Basic Fluid Energy: Pressure, GPE & KE

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Discussion Overview

The discussion centers on the expressions for the total energy of a fluid in fluid dynamics, specifically examining the equations involving pressure energy, gravitational potential energy, and kinetic energy. Participants explore the implications of different sign conventions for gravitational potential energy and how these affect calculations in contexts like haemodynamics.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants present two equations for total fluid energy: one with a plus sign for gravitational potential energy and one with a minus sign, questioning which is correct and why both are used.
  • It is noted that the difference in sign conventions may relate to whether height (h) is measured upward or downward.
  • A participant suggests that the choice of equation should depend on which makes more sense in the context of the problem, emphasizing the importance of understanding the direction of energy changes.
  • Another participant recommends using the equation with the plus sign for gravitational potential energy, stating it is the more common approach.
  • Discussion includes the application of Bernoulli's Law, noting that comparisons of pressure and flow rates at different points require careful consideration of sign conventions.
  • One participant mentions that in exams, it is necessary to find differences in total energies rather than absolute values, indicating that the reference frame affects the sign of h.

Areas of Agreement / Disagreement

Participants express differing views on the correct sign convention for gravitational potential energy in fluid dynamics, with no consensus reached on which equation is universally correct. The discussion remains unresolved regarding the best approach to take in various contexts.

Contextual Notes

Participants highlight that the choice of sign convention may depend on the reference frame and the specific context of the problem, indicating that assumptions about height measurement can lead to different interpretations of the equations.

Who May Find This Useful

This discussion may be useful for students studying fluid dynamics, haemodynamics, or related fields, particularly those preparing for exams or seeking clarification on energy equations in fluid systems.

BobP
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In fluid dynamics, the total energy of a fluid can be given as:
Pressure energy + gravitational potential energy + KE
or
P + ρgh + ½ρ(v^2)

But I have also seen the expression

P - ρgh + ½ρ(v^2)

NOTE the minus sign in the second equation.

Which is correct? Why are both equations used
Thank you
 
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BobP said:
In fluid dynamics, the total energy of a fluid can be given as:
Pressure energy + gravitational potential energy + KE
or
P + ρgh + ½ρ(v^2)

But I have also seen the expression

P - ρgh + ½ρ(v^2)

NOTE the minus sign in the second equation.

Which is correct? Why are both equations used
Thank you
In the first equation, h is measured upward, and, in the second equation, h is measured downward.

Chet
 
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Chestermiller said:
In the first equation, h is measured upward, and, in the second equation, h is measured downward.

Chet
Ok, so in an examination how do I know which to use?

PS I am studying haemodynamics (energy of blood in the body)
 
You pick whichever makes more sense. At the end of the day, any particle (fluid or otherwise) should gain potential energy if it is moved in a direction against gravity. So if one pet of a fluid flow is "above" another with respect to gravity, then moving that direction should make the ##\rho g h## term larger no matter which sign convention you choose.
 
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d
boneh3ad said:
You pick whichever makes more sense. At the end of the day, any particle (fluid or otherwise) should gain potential energy if it is moved in a direction against gravity. So if one pet of a fluid flow is "above" another with respect to gravity, then moving that direction should make the ##\rho g h## term larger no matter which sign convention you choose.
Fingers crossed it will make sense in the exam!
 
It's really pretty simple. When in doubt, pick the one with the plus sign and treat ##h## as positive in the "up" direction. I've honestly never seen it used the other way.
 
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In the usual applications of Bernoulli's Law one compares the pressure at one point to that of another to the flow rate and height at one point to that of another. Thus

P1 -P2 = ½ρ(v22 -v12) +ρg(h2 - h1)

One only has to look at the data to enter the proper values.
 
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In exams you will need to find the difference in total energies. Not absolute energy. So using proper sign conventions h can be positive negative or zero. Depends on the reference frame.
 
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Thanks all for your replies!
 

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