Section $2$: Momentum Equation Calculations

A reducing elbow is used to deflect water flow at a rate of $50k\frac{g}{s}.$ The deflection happens in the horizontal plane $($there is no change in elevation$)$ and the flow is deflected outwards by an angle of $45$ from the initial flow direction while accelerating it$.$ A plan view is shown in the figure below. The elbow discharges water into the atmosphere. The diameter of the elbow is $150mm$ at the inlet and $80mm$ at the exit.

Determine:

$($i$)$ the average velocity at the assembly exit.

$($ii$)$ the gage pressure at the entry to the elbow

$($iii$)$ The magnitude and direction of the anchoring force needed to hold the elbow in place.