EXAMPLE $7\mathrm{.}12$

Water is pumped steadily through a $90$ reducing elbow welded onto the end of a pipe and exits to the atmosphere as shown in Figure $7\mathrm{.}21$A$.$ What is the force applied to the elbow at the weld joint? Assume uniform conditions at the elbow inlet and exit and neglect gravity.

$($A$)$

$($B$)$

Figure $7\mathrm{.}21$ Schematic for Example $7\mathrm{.}12$: $($A$)$ geometry and $($B$)$ CV$.$