Correlating Gas Leakage Rates to Fluid Ingress in Sensor Seals
Correlating gas leakage rates to liquid ingress requires deriving equivalent pore radius to confirm capillary entry pressure exceeds target hydrostatic head.
Hagen Poiseuille Flow
Viscous Flow
Physical laws describing the steady, laminar movement of an incompressible fluid through a long cylindrical pipe establish the relationship between pressure drop and flow rate. This hagen poiseuille flow model governs how gases or liquids move through narrow leaks in sealed systems. It assumes the fluid is viscous and that the velocity at the pipe walls is zero.
Pressure Dependency
Flow rate varies directly with the pressure difference and the fourth power of the radius of the channel. This means a small increase in the size of a pore leads to a massive increase in the volume of the leak. The length of the leak path and the viscosity of the fluid act as inverse factors that slow the movement.
Microfluidic Accuracy
Engineers use this principle to size capillaries for precision dispensing and to predict the behavior of air in leak testing manifolds. The calculation requires the fluid to be in a laminar state where the Reynolds number remains low. When the flow becomes turbulent, this specific equation no longer provides an accurate prediction.
Physical Limitation
Strict adherence to the model requires a straight, uniform tube which rarely exists in natural material defects. Tortuous paths in a weld or a seal introduce additional resistance that the basic formula does not capture. It also fails to account for the compressibility of gases at very high pressure differentials or in vacuum conditions where molecular flow becomes the dominant mechanism.