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

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,
     v_AA_A = v_BA_B
     (2) [(4/2)²π] = v_B [(1.5/2)²π]
     8 = v_B 0.75²
     v_B = 14.22 ft/s

The mass flow rate can be calculated using the 4 ft or the 1.5 ft pipe,
    dm/dt =ρv_AA_A (= ρv_BA_B)
       = (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,
      F_y = dm/dt (v_By - v_Ay)
           = 48.70 (14.22 - 0)

F_y = 692.7 lb