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DYNAMICS - EXAMPLE


Water Flow Direction Change
  Example

 

A 4 ft diameter pipe is supported by a block as it makes a 90o turn. What is the force in the y-direction on the block due to the water direction change? Assume the specific weight, γw, of the water is 62.4 lb/ft3.

 

   
    Solution


Forces Due to
Flow Momentum Change

 

To determine the change in momentum, fluid velocity needs to be determined for the out flow. Using the conservation of mass equation,
     vAAA = vBAB
     (2) [(4/2)2π] = vB [(1.5/2)2π]
     8 = vB 0.752
     vB = 14.22 ft/s

The mass flow rate can be calculated using the 4 ft or the 1.5 ft pipe,
    dm/dt =ρvAAA (= ρvBAB)
       = (γ/g) [(4/2)2π]
       = (62.4/32.2) 12.57
       = 48.70 slug/s

The vertical reaction force must equal the change of momentum in the vertical direction,
      Fy = dm/dt (vBy - vAy)
           = 48.70 (14.22 - 0)

Fy = 692.7 lb

     
   
 
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