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An analytical solution of nondimensional hydraulic energy equation is derived in cosine form for the flow in rectangular open channels considering nonhydrostatic pressure and nonuniform velocity distributions across flow depth and friction and turbulent losses. The new inverted energy equation is a single equation describing all the three roots of the nondimensional hydraulic energy equation. The energy losses due to turbulence and bed shear are also implicitly accounted. Only two roots out of the three roots are practically significant, which denote the two alternate depths and are distinguishable for subcritical and supercritical flow, respectively. These equations yield direct determination of alternate depths in a single step, avoiding an iterative procedure. The use of the new equations is illustrated through worked-out examples. The new single-term analytical inverted equations are computationally simple and useful for academicians, field engineers, and practitioners in directly solving in a...

The velocity field and surface profile of an open channel flow with a submerged hydraulic jump from a vertical sluice gate are investigated for two different flow cases. The governing equations are numerically solved using a finite-volume method for flows having the same conditions with experiments. The volume of fluid method is used to calculate the free surface. In modeling the turbulence stresses, standard k-?, renormalization group k-?, realizable k-?, shear stress transport k-?, and Reynolds stress turbulence closure models are employed. A grid convergence index analysis is carried out to determine the discretization error for the grid-independent solution. Experimental validations of the numerical results show that in predicting the velocity field, the Reynolds stress turbulence model is the most successful among the five. It also estimates the free-surface profile of the flow successfully. © 2015 American Society of Civil Engineers.

The hydraulic characteristics of a side sluice gate were studied experimentally. It was found that the specific energy remains constant along the side sluice gate. The coefficient of discharge for the side sluice gate is related to the main channel Froude number and the ratio of upstream depth of flow to sluice gate opening for free flow. It also depends on an additional parameter: the ratio of tailwater depth to the gate opening for submerged flow. Suitable equations for discharge coefficient are obtained.

Due to construction, operation, and maintenance difficulties, usually installing very wide sluice gates in open channels is not recommended. Instead, multiple parallel gates have been used in such circumstances, which generate parallel jets. The free hydraulic jump established downstream of two vertical sluice gates with different openings was investigated theoretically and experimentally in this study. The ADV technique was used to record the flow velocity at the tailwater section of a rather large-scale experimental setup. The impact of highly non-uniform velocity distribution of the tailwater section was incorporated in the momentum formulation to develop a relationship for accurately determining the conjugate depth of such a practical case. It was indicated that the momentum correction factor plays a key role to accurately determining the conjugated depths, and it should not be neglected. Considering y0 as the upstream depth and y2 as the tailwater depth, the compiled data of the classical and...

Sluice gates are widely used for flow control in open channels. Flow through the gate may be free or submerged depending on tailwater depth. One may determine whether the flow will be free or submerged by determining the maximum tailwater level that permits free flow. This is called the distinguishing condition. This paper derives a theoretical equation for the distinguishing condition including the contraction coefficient as a parameter, based on the basic equations for free flow and the hydraulic jump. The equation is investigated using experimental data from two different gate types. The results show that the contraction coefficient varies with gate type and that this affects the distinguishing condition. The results also show that for a given upstream depth, tainter gates (radial gates) are less likely to become submerged than vertical gates due to larger contraction coefficients. The present study results are useful in the design and operation of sluice gates.

The bottom opening is a standard structure in storm sewers, provided the approach flow is supercritical. Based on extended experimentation and by using the governing flow equations, the hydraulic characteristics of bottom openings were derived. These include the approach reach, the end depth ratio, the average discharge coefficient, the tailwater depth, and the hydraulic loss across the outlet. Further, velocity distributions in the outlet zone are discussed. The results of this study reveal that the approach Froude number has a significant effect on the flow mechanism. General expressions are derived for the lower and upper nappes of the flow across the bottom opening, and a hydraulic design procedure is described. A generalized streamwise coordinate is also introduced that allows description of supercritical sewer flow. It is demonstrated that the excess discharge to the treatment station under design discharge is within the requirements of European standards.