Laserfiche WebLink
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/l 0.1111/wej.12114/pdf doi:10.1111/wej.12114 <br /> 77 the water depth in the tank(h)can be evaluated using equation 7(Bernoulli equation written between <br /> 78 the critical section and the tank where the velocity head is close to zero). <br /> 79 h=H,+AH (8) <br /> 80 Based on equations 6 and 7,equation 8 can be rewritten as: <br /> 81 h=k+(K+1) <br /> 29S, <br /> 82 <br /> (9) <br /> g , <br /> 82 Replacing h,and S,in equation(9)by expressions dependent solely on Qo„t will lead to an expression <br /> 83 relating tank water depth(h)to outflow discharge(Qo„i).However,analytically solving this equation <br /> 84 would prove cumbersome due to the sinusoidal functions involved.An alternative solution was found <br /> 85 that consisted in rewriting equation 8 into a minimization problem.Incorporating equation(1)into <br /> 86 equation(9)implies: <br /> 87 h =k +K21Dh, (10) <br /> 88 Rewriting equation 10 into the form of an objective function(objfun)gives: <br /> 1i <br /> 89 obj.fun(h,.)=Ch—k—K2+1Dhc1 (11) <br /> 90 For a given value of h,finding the value of h,that minimizes the objective function makes it possible <br /> 91 to compute the outflow discharge(Qo„i)using equation 1.Once this relation has been established,it <br /> 92 can be associated to the septic tank mass balance equation to build a time-dependent model.For a <br /> 93 septic tank,the water mass balance can be written as: <br /> 94 S—t =Qin —Q. (12) <br /> 95 where S is horizontal surface of the septic tank at the level of the invert of the outflow pipe[LZ],and <br /> 96 Qin is inflow rate [L3T-`]. <br /> 97 After an explicit discretization,equation 12 becomes: <br /> h(t+At)—h(t) <br /> 98 S At =Qin(t)—Q 111(t) (13) <br />