Basic Fluid Energy: Pressure, GPE & KE

[BobP]

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

 

[Chestermiller]

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

 

[BobP]

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)

 

[boneh3ad]

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.

 

[BobP]

d

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!

 

[boneh3ad]

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.

 

[gleem]

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.

 

[zabini]

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.

 

[BobP]

Thanks all for your replies!