End corrections for rarefied gas flows through capillaries of finite length

• Rarefied flows through moderately long capillaries are examined.
• The effective length concept has been utilized for this purpose.
• The flow rate can be estimated without time-consuming calculations.
• The simple formula derived can be used in a wide range of the channel length.

The influence of end effects on rarefied gas flows through moderately long capillaries is investigated by implementing the concept of effective capillary length, representing a sum of the real length of capillary and its increment. To calculate the length increment, a flow field near the inlet cross section of capillary is analyzed on the basis of the linearized kinetic equation. Far from the inlet inside of capillary, the solution is matched at the level of the distribution function with the one-dimensional solution corresponding to the flow in an infinite capillary. Far from the inlet outside of capillary, the gas is assumed to be in equilibrium at a specific pressure and temperature. The capillary length increment has been calculated as a function of the gas rarefaction. Using these results it is possible to estimate a flow rate through a moderately long capillary without hard calculations for the complete geometry.