Question $2(10$ points$)$

A fluid flows through a $50$ mm pipe with a velocity of $\backslash (1\mathrm{.}07\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ At the point $\backslash ($ P $\backslash )$ before the bend where the green arrow indicates the direction of flow, the fluid is still inside the pipe. After going through the bend at $\backslash ($ A $\backslash ),$ it then goes up the $10\mathrm{.}7$ m riser and exits to the atmosphere at $\backslash ($ B $\backslash ).$ Given that the density of the fluid is $800\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and the dynamic viscosity of the fluid is $\backslash (0\mathrm{.}25\backslash$mathrm$\{$~kg$\}/(\backslash$mathrm$\{$m$\}-\backslash$mathrm$\{$s$\})\backslash ),$ determine the gage pressure at point $\backslash ($ P $\backslash )$ if the total distance between $\backslash ($ P $\backslash )$ and $\backslash ($ B $\backslash )$ is $14\mathrm{.}0$ m $.$

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