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Author-produced version of the article published in Water and Environment Journal,2015,29(3),360-364. <br /> The original publication is available at:http://onlinelibrary.wiley.com/doi/10.1111/wej.12114/pdf doi:10.1111/wej.12114 <br /> h � <br /> D <br /> 57 <br /> 58 Figure 2.Relationships between critical water depth and hydraulic section and pipe diameter <br /> 59 S, _�2 (8c—sin 85 cos 8C) (2) <br /> 60 Dh�=D(85—sin 85 cos,,, (3) <br /> 4 sin 8, <br /> 61 k = (1—Cos 8,) (4) <br /> 62 where D is outlet pipe diameter[L].The angle 6,may be expressed as a function of D and hc: <br /> 63 Sc =acos(l-2k (5) <br /> D) <br /> 64 Equation I links the outflow discharge to the critical water depth in the outflow pipe.We are now <br /> 65 seeking out a relationship between critical water depth(h j and the water depth in the tank(h [L], <br /> 66 measured from the invert of the outflow pipe).Knowing the critical water depth(hd,the critical <br /> 67 energy head He[L]can be calculated with the following expression. <br /> 68 Hc =k+OU2 (6) <br /> g , <br /> 69 The head loss AH[L]between the tank and the critical section can be evaluated as a local head loss, <br /> 70 thus: <br /> 71 AH=Kout (7) <br /> gCI <br /> 72 The loss coefficient K[-]was evaluated by CFD using the OpenFOAM software package(2013)for a <br /> 73 100 mm diameter pipe and a flow rate ranging from 0.10 to 1.50 L/s. The conclusion of the numerical <br /> 74 simulations is that the loss coefficient K is approximately 0.4 for the whole discharge range.Using this <br /> 75 value and an estimation of the numerical uncertainty based on a grid sensitivity analysis,the <br /> 76 uncertainty on the outflow discharge(Qa„t)for a given water depth(h)was evaluated as 5%.Finally, <br />