(Solved): A \( 90^{\circ} \) eibow in a horizontal pipe is used to direct water flow upward at a rate of \( 4 ...

A \( 90^{\circ} \) eibow in a horizontal pipe is used to direct water flow upward at a rate of \( 45 \mathrm{~kg} / \mathrm{s} \). Another identical elbow is attached to the existing elbow such that the water flow makes a U-turn as shown in the second figure. The diameter of the entire elbow is \( 10 \mathrm{~cm} \). The elbow discharges water into the atmosphere, and thus the pressure at the exit is the local atmospheric pressure. The elevation difference between the centers of the exit and the inlet of the elbow is \( 50 \mathrm{~cm} \). The weight of the elbow and the water in it is considered to be negligible. Take the momentum-flux correction factor to be \( 1.03 \) at both the inlet and the outlet. Take the density of water to be \( 1000 \mathrm{~kg} / \mathrm{m}^{3} \). a) If another (identical) elbow is attached to the existing elbow so that the fluid makes a U-turn, determine the gage pressure at the center of the inlet of the elbow. b) If another (identical) elbow is attached to the existing elbow so that the fluid makes a U-turn, determine the magnitude of anchoring force needed to hold the elbow in place.