# Day 7

Flow Resistance in Tubings

In **Poiseuille’s equation** the flow resistance of the tubing dictates the flow rate at a given pressure. When choosing tubing with larger diameter, the flow resistance is dropping dramatically, thus a much smaller pressure is needed to drive a larger current (=volume flow). The exact formula is: 8*η*L/(π*r^{4}) * Q = p

with the dynamic viscosity nu, the length of the tubing L, the inner diameter of the tubing r, the flow rate Q and the applied pressure p. The term **8*η*L/(π*r ^{4})** can be summarised as laminar flow resistance R and then the analogy to Ohm’s law is visible. Similarly, many other electronic laws also apply to Microfluidics, e.g. Kirchhoff’s laws of putting resistors (= tubing) in series or in parallel.

What can be immediately seen, is the strong dependence of the flow resistance on the tubing diameter r. Doubling the inner diameter results in a drop of the resistance by a factor of 16, thus 16 times more fluid is flowing at the same pressure.

Generally for tests and experiments, it is suggested to adapt the tubing diameter and length so that you can use a comfortable pressure range of the used devices.