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Fluid with laminar flow going through a constriction in a pipe has low

  1. Nov 15, 2008 #1
    Hi

    What is the fundamental reason why a fluid with laminar flow going through a constriction in a pipe has lower pressure?

    Pressure is defined as force per unit area so the fluid particles must be hitting the pipe wall in the constriction with less force.

    Beetroot
     
  2. jcsd
  3. Nov 15, 2008 #2

    arildno

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    Re: Bernoulli

    1. The conservation of mass tells us that the average velocity in the constricted cross-section must be higher than in a non-constricted section.
    2. Thus, those fluid particles traveling along, must have experienced an ACCELERATION
    3. In the inviscid fluid, this acceleration can only be achieved if the pressure in the non-constricted region is higher than the pressure in the constricted region.
    4. Suppose that somehow the pressure in the constricted region were to increase to the level in the non-constricted region (say, a plug was inserted),. What would happen?
    Well, the water prior to the constriction might try to squeeze itself through the wall (not likely to happen..), yet in that case, the actual pressure there would go up, leading either to a reversal of the flow direction, or by the collapse of the cause for the pressure increase in the constricted region (for example by expelling the plug).
     
  4. Nov 15, 2008 #3

    rcgldr

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    Re: Bernoulli

    The conservation of mass flow ... Assuming mass isn't continously accumulating at a point in the pipe, the mass flow along the pipe is constant, so the fluid velocity is inversely proportional to the cross sectional area.

    Flow doesn't have to be laminar. The ideal case is when there is no viscosity or friction with the pipe walls, so that the pipe doesn't perform any work on the fluid. Otherwise, the pressure decreases with distance traveled in the pipe as the fluid flows towards a low pressure exit point at the end of the pipe, even with a constant diameter pipe.

    That's another way of looking at it. The total energy of a volume of fluid or gas is related to the speed and mass density of the molecules. Pressure is related to the momentum of the molecules as they collide with the pipe. If no work is done, and if the molecules have net increase of component of speed^2 in the direction of flow, then that corresponds with a net decrease in the component of speed^2 perpendicular to the direction of flow, and vice versa, assuming that temperature hasn't changed.

    Although not directly related, here's a link to a web page discussion the relationship between the Kelvin temperature scale, kinetic energy, heat, and potential energy (Van der Waals force):

    molecule motion.htm
     
  5. Nov 16, 2008 #4
    Re: Bernoulli

    Hi

    So the particles in the constriction are hitting the pipe wall with less force, that has been established. But is the reduction in force due to:

    1) The particles hitting the wall less often, due to their increased velocity, or
    2) The particles hitting the wall with less force because the velocity component in the direction of flow is greater than the axial component.

    Beetroot
     
  6. Nov 16, 2008 #5

    russ_watters

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    Re: Bernoulli

    The others said why the velocity changes, but you asked why the pressure changes. Velocity changes due to conservation of mass - pressure changes due to conservation of energy.
     
  7. Nov 16, 2008 #6

    rcgldr

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    Re: Bernoulli

    Mass flow is constant, so the rate of collisions with the wall is also constant.
    Correct, the average speed of the molecules is constant in this case, so if there's a net flow in a particiular direction, the velocity perpendicular to that flow is a bit less.
     
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