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Bernoulli's principle

  1. Mar 25, 2015 #1
    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. jcsd
  3. Mar 25, 2015 #2
    There's nothing wrong with your derivation, but your statement is wrong. It's "pressure" not "pressure energy per unit volume".
     
  4. Mar 25, 2015 #3
    i have stuyied that pressure energy it not only prssure
    that is all the energies are constant at every point of the crossection
     
  5. Mar 25, 2015 #4

    Mark44

    Staff: Mentor

    I've never heard of "pressure energy." Pressure is defined as force per unit of area -- http://en.wikipedia.org/wiki/Pressure
     
  6. Mar 25, 2015 #5
    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.
    For more info., refer: http://en.wikipedia.org/wiki/Bernoulli's_principle
     
  7. Mar 25, 2015 #6
    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
  8. Mar 25, 2015 #7

    russ_watters

    User Avatar

    Staff: Mentor

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


    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
  9. Mar 25, 2015 #8
    Thanks russ
     
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