What is the net force needed to hold the orifice plate shown in place? Note, the

Question

What is the net force needed to hold the orifice plate shown in place? Note, the pressure on the downstream side of the plate is atmospheric while the pressure upstream (at section 1) is not.

Explanation / Answer

{Upstream Pipe Area} = (A_1) =      = (Pi/4)*(D_1)^2      = (Pi/4)*(40.0e-2 m)^2      = 0.125664 m^2 {Downstream Pipe Area} = (A_2) =      = (Pi/4)*(D_1)^2      = (Pi/4)*(10.0e-2 m)^2      = 0.00785398 m^2 For incompressible flow (water), we apply continuity equation to upstream and downstream sides:      *(A_1)*(V_1) = *(A_2)*(V_2)      ---->   (V_2) = (A_1)*(V_1)/(A_2)      ---->   (V_2) = (0.125664)*(5.0)/(0.00785398)      ---->   (V_2) = 80.0002 m/sec Applying Bernoulli's Equation to theconstant height flow, we obtain:      (P_1) + (1/2)**(V_1)^2+ *g*H = (P_2) + (1/2)**(V_2)^2 +*g*H      ---->   (P_1) = (P_2) + (1/2)**(V_2)^2 - (1/2)**(V_1)^2      ---->   (P_1) = (101325) +(1/2)*(1000)*(80.0002)^2- (1/2)*(1000)*(5.0)^2      ---->   (P_1) = 3288841 Pa      {Force On Plate} = F =           = ((P_1) -(P_2))*{Plate Ring Area}           = ((P_1) -(P_2))*((A_1)- (A_2))           = ((3288841) - (101325))*((0.125664) - (0.00785398))           = 3.755e+5 Newtons .

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