為保育河川及避免河川泛濫，一般使用計畫洪水流量及斷面幾何條件與粗糙度並應用曼寧流速公式來設計工程。但河川水流通常在洪水時，由主深槽漫淹到兩側洪水平原，形成有主深槽及洪水平原側槽的複式斷面。
洪水平原之粗糙度大於主深槽粗糙度。要規劃全斷面水流相關的工程需考慮主深槽及洪水平原側槽的合成粗糙度，以應用於規劃保育及防洪計畫時分析計算流量之水位，以及主槽與側槽之通洪能力。
基於防洪工程之計畫洪水需要由各分槽分擔，本研究選用以質量守恆發展之Lotter公式推算分槽曼寧n值之等價曼寧n值為全斷面之合成糙度，並以實驗定床複式斷面規則渠道，流況為定量緩變速流實驗結果驗證等價曼寧n值可用於計算複式斷面渠道之縱向水面線，並用於設計防洪工程。
應用上述縱向水面線及洪水平原側槽之曼寧n值可計算側槽之平均流速及通洪能力，用於設計防洪工程之護岸及河川保育設施。最後用二維模式ARMB -2D演算複式斷面河道之流場，討論用等價曼寧n值推估主深槽及側槽水理特性，顯示等價曼寧n值有良好之實用性。

As for planning and designing engineering projects or disaster managements, it is necessary to understand characteristics of the river, such as the slope, resistance, and make- up of riparian vegetation. Engineers often use Manning formula to compute water level, velocity, and discharge. To conserve rivers and avoid flooding, engineers usually consider the discharge and the section geometry of the project area they are working on in a river. Water flow often changes in different seasons. When flooding occurs, the water level rises to the floodplains and forms complex sections. Due to vegetation growth in the floodplains, the roughness of the main channel and floodplains are different. It is necessary to use the equivalent coefficient of roughness to get more accurate calculations in order to design sustainable engineering facilities and to plan for natural conservation.
The total discharge of the river is equal to the discharge of the main channel and floodplain. Thus, this research uses Lotter’s assumption, which follows mass balance to obtain the equivalent coefficient of roughness. Because the equivalent coefficient of roughness is often greater than the coefficient of roughness of the main channel, thus using the equivalent coefficient of roughness can get a more accurate water level calculation. Then, the average velocity of the floodplain can be calculated using the longitudinal water surface line, and then the equivalent coefficient of roughness are useful for designing revetment and river conservation facilities.
Finally, using two-dimensional Alluvial River-Movable Bed-Two Dimensional Model (ARMB-2D) allows us to calculate the flow field of the compound section. It can also be used to check if the equivalent coefficient of roughness are good for calculating the hydrodynamic characteristics or not. The result demonstrates the effectiveness of using the equivalent coefficient of roughness.

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