Biomedical Engineering: Bridging Medicine and Technology 1st Edition by Veronique Tran,Mark Saltzman

Exercise 2

Intravenous injections are commonly performed with a hypodermic needle and syringe. Assume that the dimensions of the needle are length = L, radius of the needle = 3.3 × 10−4 m, radius of the syringe = 5 × 10−3 m, and that the drug solution has the properties of water.
a. Assume that 1 mL of a drug solution must be injected over a 3-second period. Will the flow through the needle be laminar or turbulent?
b. Derive a general expression for the force that must be applied to the plunger in the syringe to accomplish an injection of V milliliters of drug solution in T seconds.
c. What is the force required to achieve the conditions in a?
d. Plot the force applied versus flow rate (V/T ) for three values of needle radius: 1 × 10−4 m, 3.3 × 10−4 m, and 10 × 10−4 m. How does the radius of the needle influence the force required to achieve a given flow rate? (Problem adapted from Domach, M.M., Introduction to Biomedical Engineering, Prentice Hall; p. 174)