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Calculating force to displace water

  1. Feb 3, 2010 #1
    I am trying to determine the force required to displace water as shown in the attached picture.

    My problems here are that I am displacing water using a vertical plunger moving downward at 25cm/sec also as seen in the picture the plunger is at 45degrees.

    I am confused as to how to calculate the force required to do this

    Gravity in this case is working to our advantage when the plunger is going downwards and working against us on when the plunger is returning to its original position.

    What I know:
    Weight of plunger = 6kgs
    125kgs of water of water displaced by plunger at full extension.
    Distance = 50cm = plunger moves from start position 50cm downwards.
    Time= 2 sec for plunger to move downward 50cm.
    10000kg of water in the tank.
    Horizontal force of water in tank= 375kg force per unit area = 3678.75 N

    Can someone give me some insight into how this might be calculated? I dont think its as simple as P=F/a!

    Attached Files:

  2. jcsd
  3. Feb 3, 2010 #2

    Start with Newton's first law for the plunger since it moves with constant velocity. You have a normal force, a downward weight force, and an upward buoyant force:

    F_net = 0

    N + W + F_b = 0

    In the above equation, the unknown of interest is the normal force. The weight force can be calculated with -m*g and the buoyand force is rho_water*V_displaced*g.

    N - m*g + rho*V*g = 0

    The reason this problem is a bit tricky is because the volume of the plunger underwater is variable. Calculate V as a function of time using geometry. Then you can solve for the normal force as a function of time. The volume of water in the container is not relevant to this problem.
  4. Feb 3, 2010 #3
    Sorry, I don't think that's an easy problem. It is P=F/a, the hard part is figuring out what P is! The static case is pretty simple, but when the water is flowing past an object at ~25cm/s I don't know. It should be fairly straightforward to estimate the order of magnitude but if you want more accuracy than that the problem gets a lot harder. I'll let the hydrodynamics people comment, it's not really my area. I guess the first thing to look at would be the Reynold's number to decide if the drag is pressure dominated or viscosity dominated and to decide what level of accuracy you need; then go from there either with an analytical approximation or a computer simulation - whatever suits. Hydrodynamics is notorious for computation difficulty.
  5. Feb 3, 2010 #4
    Gazebo dude is correct. My solution would be the correct solution at low speed, but at 25 cm/s drag forces would likely be significant. With the changing orthographic projection of the plunger, this force would be variable despite the constant speed. You might be able to model the drag force with the "drag equation" (look it up on Wikipedia).
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