Free Surface Slopes at Controls in Channel Flow

It is commonly held that the slope of a free water surface in steady open channel flow is indeterminate at a control section. It is shown that the surface slope is finite and, subject to certain approximations, determinate. Expressions are derived for the surface slopes of critical flows over a smooth weir and through a smooth contraction. Experiments confirmed the validity of these expressions up to the surface slopes of tan^-¹0.3 for weirs and tan ^-¹0.8 for contractions. It is shown that the same expressions could have been obtained using the one-dimensional energy equation, even though the assumption of hydrostatic pressure is not valid. The expression derived for the water surface slope yields a well-conditioned equation for numerical calculation of water surface profiles through a control. The possibility of using surface slope at a control section as a rating parameter is mentioned.