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Bernoulli's principle, flow rate, velocity and pressure

  1. May 23, 2014 #1
    Hello,

    I need some help understanding Bernoulli's principle, flow rate, velocity and pressure.

    I understand that when the diameter of a pipe decreases, the velocity will increase and the pressure will decrease. But I am having a hard time applying this to a practical application.

    For example, for a shower I would want to maximize the water pressure. So for a given flow rate I would want to increase the pipe diameter to increase the pressure.

    But what about filling up a bath tub? For a given flow rate, what size pipe would fill up the bathtub the fastest? Would I want the opposite to increase the speed? Or do I still want a larger diameter so I have a greater volume of water?

    I feel like I am not understanding something very basic here.
     
  2. jcsd
  3. May 23, 2014 #2
    Since filling the bathtub is based on volume of water in the tub, you want to maximize the volumetric flow rate.
     
  4. May 28, 2014 #3
    The quantity you're looking for is the DYNAMIC pressure of the fluid. This increases with increasing velocity of the fluid. Bernoulli's equation talks about the STATIC pressure at a point decreasing with increasing velocity for irrotational and inviscid flows. This is what a barometer attached to that point would measure. But the pressure at which your water is supplied is a third quantity and cannot possibly depend on what you choose to do with the geometry of the delivery pipe.

    As for your second question, if you have a given flow rate (say 1 litre/min ) then a bathtub that has a 15 litre capacity will take 15mins to fill up. It doesn't matter what you do with the flow conditions at the outlet.
     
  5. May 28, 2014 #4
    A word of caution when you apply bernoulli's equation. It's simply a statement of energy conservation applied to fluid dynamics. So ensure your system is closed ( no energy or mass flow in or out ) and that the flow is sufficiently approximated as inviscid (no thermal losses )
     
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