$3.$ Pipe Flow Pressures Loss $\backslash (2\backslash$mathrm$\{$ft$\}^\{3\}/\backslash$mathrm$\{$sec$\}\backslash )$ of $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$FSAE$\}30\backslash )$ oil flows in a $100$ foot long horizontal galvanized iron pipe. The oil enters the piping section at gage pressure $20$ psig. Assume fully$-$developed laminar flow.

a$)$ Determine the oil frictional pressure drop and exiting pressure if the pipe inner diameter is $\backslash (6^\{\backslash$prime $\backslash$prime$\}\backslash ).$ Note that it may be possible to use Pouiselle's Law. Also, sketch the oil velocity profile.

b$)$ Determine the oil frictional pressure drop and exiting pressure if the pipe inner diameter is $\backslash (0\mathrm{.}6^\{\backslash$prime $\backslash$prime$\}\backslash ).$ Also, sketch the oil velocity profile.

$4.$ Fluid Force Calcs: The image to the right is of a horizontal pump with a $\backslash (3^\{\backslash$prime $\backslash$prime$\}\backslash )$ diameter inlet and $\backslash (2^\{\backslash$prime $\backslash$prime$\}\backslash )$ diameter outlet. $\backslash (0\mathrm{.}2\backslash$mathrm$\{$ft$\}^\{3\}/\backslash$mathrm$\{$sec$\}\backslash )$ of $\backslash (68^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ mercury flows steadily through the pump. The pump inlet pressure is $4$ psig while the outlet pressure is $51$ psig.

a$)$ Determine the mercury inlet and outlet speeds.

b$)$ Draw a FBD of the mercury in the pump. Show the $3$ horizontal forces on the mercury. One force should be $\backslash (\backslash$mathrm$\{$FPHg$\}\_\{\backslash$mathrm$\{$g$\}\}\backslash )($the overall force of the pump on the mercury$).$

c$)$ Determine the net horizontal force on the mercury in the pump.

Give both the magnitude for this force in pounds and its direction.

d$)$ Determine the horizontal force $($direction and magnitude$)$ of the mercury on the pump.