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 N
2 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≡(π
1/2/2)×(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.
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