Rectangular weir equation

Equations 8.27 and 8.28 give the volumetric flow rate Q through a rectangular weir when there is no friction in the system. 

To derive the equation that is used to calculate the flow in rectangular weirs, refer to Figure 3.2. As shown, the weir height is P. The vertical distance from the tip of the crest to the surface well upstream of the weir at point 1 is designated as H. H is called the head over the weir. 

The cross-sectional area of flow at the control section is y L, where L is the length of the weir. This will be multiplied by U, to obtain the discharge flow Q at the control section, which, by the equation of continuity, is also the discharge flow in the channel. Using Equation (3.5) for the expression of y and Equation (3.6) for the expression for V), the discharge flow equation for the rectangular weir becomes... 

Two things must be addressed with respect to Equation (3.7). First, remember that hi and the approach velocity were neglected and y2 was made equal to y + P-Second, the L must be corrected depending upon whether the above equation is to be used for a fully contracted rectangular weir or the suppressed weir. 

Explain in detail whether or not the following equation for flow through a rectangular weir is dimensionally consistent. (This is the modified Francis formula.)... 

The equation for the volumetric flow rate q in m s for a rectangular weir is given by... 

Flow measurement in open unpressurised channels is a requirement generally associated with waste water systems and sewers. The use of a weir or notch to measure the flow of a liquid presenting a free surface is described in Volume 1, Section 6.3.8. The flow through a rectangular notch (Fig. 6.7a) is given by (Volume 1, equation 6.42) ... 

Pa-s (1 to 150 cP) and surface tension over the range of 0.03 to 0.07 N/m (30 to 70 dyn/cm). His equation predicts about an 8 percent increase in flow for a liquid of 0.1-Pa-s (100-cP) viscosity compared with water at 0.001 Pa s (1 cP) and about a 1 percent increase for a liquid with one-half of the surface tension of water. For fluids of moderate viscosity, Ranga Raju and Asawa [Proc. Am. Soc. Civ. Eng., J. Hydraul. Div., 103 (HY 10), 1227-1231 (1977)] find that the effect of viscosity and surface tension on the discharge flow rate for rectangular and triangular-notch ((j) = 45°) weirs can be neglected when... 

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