III. Water flows through a $50-mm$ ID pipe containing a $60$ bend. The pressure at the pipe inlet is $300$ kPa $($absolute$),$ and the pressure at the outlet is $200$ kPa $($absolute$).$ The bend can withstand a force of $25$ N in the x $-$direction. The pipe is oriented such that the flow is horizontal at the inlet and exits at an angle of $60$ from the horizontal. Assume the water density is $1000k\frac{g}{m^3}$ and neglect any changes in elevation or energy losses other than those associated with pressure changes. Determine the following: $($a$)$ The maximum flow rate of water through the bend that satisfies the force limit in the x $-$direction $($b$)$ The force in the y $-$direction acting on the pipe bend.