The flow rate of a rarefied gas through a long rectangular channel with a very small height (a) to width (b) ratio (a/b) was experimentally investigated using N2 and Ar for a wide range of the Knudsen number (Kn). Kn is defined as the ratio of the height (a) to the mean free path. The dimensions of the rectangular channel are as follows: a=0.1 mm, b=50 mm, and the length (ℓ)=100 mm. As the inlet gas pressure increases, the conductance decreases from the value in the free molecule regime and reaches the Knudsen minimum at Kn≈1.2, which is approximately 0.46 times the value in the free molecule regime.
The reduced flow rate (G) has been derived from the experimental data as a function of the local rarefaction parameter δ≡(π1/2/2)×(1/Kn), assuming fully developed gas flow. The rate (G) is defined by the following equation: G=Qm/(a2b/v0)/(dp/dx); where Qm, v0, and (dp/dx) are the mass flow rate, most probable molecular velocity, and local pressure gradient at a longitudinal coordinate x, respectively. For the above rectangular channel, the value of G is minimum when the value of δ is 0.9. Finally, the pressure distribution along the channel has been calculated taking into consideration the value of G.
