# Basic fluid energy

1. Nov 30, 2015

### 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)

Which is correct? Why are both equations used
Thank you

2. Nov 30, 2015

### Staff: Mentor

In the first equation, h is measured upward, and, in the second equation, h is measured downward.

Chet

3. Nov 30, 2015

### BobP

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

PS I am studying haemodynamics (energy of blood in the body)

4. Nov 30, 2015

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.

5. Nov 30, 2015

### BobP

d
Fingers crossed it will make sense in the exam!

6. Nov 30, 2015

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.

7. Nov 30, 2015

### 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.

8. Dec 4, 2015

### 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.

9. Dec 5, 2015