Problem #$10(9$ points$)$

The figure below shows a situation where a heterogeneous incompressible fluid is flowing through a pipe. The radii of the sections are $r_1=1\mathrm{.}00cm,r_2=5\mathrm{.}00cm,r_3=5\mathrm{.}00cm,r_4=7\mathrm{.}00cm.$ Sections $3$ and $4$ are $3\mathrm{.}00$ cm below sections $1$ and $2.$ Choose one of the following to be the fluid in this problem: $($Chocolate milk: ${}_c=1\mathrm{.}05E+03\frac{(kg)}{m^3}),($Maple Syrup: ${}_m=1\mathrm{.}37E+03\frac{(kg)}{m^3}),($Liquid Soap: ${}_s=1\mathrm{.}01E+03\frac{(kg)}{-g}),($Fresh Orange Juice: ${}_o=1\mathrm{.}04E+03\frac{(kg)}{m^3},($Vegetable Oil: ${}_v=915*\frac{(kg)}{m^3})$

Question #$1(3$ points$)$

Write down the relevant Bernoulli equation that relates sections $2$ and and $4.$ Keep everything as variables and solve for the pressure in section $4.$

Question #$2(3$ points$)$

If the speed of the fluid in section $1$ is $137.\frac{m}{s},$ what is the speed in section $2?$

Question #$3(3$ points$)$

The pressure in section $2$ is $4\mathrm{.}20$ Pa $,$ what is the pressure in section $3?$