You are working for a company to develop a system for dispensing medication in a controlled

manner over a period of weeks. The medication is kept in a small pressurized tank. The device

uses a valve and a thin tube to release the medication into the bloodstream four times per day. The

engineer developing the injection system tells you that the tube is $3\mathrm{.}2$ cm long and has a diameter

of $65\backslash$mu m$.$ The medicine has a viscosity of $1\mathrm{.}8$ mPa $$ s$.$

$($a$)$ You are asked to determine how much time the valve should be open to deliver a dose of

$75\backslash$mu L if the pressure in the holding tank is $4\mathrm{.}2$ atm above the pressure in the bloodstream.

$($b$)$ It turns out that the engineer misremembered and the value provided was the radius instead

of the diameter. What dose will the patient actually get if you don$$t adjust the time from part

$($a$)?$