Problem $4$: An intravenous $($IV$)$ system is supplying saline solution to a patient at the

rate of $0\mathrm{.}120$cm$3/$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 $20$C $.)$

$(2$pt b$)$ Calculate the new flow rate if the height of the saline solution is decreased to $1\mathrm{.}50$

m$.(1$pt$)$