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Having trouble using bernoulli eq.

  1. Aug 20, 2006 #1
    So, i'm tweaking my understanding of applying Bernoulli's equation, and i'm having a problem understanding the change in pressure and velocity when a fluid flows down a tube of constant diameter. The way i see it; either the pressure changes with height and the velocity stays the same, or the velocity changes (increases) with the falling height and the pressure stays the same. It dosn't seem like it could be both (you need 2 eq. for 2 variables), but i could be wrong. Can someone point out the correct way to interpet Bernoulli's eq. for this arrangement, and maybe even tell me what i'm missing from my understanding. I'll check back here as soon as I get back from work tonight. Thanks in advance for the help!
     
  2. jcsd
  3. Aug 21, 2006 #2

    andrevdh

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    I think the problem you foresee is that the diameter of the stream normally decreases as it falls down. This should create a region of low pressure (vacuum?) under normal conditions. I would guess that a pipe will prevent this from happening thereby keeping the flow constant and preventing the stream from accelerating (siphoning fuel out of a tank delivers a constant stream) ??? Maybe we should ask a plumber what happens (or investigate it ourselves).
     
    Last edited: Aug 21, 2006
  4. Aug 21, 2006 #3
    Good point. But not necesary, i think i have it now. Like you said, the stream narrows when its not in a pipe. And what I kept forgeting is: the pressure cant really be all that different in a pipe where the water is falling. I figured this by considering a pipe closed at one end, and then getting opened up. When its closed, and the water isn't moving, there is a pressure gradient of increasing pressure going down the pipe. At the moment the cap (or faucet) gets oppened up, the pressure at the bottom starts to drop to the external pressure (of the atmosphere). And as the pressure drops, the water starts to move, exactly as bernoulli's equation describes. The pressure at any point in the pipe cant be lower than the externally pressure, or the water would slow down (pressure is just the weight of the atmosphere and water acting on itself, right?) Eventually the whole pipe converts to external pressure and water is all accelerating down the pipe at a constant rate.
    So all i really need (given that diameter is constant) is the part that gives velocity in terms of potential and kinetic energy (just like an ordinary kinematics problem), since pressure is constant.
    Dont worry, I'll keep working at it and get the correct model.:wink:
    Thanks for the help!
     
    Last edited: Aug 21, 2006
  5. Aug 21, 2006 #4

    andrevdh

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    Remeber that the eoc requires that the speed of the fluid stays the same throughout the pipe if its diameter is constant. [signing off now - time to go home in South Africa]
     
  6. Aug 21, 2006 #5
    OK, good night then.
    And roger on the EoC: IF mass flow rate can't vary in a tube (flow is laminar and fluid is incompressible), and cross sectional area remains constant, then the only thing that can vary with height is pressure.
    Looks like i'm still stuck....
     
  7. Aug 22, 2006 #6

    andrevdh

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    I see two possibilities regarding your problem. Either the liquid is in free fall in the tube (and it might detach from the walls) or the tube is connected to the bottom of a tank and there exist a pressure difference between the top and bottom of the column of liquid.
     
  8. Aug 22, 2006 #7
    You're quite right. I talked this over with some class mates who have a better understanding than i do, and they agreed, saying that it has to be a pressure change, not a velocity change. It seems counter intuitive to me, but it does help me get my assginment done. So I'll take that as my final answer.
    Thanks for all the help! I really appretiated it. :smile:
     
  9. Aug 22, 2006 #8

    andrevdh

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    It's a pleasure. I will maybe investigate it experimentally and post the results in the future.
     
  10. Aug 22, 2006 #9
    If the diameter of the pipe is constant and vertical, then the stream of water will change is potential energy (in the form of Edit: gravitational energy) into kinetic energy, (in the form of velocity) and pressure will remain constant.

    If the pipe is constant diameter and horizontal, the pressure and velocity will remain constant. (provided that the pipe is perfectly smooth).
     
    Last edited: Aug 22, 2006
  11. Aug 23, 2006 #10

    andrevdh

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    How do you come to the conclusion that the pressure of the fluid will remain contant if it is flowing down a vertical pipe?
     
  12. Aug 23, 2006 #11
    Whoopsies. You're right. For the vertical pipe, the velocity is constant, and the pressure changes. (increases as it goes down)

    Quite conter-intuitive actually. If the pipe is open to atm at one end, the end that is closed has to be at a pressure below atmospheric for the flow to occur. The hydrostatic pressure allows for this low pressure.
     
    Last edited: Aug 23, 2006
  13. Aug 24, 2006 #12

    andrevdh

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    Yes the decreasing pressure in the pipe seems very strange, but I think all that it means is that the pipe is actually "sucking" the water out of the tank as flows down in the pipe (the hanging water column in the pipe pulls the water out of the tank).
     
  14. Aug 25, 2006 #13

    andrevdh

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    The graph shows a recording of the weight of the water that was deposited by a vertical constant diameter plastic pipe connected to a tank of water. The beaker hanged from a Pasco force sensor that recorded the weight of the beaker and the water as the water drained into it (the sensor displays a force that pulls on it as a negative quantity). It is clear that the water arrived at a contant rate at the bottom implying that the exit velocity was contant. We find that water flowing downwards in a constant diameter pipe do not accelerate out of the pipe, but exits at a constant speed, contrary to what one would expect. This explains why the water pressure decreases upwards in the pipe - the weight of the water is pulling it downwards but the pipe is preventing it from accelerating resulting in a decrease in water pressure at increased heights.
     
    Last edited: Nov 29, 2006
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