For the smoke filling in enclosures with floor leaks and growing fires, a comprehensive governing equation has been set up by Copper. However, this governing equation can hardly be exactly solved analytically because it is inseparable. Up to now, the existing analytical solutions for it are all approximate, including the so-called SFPE solution, the Deli-2 solution, the Deli-3 solution, etc. Among these approximate solutions, the SFPE solution almost always overestimates the smoke-interface height, while the Deli-2 solution almost always underestimates the interface height. In general, the Deli-3 solution is the most accurate but it can generate considerable error when the smoke interface is near the floor level. In this note, a new approximate solution is derived, which is actually a correction of the SFPE solution. The basic idea of the new solution is to resume the effect of the expansion term that is neglected in the deduction of the SFPE solution. It is found that, while the smoke interface in not very close to the floor level, the accuracy of the new solution is generally of the same order of magnitude as that of the Deli-3 solution; while the smoke interface is near the floor level, the accuracy of the new solution can be one order of magnitude higher than that of the Deli-3 solution. Moreover, it is shown that the Deli-2 solution is the limit of the new solution as the non-dimensional heat release rate approaching to infinity.

对于地板漏水和火势不断扩大的围墙内的烟雾填充，Copper 建立了一个综合的控制方程。然而，这个控制方程很难被精确地解析解，因为它是不可分割的。到目前为止，现有的解析解都是近似解，包括所谓的SFPE解、Deli-2解、Deli-3解等。在这些近似解中，SFPE解几乎总是高估烟雾——界面高度，而 Deli-2 解决方案几乎总是低估界面高度。一般来说，Deli-3 解决方案是最准确的，但当烟雾界面接近地板水平时，它会产生相当大的误差。在这篇笔记中，推导出了一个新的近似解，它实际上是对SFPE解的修正。新解的基本思想是恢复SFPE解推导中被忽略的展开项的影响。发现，虽然烟雾界面不是很接近地平面，但新解的准确度一般与Deli-3解的准确度处于同一数量级；当烟雾界面接近地面时，新解决方案的精度可以比 Deli-3 解决方案高一个数量级。此外，随着无量纲放热率接近无穷大，Deli-2 解是新解的极限。新解的准确率一般与Deli-3解的准确度处于同一数量级；当烟雾界面接近地面时，新解决方案的精度可以比 Deli-3 解决方案高一个数量级。此外，随着无量纲放热率接近无穷大，Deli-2 解是新解的极限。新解的准确率一般与Deli-3解的准确度处于同一数量级；当烟雾界面接近地面时，新解决方案的精度可以比 Deli-3 解决方案高一个数量级。此外，随着无量纲放热率接近无穷大，Deli-2 解是新解的极限。