.
 
  • #13
vijayramakrishnan said:
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.
 
  • #14
boneh3ad said:
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?
 
  • #15
vijayramakrishnan said:
sir,so does the third term represent the hydrostatic pressure?

What do you think and why?
 
  • #16
vijayramakrishnan said:
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?
 
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  • #17
vijayramakrishnan said:
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,
 

1. What is the P Equation in Fluid Statics and Dynamics?

The P Equation, also known as the Bernoulli's Equation, is a fundamental equation in fluid mechanics that describes the relationship between fluid pressure, velocity, and elevation in a continuous, steady flow.

2. How is the P Equation derived?

The P Equation is derived from the conservation of energy principle, specifically the conservation of mechanical energy in a steady flow. It takes into account the potential energy, kinetic energy, and pressure energy of the fluid.

3. What are the assumptions made in the P Equation?

The P Equation assumes that the fluid is incompressible, inviscid, and has a steady, continuous flow. It also assumes that there is no external work done on the fluid and that the fluid is flowing along a streamline.

4. What are the applications of the P Equation?

The P Equation has various practical applications in engineering and physics, such as calculating the lift force on an airplane wing, predicting the flow rate in pipes, and understanding the flow of blood in the human circulatory system.

5. How is the P Equation used in real-world scenarios?

The P Equation is often used in conjunction with other equations and principles in fluid mechanics to solve complex problems and analyze fluid flow in real-world scenarios. It is also used to design and optimize various engineering systems, such as pumps, turbines, and aircraft wings.

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