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4 Author-produced version of the article published in Water and Environment Journal,2015,29(3),360-364. The original publication is available at:hftp://onlinelibrary.wiley.com/doi/10.1111/wej.12114/pdf do!:10.1111/wej.12114 30 Two possible approaches were identified: (i)using a tank model where the law governing outflow is 31 obtained by a statistical learning or neural network method(Vazquez et al., 1999)or(ii)the overflow 32 analogy.A statistical learning or neural network method is able to mimic complex hydraulic systems 33 without the need to compile advanced knowledge of the constitutive elements.However,it requires a 34 large dataset for model learning,which is not compatible with our needs.The overflow analogy is 35 based on a simple mechanistic approach based on the assumption that critical flow occurs at the outlet 36 of the septic tank.In this paper,we briefly present the model and its practical implementation,and 37 then report selected results based on several hydrographs. 38 Model presentation 39 Model equations 40 Figure 1 presents a sketch of the usual design of a septic tank.The upstream section of the outflow 41 pipe of a septic tank is a local maximum of the bottom profile.With no downstream influence 42 (guaranteed by the large slope of the pipe,which is usually over 0.5%;AFNOR,2007),this 43 configuration is responsible for producing critical flow(Hager 1999). Critical flow is the transition 44 between subcritical flow(here,a nearly horizontal water surface with a very small velocity in the 45 septic tank)and supercritical flow(here,a fast flow in the outflow pipe).The occurrence of critical 46 flow guarantees a direct relationship between water level h in the tank and the outflow discharge(Q,,u, 47 [L3T"']).We used this relationship in association with a water mass balance in the septic tank to build 48 a time-dependent model. Inlet F��4 let _4 1 Zh refilt 49 50 Figure 1.Sketch of the water flow through a septic tank 51 The discharge Qa,,,corresponding to the critical water depth h,[L] can be evaluated considering a 52 Froude number equal to unity(transition from subcritical to supercritical flow),according to: 53 Q.=S� gD,,� (1) 54 where Qo„,is outflow discharge [L3 T"1],S,is critical cross-section[L2],g is gravitational acceleration 55 [L T-2]and Dh,is critical hydraulic diameter[L].Both S,and Dh,are linked to the critical water depth 56 (h,)by relationships(Equations 2,3 and 4)using the angle 8,as illustrated in Figure 2.