Effective Layered System Analysis for Hydraulic Engineering
Explore the concept of computing equivalent hydraulic conductivity for layered systems to apply Darcy's Law efficiently. Learn the principles behind head loss, flow distribution, and key equations for hydraulic analysis in complex systems.
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Presentation Transcript
K1 H1 H K2 H2 K3 H3 It is often useful to compute an equivalent k for a layered system so that Darcy s Law can be applied directly to the system as a whole.
V For this case, the following must hold: 1. Head loss is the same through each layer i1 = i2 = i3 2. Flow equals sum of individual flows qtotal = q1 + q2 + q3
Thus, q = q1 + q2 + q3 vH = v1H1 + v2H2 + v3H3 keqieqH = k1i1H1 + k2i2H2 + k3i3H3 (width = 1) since i's are the same, divide by i: keqH = k1H1 + k2H2 + k3H3 n keq= i=1 kiHi Hi keq=k1H1+ k2H2+ k3H3 n i=1 H
V For this case, the following must hold: 1. q will be the same through each layer htotal = h1 + h2 + h3
q = q1 = q2 = q3 v = v1 = v2 = v3 keqieq = k1i1 = k2i2 = k3i3 keq( h/H) = k1i1 = k2i2 = k3i3 h = h1 + h2 + h3 h = H1i1 + H2i2 + H3i3
i3=keqh i1=keq h i2=keq h Hk3 Hk1 Hk2 h =H1keq h +H2keq h Hk2 +H3keq h Hk3 Hk1 Divide by h and solve for keq: n H k2+H3 i=1 Hi Hi ki keq= keq= H1 k1+H2 n k3 i=1
