Journal of Hydraulic Engineering

A single equation model for predicting the velocity distribution in bounded shear flow is presented. This equation predicts the velocity profile in the viscous sublayer, the buffer zone, the logarithmic or inertial zone, and the outer or wake region in conduit and channel flows provided that secondary or crossflow is weak or absent. The model has been verified using measured velocity profile data from several conduit and channel flows with different degrees of boundary roughness and with a range of gross flow Reynolds numbers.

In closed conduit water flows containing a small amount of free air, an air void can form at a bend which connects a vertical shaft to a horizontal tunnel. A sudden reduction in the water flow rate can cause this void to vent back up the shaft. Tests were conducted on eight perspex pipe bends whose center‐line radius varied from 0.5 times–1.5 times the pipe diam, and over a range of pipe diameters from 2.8 in.–7.5 in. (0.072 m–0.190 m). The air volumetric flow rate was up to 2% of the water volumetric flow rate. A combined theoretical and analytical approach yielded equations which can be used to predict void formation and venting at a downshaft‐tunnel bend. Extrapolation of the results shows that these voids will not occur in large diameter bends with moderate air flows.

The near field plume dilutions from ocean outfall line diffusers consisting of evenly spaced risers with clusters of two to eight ports per riser have been measured in a two‐dimensional sectional hydraulic model. Tests were run under both idealized and measured ocean current and stratification conditions. A mathematical model was successfully correlated with tests not involving ambient currents, thus providing a useful design tool. The laboratory results show that, for the cases studied, the initial dilution is at most a weak function of whether the discharge ports are clustered or evenly distributed along the diffuses and that the minimum dilution increases with decreasing port size (limited, ultimately, to that of a line source). Therefore, the most cost effective design for riser equipped ocean wastewater diffusers may involve the smallest port diameters permitted by other design considerations, and clustering many ports per riser to decrease the number of risers needed.

A new approach to the least cost design of water distribution networks has been developed. The method is based on traditional techniques of pipe network analysis by computer; initially assumed pipe diameters are successively adjusted using an optimization technique which is based on a cost function incorporating the various capital and operating costs. Final design total costs for a given network have been found to be approximately the same regardless of the initially assumed values of pipe diameter although the final arrangements of pipe diameter are not necessarily identical. Since the method considers all physical components of the network, both from the point of view of the flow and pressure distribution and the costs, the design represents the global optimum as opposed to a typical element optimum which has been considered by other workers. The method contains no constraints such as assumed fixed pressure heads or pipe flows and may be applied to either closed loop or open loop networks of any size. Provided a computer program for analyzing pipe networks is available, the optimization technique developed represents a simple addition to the basic program.

The Schwarz‐Christoffel theorem is extended to transform curved boundaries, thus, making it possible to compute the pressure acting on the inner curved surface of an annular wing. A radial section of the surface has an airfoil curve; it is approximated with two straight lines (boundaries), which can then be transformed by using the Schwarz‐Christoffel theorem. The transformation is completed by using the binomial theorem to expand the integrand and by employing an iterative scheme to determine the junction point of the lines. The nondimensional computed and experimental pressures are found to be in agreement.

A theoretical distribution for the streamwise mean velocity of a single three‐dimensional turbulent free jet can be derived by following Reichardt's inductive theory. Using an integral type approach, a relationship for the decay of the maximum velocity on the axis of the jet is found. Further, it is possible to predict both the mean momentum flux and mean velocity profiles for three‐dimensional multiple jets by superimposition. Experiments are conducted on three‐dimensional jets issuing from single and multiple holes placed in line. The observed mean velocity distributions are in agreement with the theoretical profiles.

Velocity distribution in a smooth rectangular channel is studied by dividing the channel into four regions. Region, 1 comprises of the inner region of the bed and the outer region of the side wall. Region 2 belongs to the inner regions of both the bed and the side wall. Region 3 consists of the inner region of the side wall and the outer region of the bed. Region 4 forms the outer regions of both the bed and the side wall. The aspect ratio is varied from 2.0 to 8.0 and the Froude number from 0.2 to 0.7. Experiments included the aspect ratio of 1.0 also for Froude numbers of 0.2 and 0.3. The range of Reynolds number defined in terms of the hydraulic radius and the cross sectional mean velocity lies between ${10}^4$ and $7\times {10}^4\text{.}$

To assess the likely impact of rain amount forecasting on the operation of the City of Montreal's combined stormwater and sewage wastewater disposal system, studies have been conducted to test the accuracy with which rain amounts over the city can be forecast a few hours ahead. At coarse resolution, errors were of the order of 68% at 1 hr lead time. Procedures for the studies are given.

Most physical properties of water are thermal dependent. In many instances of hydraulic engineering, this dependency is considered to be significant. In other instances, the dependency is recognized, necessitating manual modification of constants when problems are solved for nonstandard temperature conditions. There is need for a set of mathematical estimators describing thermal dependence, suited for rapid employment in engineering algorithms. Using such estimators, overall thermal sensitivity can be readily specified. Six equations are proposed describing the thermal variability of fundamental water properties. These equations are empirical approximations based on zero or one temperature transformation and two or three constants. These equations were determined through a search of functional relationships minimizing squared deviations from a regressed line. Each equation, linearly transformed, yielded an R² correlation term greater than 0.999. The six equations are substantially shorter than mathematical models found in physical literature. These equations describe the thermal dependence of properties with a degree of accuracy more than adequate for most hydraulic engineering computations. The thermal dependence of many other physical properties of water can be derived from the six properties evaluated.

A new mechanism is introduced to explain the intriguing movement of antidunes. It is suggested that this mechanism may exist concurrently with sediment erosion-deposition patterns used heretofore to explain the apparent movement of antidunes. The mechanism introduced herein may be responsible for bulk movement of antidunes.

A theoretical expression for permissible velocity correction factor used in open channel hydraulics is derived. The concept of critical unit tractive force is employed in the theoretical derivation. The theoretical relation is compared with an empirical curve currently in use. The agreement is found to be good.

Available information on boundary layer development beyond the crest of a spillway is reviewed. Self-aeration of the flow begins at a critical point where the boundary layer has thickened sufficiently to induce turbulence at the surface, and the calculation of this location is an important aspect of chute spillway design. A new formulation is derived that is believed to be applicable to non-standard profiles as well as to standard crest profiles leading to a chute of constant slope. This equation allows for surface roughness and the influence of flow acceleration.

Simulated results from many urban runoff models are sensitive to the value used for impervious area. This paper explores the use of effective impervious area versus total impervious area for input to these models. Total impervious areas may be appropriate for black-box models but not for deterministic models. Potential problems of using total impervious area in deterministic models include that (1) runoff volumes and peak flows may be substantially overestimated for ungaged watersheds, (2) simulated changes in runoff due to increasing intensity of land use are likely to be smaller if total impervious area is used rather than effective impervious area, and (3) overestimates of infiltration parameters are likely if the model is calibrated using total impervious area and measured runoff data. Impervious-area data collected from 19 urban watersheds in the Denver metropolitan area showed strong relationships between effective impervious area, total impervious area, and land use.