$[25$ points$]$ Air with density ${}_{\text{a}\text{i}\text{r}}=2\mathrm{.}57{10}^{-3}$ slugs $\frac{?}{f{t}^3}$ discharges from a $3-$in$.$diameter nozzle and str$$ikes a curved v$$ne$,$ as shown in the following figure. A stagnation tube connected to a water U$-$tube manometer is located in the free air jet, with a reading of $6$ inches. The weight of water is ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=62\mathrm{.}42l\frac{b}{f}{t}^3.$ Neglect the weight of air in the calculation. Assume the steady flow to be incompressible and frictionless.

Determine the horizontal component of the force $($magnitude and direction$)$ required to hold the curved vane stationary.