For a steady incompressible flow of water through the reducing elbow in Fig. 10.9, the entrance area A_{1} is 30 cm^{2} and the exit area A_{2} is \frac{1}{2}A_{1}. The mean velocity \overline{\nu }_{1} entering the elbow is 5 m/s with an inlet pressure of 5 Pa and outlet pressure equal to atmospheric. Find the total force required to hold the bend in place. Control Volume and Semi-empirical Methods FIGURE 10.9 Academic experiment to determine the support reactions due to a fluid flowing through an elbow. Shown, too, is a possible control volume that ignores possible effects of the fluid-induced shear stresses.