Problem $4$: An intravenous $($IV$)$ system is supplying saline solution 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 than hinnd in the natient's vein is $8\mathrm{.}00$ mm Hg $.($Assume that the temperature is $20C.)$

$($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

$($b$)$ Calculate the new flow rate if the height of the saline solution is decreased to $1\mathrm{.}50$

$Q=$

$($c$)$ At what height would the direction of flow be reversed? $($This reversal can be a