Problem $4$: An intravenous $($IV$)$ system is supplying saline solution to a patient at the rate of $0\mathrm{.}120c\frac{m^3}{s}$ through a needle of radius $0\mathrm{.}150$ mm and length $2\mathrm{.}50$ cm $.$ What pressure is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution to be the same as that of water? The gauge pressure of the blood in the patient's vein is $8\mathrm{.}00$ mm Hg $.($Assume that the temperature is $20C.)(2$pt$)$

$($a$)$ Verify that a pressure of $1\mathrm{.}62{10}^4\frac{N}{m^2}$ is created at a depth of $1\mathrm{.}61$ m in a saline solution, assuming its density to be that of sea water. $(1$pt$)$

C$)$ calculate the new flow rate if the height of the saline solution is decreased to $1\mathrm{.}50$m$.$

Please answer all parts a$-$c