# Flow over rectangular sharp-crested weirs

## Abstract

Sharp-crested weirs are the simplest form of over-flow spillway that commonly used to determine the flow rate in hydraulic laboratories, industry and irrigation systems, where highly accurate discharge measurements are needed. In this study, the experimental upper and lower nappe profiles in rectangular sharp-crested weirs are fitted by quadratic and cubic equations, respectively. In addition, free-vortex theory is used to simulate flow over this kind of weirs and determine discharge coefficient. Physical models of sharp-crested weirs with various widths and heights were considered. The proposed method agrees well with the experimental observations. Also, the experimental data indicate that the suggested equation presents reasonable results for the range of 0 < *h*/*P* < 9.

## Keywords

Discharge Coefficient Maximum Elevation Velocity Head Weir Crest Suggested Equation## List of symbols

*B*Channel width (m)

*b*Weir width (m)

*C*Constant value in free-vortex theory (m

^{2}/s)*C*_{d}Discharge coefficient of the weir (−)

*g*Ratio of weight to mass (m/s

^{2})*h*Upstream head (m)

*H*Total head upstream of the weir (m)

*k*Correction coefficient (−)

*L*Thickness of weir crest (m)

*P*Weir height (m)

*q*Discharge per unit width (m

^{2}/s)*Q*Weir discharge (m

^{3}/s)*r*Radius of the streamline at a given point (m)

*R*_{b}Radius of streamline curvature at lower nappe of profile in the distance of OB (m)

*R*_{s}Radius of streamline curvature at upper nappe of profile in the distance of OB (m)

*V*Velocity of the streamline at a given point (m/s)

*V*_{0}Upstream velocity (m/s)

*V*_{b}Lower nappe velocity at the section of maximum elevation of lower nappe (m/s)

*x*Cartesian coordinate in direction of flow (m)

*y*Cartesian coordinate perpendicular to flow (m)

*Y*Flow depth at the section of maximum elevation of lower nappe (m)

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