Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Civil and Environmental Engineering

Committee Chair(s)

J. Paul Tullis


J. Paul Tullis


Gary P. Merkley


William J. Rahmeyer


Gilberto Urroz


Much work has been published regarding discharge coefficients for various weir structures. What has not been published to the same extent are the effects of model scale associated with the weirs being studied. If laboratory weirs are too small, scale effects can affect the magnitude of the discharge coefficient. These errors may be significant if the weir serves as a control structure for an emergency spillway. It is imperative that discharge be accurately predicted to enable safe design and operation.

Numerical and physical means were employed to analyze the effects of scale associated with Froude Modeling of weirs with sharp and flat crests. An inverse formulation for the ideal flow of water over a weir was developed. The formulation appeared to be sound; however, the numerical method failed because the boundary condition on the free surface had multiple roots, which were almost equal in magnitude and sign.

Laboratory data were collected and analyzed to determine the existence of scale effects and the flow conditions under which they were manifested. Results indicate that scale effects are present even with relatively large model sizes (12 inches high with a crest thickness of 24 inches). The scale effects appear to be associated with the size of the weir-wall and the viscosity. Although the viscosity was not altered, the results show a characteristic Reynolds Number for a given crest thickness-to-height ratio where scale effects cease to exist for increasing total head.

Several graphs defining the conditions where scale effects exist for a given weir size were developed. Use of the graphs allows one to determine the minimum total head (piezometric plus velocity head) that one may operate a given size of weir or size a weir given the minimum total head to be tested to avoid scale effects.

A design curve for discharge coefficients was developed to be used for determining the capacity of prototype weirs. The curve can be used to determine the discharge coefficient for new or existing hydraulic control structures.