# Pressure energy(fluid mechanics)

1. Sep 19, 2009

### Godwin Kessy

Can any one please help me on the term pressure energy what does it really mean and If possible the calculations involved with it!!

2. Sep 19, 2009

### Staff: Mentor

Pressure times volume is energy. So if that product changes then the energy has changed.

3. Sep 20, 2009

### thrillhouse86

Strictly speaking isn't change in volume times a constant pressure energy ?
so if you had a situation where your volume stayed constant but your volume changed you would have a change in enthalpy ? i.e
dU = TdS - PdV
dH = TdS + VdP

4. Sep 29, 2009

### Godwin Kessy

But what is really that volume and the pressure.
May you please elaborated it, Probably by using the model for the derivation for Bernouli's Theorem!

You know what, I know its reasonable for the pressure energy to be involved i the calculations for bernouli's theorem, But I was shocked when it was written that;

Pressure energy=mgh

Thank you!!

5. Sep 29, 2009

### Godwin Kessy

Excuse me! Am really out of phase for what you just explained!
May you tell ,e in detail may be would solve my problem!
But I was in the derivation for Bernouli's theorem,
How can pressure energy=mgh
Where h=Height above the point of which total energy is to be calculated!

And seriously am not yet familiar with enthalpy so may you elaborate more!
Thank you!

6. Sep 29, 2009

### Staff: Mentor

It is any volume that you are interested in and the pressure within that volume. For instance, if you are interested in the work done by a piston as it expands then you would take the pressure inside the piston times the volume of the piston at the beginning of the power stroke and at the end of the power stroke. The difference is the work done by the piston during the expansion.

Similarly, if you are interested in the work done by the heart in one heartbeat you can plot the left ventricular pressure by the left ventricular volume and find the area enclosed over one heartbeat.

If you are interested in the amount of work being done on a differential element of a fluid flow you can do the same thing.

You should be shocked, it is not true in general. For instance, in outer space g=0, so mgh = 0, but pressure times volume is still energy and pistons and compressors don't run without energy input! Also, consider on earth, you can heat a gas inside a closed container, this will increase P and therefore increase PV without changing mgh.

7. Oct 2, 2009

### Godwin Kessy

Seriously it is true am telling you! May be you should look it over and help me out!
Its under the derivation of Bernouli's theorem!

8. Nov 25, 2010

### Zeppos10

9. Nov 25, 2010

### Staff: Mentor

you didn't get what Dale meant by "general". There are many different types of pressure energy including several others in bernoulli's equation. Pressure due to gravity is only one type.

10. Nov 26, 2010

### rcgldr

Not quite, it's an inverse relationship. Bernoulli's equation multiplied by volume results in:

static_pressure_energy + kinetic_energy + gravitational_potential_energy = constant

(Note Bernoulli's equation assumes no external work is performed).

For the gravitational component, using water as an example, as depth increases, static_pressure_energy increases, gravitational_potential_energy decreases, and vice versa.