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Fluid Mechanics Question -- fluid on block?

  1. Jan 25, 2017 #1
    1. The problem statement, all variables and given/known data
    A block has dimensions 0.015 x 0.2 x 0.1 meters and weighs 6 newtons. A 15mm-diameter jet of water is deflected by the block. Find the flow rate needed to tip the block.
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    2. Relevant equations
    Mass conservation: ∂/∂t ∫(control volume)ρ d∀ + ∫(control surface) ρv•n dA = 0
    Momentum conservation: ∂/∂t ∫(control volume)ρv d∀ + ∫(control surface) ρv(v•n) dA = ∫(control surface) p*ndA + Viscous forces + ∫(control volume)ρgd∀

    3. The attempt at a solution
    I know this is steady state, so the first term in each equation (time derivative of mass in the control volume) is zero. I am trying to use a control volume that follows the streamlines, to make the surface integrals easier. However, I don't know what area to use as the output, or even how to approach finding it. Also, how should I relate the force on the block to the force required to tip the block? I assume it has to do with a Moment balance, but I'm not sure how to do that.

    I don't want you to solve the problem for me, just some direction would be nice. Thanks!
     
  2. jcsd
  3. Jan 25, 2017 #2

    Baluncore

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    Science Advisor

    The centre of mass of the block must be pushed above the right hand side edge of the base before the block will fall freely. Getting the block to start tipping will be the critical force.

    As the block starts to tip, the moment of the water jet impact about the RHS base edge will be equal to the moment of the centroid of block mass about the same edge.

    If I remember rightly, the dynamic force due to impact of a flow will be proportional to half the flow rate * density * velocity squared. You had better check that by application of conservation laws to the flow path of the fluid.
     
  4. Jan 25, 2017 #3
    What is the x component of momentum of the fluid flowing upward and downward along the block along the contact area? How much x momentum does the fluid have after it contacts the block and spreads along the surface? What control volume can you use?
     
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