A catheter is a specialised needle intended for long-term insertion into a vein in a patient's arm. Engineers are redesigning them to cause less discomfort and damage. An intravenous chemotherapy system is based on a new catheter design. A liquid drug flows to the patient from a plastic bag via through a smooth plastic tube. The liquid drug completely fills the tube at the start of the procedure. The bag is at atmospheric pressure and it is 0.75 m vertically above the catheter. The tube is 2 mm in diameter and 2.0 m long. The average blood pressure in the vein is 6500 Pa gauge. The density of the liquid drug being supplied is 1020.4 kg/m
3 and its dynamic viscosity is 2 x 10-3 Pa.s. Exactly 314 mL of the drug must be supplied. In a laboratory experiment, you measured a fitting head loss for the catheter equivalent to 0.068 m of the liquid drug.
(a) What is the key assumption you must make to do this problem?
(b) How long will it take to supply the required amount of drug?
(c) Show by calculation that the key assumption you made was correct.