Hydrostatic Forces on submerged area

$/6\mathrm{.}0$

A jet of water flowing freely in the atmosphere $($x$-$direction$)$ hits a curvel If the vane is assumed frictionless, determine the magnitude of the resul by the vane and its direction.

Given that water density is $1\mathrm{.}94$ slug$/f{t}^3$

The velocity of the water jet is $10\mathrm{.}8f\frac{t}{sec}$

The diameter of the pipe is $2$ in $.$

Ignore the weight of water on the vane

Solution:

$1.)$ The curved vane resists the hydrodynamic force $($F$)$ of the jet.

$V_z=V_{\text{o}\text{u}\text{t}y}=$

$V_x=V_{inx}=$

$V_{iny}=V_{\text{o}\text{u}\text{t}x}=$

$2.)$ Flow rate $Q=$

$3.)$ For a fixed deflector

$F_x=Q(v_{\text{o}\text{u}\text{t}x}-v_{inx})=$

$F_Y=Q(v_{\text{o}\text{u}\text{t}y}-v_{iny})=$

$4.)$ Thus, magnitude of the resistant force is $F=$ Direction of the resistant force is $=$