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 $65$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

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