Question 3: (40 points)
As shown in the schematic, water from a horizontal pipe flows into a two-outlet connector piece at point 1, and exits the connector through Outlets 2 and 3 as free jets with a speed of 15 m/s from each outlet. Cross-sectional areas of the constant-diameter pipe, Outlets 2 and 3 are given in the schematic. Water exits Outlet 3 in the horizontal direction (i.e. +x direction) and Outlet 2 in the vertical direction (i.e. +z direction).
What are the horizontal (x) and vertical (z) components of the force exerted on the connector?
[Hint: Assume negligible viscous and gravity effects. The density of water, $\rho_{water} = 1000$ kg/m³; atmospheric pressure outside the pipe and connector throughout].
Area=$A_{pipe} = 1 m^2$
U = 15 m/s
$A_2 = 0.3 m^2$
$A_3 = 0.5 m^2$
