(Solved): 10. (15 pts) A reducing elbow in a horizontal pipe is used to deflect water flow by an angle \( \t ...

10. (15 pts) A reducing elbow in a horizontal pipe is used to deflect water flow by an angle \( \theta= \) \( 135^{\circ} \) from the flow direction while accelerating it. The elbow discharges water into the atmosphere. The cross-sectional area of the elbow is \( 100 \mathrm{~cm}^{2} \) at the inlet and 20 \( \mathrm{cm}^{2} \) at the outlet. The elevation difference between the centers of the outlet and the inlet is \( 30 \mathrm{~cm} \). The flowrate of the water is \( 20 \mathrm{~kg} / \mathrm{s} \), the mass of the elbow and the water in it is \( 40 \mathrm{~kg} \). Determine the anchoring force needed to hold the elbow in place. Take the momentumflux correction factor to be \( 1.03 \) at both the inlet and outlet, and the density of water is \( 1000 \mathrm{~kg} / \mathrm{m}^{3} \). \( (15 \mathrm{pts}) \)