Question

Intravenous injections are commonly performed with a hypodermic needle and syringe. Assume that the dimensions of the needle are length = L = 1 cm, radius of the needle = 3.3x10‐4 m, radius of the syringe = 5x10‐3 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 sec 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 in order to accomplish an injection of V mL of drug solution in T sec.

c) What is the force required to achieve the conditions in part a?

Answer 1

b.)

For expression ,

Q = V/T

∆P = 8QμL/πr⁴

^{F = P*A}

F =  8(V/T)*0.01*1/πr⁴

c.)

∆P = 8QμL/πr⁴

=8*0.333*0.01*1 /(3.14*0.033⁴)

= 7154 p

F = Pressure * Area

= 7154 * (3.14* 5²)

= 561589 dyn