Final answer:
The volume flow rate of a liquid through a hypodermic needle can be determined using Poiseuille's law, which relates the flow rate to the pressure difference, radius of the needle, length of the needle, and fluid viscosity.
Step-by-step explanation:
The law used to determine the volume flow rate of a liquid through a hypodermic needle is Poiseuille's law. This law is applicable to laminar flow, which is typically the case with fluids in medical applications like IV systems. Poiseuille's law can be expressed in the following relationship:
(P2 - P1)πr^4 / (8ηl), where:
- P2 is the pressure at the entrance of the needle,
- P1 is the pressure at the exit (often in the patient's vein),
- π is the mathematical constant Pi,
- r is the radius of the needle,
- η is the fluid's viscosity,
- l is the length of the needle.
Flow rate is directly proportional to the pressure difference and the fourth power of the radius of the needle, and inversely proportional to both the length of the needle and the fluid's viscosity. This allows us to calculate the necessary pressure at the entrance of the needle to achieve a desired flow rate.