Free surface flow in open-channel transitions is characterized by distributions of velocity and pressure that deviate from uniform and hydrostatic conditions, respectively. Under such circumstances the widely used expressions in textbooks [e.g.,E=h+U2/(2g) and hc=(q2/g)1/3] are not valid to investigate the changes in velocity and depth. A depth-averaged form of the Bernoulli equation for ideal fluid flows introduces correction coefficients to account for the real velocity and pressure distributions into the specific energy equation. The behavior of these coefficients in curvilinear motion at and in the neighbourhood of control sections was not documented in the literature. Herein detailed two-dimensional ideal fluid flow computations are used to characterize the entire velocity and pressure fields in typical channel controls involving transcritical flow, namely the round-crested weir, the transition from mild to steep slope and the free overfall. The detailed two-dimensional ideal fluid flow solution is used to study the behavior of the depth-averaged coefficients, and a novel generalized specific energy diagram is introduced using universal coordinates. The development is used to pursue a simplified critical flow theory for curved flow, relevant to water discharge measurement with circular weirs.
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机译：明渠过渡中的自由表面流的特征是速度和压力的分布分别偏离均匀和静水压条件。在这种情况下，教科书中广泛使用的表述[例如，E = h + U2 /（2g）和hc =（q2 / g）1/3]不适用于研究速度和深度的变化。理想流体的伯努利方程的深度平均形式将校正系数考虑在内，以将实际速度和压力分布考虑在比能量方程中。这些系数在控制部分及其附近的曲线运动中的行为尚未在文献中记录。在这里，详细的二维理想流体流量计算用于表征涉及跨临界流的典型通道控制中的整个速度场和压力场，即跨顶堰，从缓坡到陡坡的过渡以及自由倾覆。详细的二维理想流体流动解被用于研究深度平均系数的行为，并使用通用坐标引入了新颖的广义比能图。该开发用于追求简化的用于弯流的临界流理论，该理论与圆形堰的排水量测量有关。
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