# Bernoulli's principle and work energy theorem

1. Mar 25, 2015

### naman007

for a stream line flow of ideal liquid (non-viscous) imcompressible the sum of pressure energy per unit volume kinetic energy per unit volume , potential energy per unit volume remains constant
mathematically
P+1/2roV2+ROGH=constant
consider a fluid flowing in a pipe of various crossections
we consider 2 regions ,
at region 1 the workdone =P1V
workdone at region 2 =P2V
total workdone =P2V-P1V
= V(P1-P2)
Change in gravitational potential energy
U=ro×g×V(H2-H1)
the change in kinetic energy
= 1/2×ro×V(V2-V1)
where v1 and v2 are the speed of liquid
aplling work energy theorem
(P1-P2)V=ro×g(H2-H1) + 1/2ro(V2-V1)
P1+ro×gh1+1/2rov1=P2+ro×gh2+1/2rov2
that is P+ro×gh+1/2ro×v= constant

2. Mar 25, 2015

### Meron

There's nothing wrong with your derivation, but your statement is wrong. It's "pressure" not "pressure energy per unit volume".

3. Mar 25, 2015

### naman007

i have stuyied that pressure energy it not only prssure
that is all the energies are constant at every point of the crossection

4. Mar 25, 2015

### Staff: Mentor

I've never heard of "pressure energy." Pressure is defined as force per unit of area -- http://en.wikipedia.org/wiki/Pressure

5. Mar 25, 2015

### Meron

Yes, but to the statement you have provided and the way you derived the equation, it would be pressure.
Pressure energy is not the same as pressure.

6. Mar 25, 2015

### naman007

ok ok i understand but ,it is the energy that the pressure exerts at every point of the fluid in a pipe thats why it is pressure energy per unit volume

Last edited: Mar 25, 2015
7. Mar 25, 2015

### Staff: Mentor

It sounds wrong, but it is a common descriptor for the term:
http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

It's probably just an attempt to find a less cumbersome label to the term than energy (work) arising from force and distance, per unit volume, so the force comes from pressure. Energy....from....pressure. Pressure energy. Or maybe it is less confusing that saying work per unit volume (similar to the other terms, kinetic energy per unit volume and potential energy per unit volume) when all you see in the equation is pressure. Either way, the descriptor is what it is so that people recognize where it came from:
f*d/v=p

If the other two terms are *something* energy per unit volume, then the "pressure" term must be too, otherwise they couldn't be in an equation together.

In any case, naman007, I'm not seeing a question anywhere in any of your posts....do you have one?

Last edited: Mar 25, 2015
8. Mar 25, 2015

Thanks russ