Question

Homework 6 - Due October 17, 2019 40. The confined aquifer in the figure is bounded on each side by rivers with different water levels. The aquifer is homogeneous and isotropic, and flow is steady and essentially one- dimensional in the x direction. The governing equation of flow for this aquifer is 12 = 0 = 0 The general form of the governing equation for flow in a confined aquifer is However, for this aquifer, the simplified equation above is sufficient. Justify all of the simplifications. 2 = 43.0 m-V M 74 .- = 40.0 m confining layer b = 30 m K = 6.2 m/d River 1 River 2 L=400 m 41. For the aquifer in Problem 40, state the boundary conditions and use them to solve the governing equation to obtain an expression for h(x) in terms of known values and the independent variable .x. Sketch the head distribution on the figure, describe its shape, and justify this behavior using Darcy's law.

Answer 1

cround surface {=4zom)La ho=43m| ---- Lolz40 m) RZO Ta sconfining layer 1 th K = 6.2m/d b=30m to. River Th=40m -----2=0 $ L=400m k there is no recharge, (R=0) and the flow simplifies to that of steady 1-D flow in as confined aquifer - As the flow is in se-direction only on integrating twice + h = 4x+C On substitution of the boundary cond" h=ho at x=0 h=Gxtho Also at & x=L, h = ho

2 - and hence G = -Cho-hy) Thus', [h= ho ho hudu! This is the equation of hydraulic grade line, which is shown to vary linearly from ho to hi * By Darcy daw, the discharge per whit width of the aquifer is- = -kB she -Ko [- thorhill #1 2 = (ho-hi) kB] Now putting all the values given in the question - 9 = (43,740) * 6-2 * 30 19 - 1.395 m/day/m