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多年来,在医用物理学的教学中一直存在着一个表面上看来似乎相互矛盾的问题,即从连续性方程 q_0=Sv=常量来看,当流管半径 r 增大,其截面积 S 亦增大,则流速 v 越小.若对粘滞流体而言,只要是稳定流动,上述连续性方程仍然成立,只不过应将流速 v 看作对应截面的平均流速。然而粘滞流体在作稳定流动的过程中还要遵守泊肃叶公式,即 q_0=(πr~4△p)/(8ηl),其中 q_0=S为流过某一截面的流量。表面上看,当流管半径 r 增大时, 似乎也随 r 的增大而增大,与前述连续性方程的结论存在着矛盾.
For many years, there has been a seemingly contradictory problem in the teaching of medical physics. From the perspective of the continuity equation q_0=Sv=constant, when the flow tube radius r increases, its cross-sectional area S also increases. Increase, then the smaller the flow velocity v. If viscous fluid, as long as the flow is stable, the above continuity equation is still established, but the flow velocity v should be regarded as the average flow velocity of the corresponding cross section. However, the viscous fluid must follow the Poiseuille formula in the process of steady flow, that is q_0 = (πr ~ 4Δp)/(8ηl), where q_0 = S is the flow through a certain section. On the surface, when the flow tube radius r increases, it seems to increase with r, which is inconsistent with the conclusion of the continuity equation.