管道氣體流可壓縮性引致誤差之分析

由於摩擦阻力作用或管道斷面積變化的關係，管道氣體流的壓力沿程會有變化，因此氣體密度及流速亦隨之而變以滿足質量守恆原理。然而為實際應用上的方便，卻常見在密度為固定不變的假設條件下進行流況分析，結果有時會出現較大誤差。為釐清此一假設所引致之可能誤差，本文以理想氣體定律所定義之密度、壓力與溫度之間的關係為基礎，探討兩類管道氣體流之沿程壓力變化；第一類為馬赫數M ＜ 0.3（亦即M^2 ＜＜ 1）的均勻管道等溫氣體流，第二類為M ＜ 1的管道斷面變化段之無摩擦阻力絕熱氣體流。第一類的分析結果顯示，未考慮密度沿程變化之壓降值Δp^*較有考慮者之Δp偏高；第二類的結果顯示，壓降（或壓升）值Δp^*較Δp偏低（或偏高）依斷面積變化為束縮（或擴張）而定。同時，本文並分別推導建立這兩類管道氣體流之Δp^*與Δp之關係，以便作為修正密度沿程變化之效應。

關鍵字

可壓縮性；溫等流；絕熱流；壓力變化；誤差分析

並列摘要

Due to frictional resistance or variation of cross-sectional area, the pressure of gas flow in conduit changes along the main flow direction, and its density and velocity also change accordingly so as to satisfy the principle of mass conservation. However, for the convenience in practice, it is often seen that the density is assumed to remain constant throughout in the analysis of flow characteristics. As a result, significant errors may appear in some cases. In order to clarify the possible errors induced by such an assumption, this article is to analyze pressure changes for gas flow in two kinds of conduits, based on ideal gas law which defines the relations among density, pressure and temperature. The first kind is isothermal gas flow in uniform conduit, with Mach number M ＜ 0.3 (i.e., M^2 ＜＜ 1), and the second one is frictionless adiabatic flow in conduit having nonuniform cross-section, with M ＜ 1. For the first kind, the result indicates that the pressure drop under the assumption of constant density, Δp*, is higher than that under variable density, Δp. For the second kind, the pressure drop (or rise) Δp* is lower (or higher) than Δp, depending on the nature of cross-sectional variation being convergent (or divergent). In the meantime, a relationship between Δp and Δp* is derived for error correction in each kind, respectively.

並列關鍵字

Compressibility ； Isothermal flow ； Adiabatic flow ； Pressure change ； Error analysis

國際替代計量

管道氣體流可壓縮性引致誤差之分析

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