Table 1 End effect for channel with finite length: the length increment \(\Delta L_0\) obtained from Eqs. (14) and (15)
From: Highly rarefied gas flows in rough channels of finite length
\(\frac{L_0}{H}\) | \(\alpha\) | \(\frac{\Delta L_0}{H}\) | \(\frac{1}{(L_0+2\Delta L_0)/H}\) | \(\frac{L_0}{H}\) | \(\alpha\) | \(\frac{\Delta L_0}{H}\) | \(\frac{1}{(L_0+2\Delta L_0)/H}\) |
|---|---|---|---|---|---|---|---|
5 | 1 | \(1.258\times 10^{0}\) | \(1.331\times 10^{-1}\) | 200 | 1 | \(3.136\times 10^{0}\) | \(4.848\times 10^{-3}\) |
\(10^{-1}\) | \(7.020\times 10^{0}\) | \(5.252\times 10^{-2}\) | \(10^{-1}\) | \(2.056\times 10^{1}\) | \(4.147\times 10^{-3}\) | ||
\(10^{-2}\) | \(1.359\times 10^{1}\) | \(3.107\times 10^{-2}\) | \(10^{-2}\) | \(1.700\times 10^{2}\) | \(1.852\times 10^{-3}\) | ||
\(10^{-4}\) | \(1.533\times 10^{1}\) | \(2.805\times 10^{-2}\) | \(10^{-4}\) | \(7.401\times 10^{3}\) | \(6.666\times 10^{-5}\) | ||
10 | 1 | \(1.595\times 10^{0}\) | \(7.581\times 10^{-2}\) | 500 | 1 | \(4.801\times 10^{0}\) | \(1.962\times 10^{-3}\) |
\(10^{-1}\) | \(9.731\times 10^{0}\) | \(3.394\times 10^{-2}\) | \(10^{-1}\) | \(1.910\times 10^{1}\) | \(1.858\times 10^{-3}\) | ||
\(10^{-2}\) | \(2.268\times 10^{1}\) | \(1.806\times 10^{-2}\) | \(10^{-2}\) | \(1.729\times 10^{2}\) | \(1.182\times 10^{-3}\) | ||
\(10^{-4}\) | \(2.695\times 10^{1}\) | \(1.565\times 10^{-2}\) | \(10^{-4}\) | \(1.674\times 10^{4}\) | \(2.944\times 10^{-5}\) | ||
20 | 1 | \(2.051\times 10^{0}\) | \(4.149\times 10^{-2}\) | 1000 | 1 | \(5.530\times 10^{0}\) | \(9.891\times 10^{-4}\) |
\(10^{-1}\) | \(1.325\times 10^{1}\) | \(2.151\times 10^{-2}\) | \(10^{-1}\) | \(9.757\times 10^{0}\) | \(9.809\times 10^{-4}\) | ||
\(10^{-2}\) | \(4.219\times 10^{1}\) | \(9.580\times 10^{-3}\) | \(10^{-2}\) | \(1.724\times 10^{2}\) | \(7.436\times 10^{-4}\) | ||
\(10^{-4}\) | \(5.798\times 10^{1}\) | \(7.355\times 10^{-3}\) | \(10^{-4}\) | \(1.647\times 10^{4}\) | \(2.947\times 10^{-5}\) | ||
50 | 1 | \(2.698\times 10^{0}\) | \(1.805\times 10^{-2}\) | 2000 | 1 | \(5.656\times 10^{0}\) | \(4.972\times 10^{-4}\) |
\(10^{-1}\) | \(1.788\times 10^{1}\) | \(1.166\times 10^{-2}\) | \(10^{-1}\) | \(6.036\times 10^{0}\) | \(4.970\times 10^{-4}\) | ||
\(10^{-2}\) | \(9.926\times 10^{1}\) | \(4.024\times 10^{-3}\) | \(10^{-2}\) | \(1.604\times 10^{2}\) | \(4.309\times 10^{-4}\) | ||
\(10^{-4}\) | \(2.484\times 10^{2}\) | \(1.829\times 10^{-3}\) | \(10^{-4}\) | \(1.524\times 10^{4}\) | \(3.079\times 10^{-5}\) | ||
100 | 1 | \(2.911\times 10^{0}\) | \(9.450\times 10^{-3}\) | 5000 | 1 | \(5.676\times 10^{0}\) | \(1.995\times 10^{-4}\) |
\(10^{-1}\) | \(1.997\times 10^{1}\) | \(7.146\times 10^{-3}\) | \(10^{-1}\) | \(6.932\times 10^{0}\) | \(1.994\times 10^{-4}\) | ||
\(10^{-2}\) | \(1.497\times 10^{2}\) | \(2.504\times 10^{-3}\) | \(10^{-2}\) | \(3.054\times 10^{1}\) | \(1.976\times 10^{-4}\) | ||
\(10^{-4}\) | \(1.191\times 10^{3}\) | \(4.028\times 10^{-4}\) | \(10^{-4}\) | \(1.471\times 10^{4}\) | \(2.905\times 10^{-5}\) |