Problem 4 The figure below shows the cross section of a leve

Problem 4. The figure below shows the cross section of a levee that is underlain by a 2-m-thick permeable sand layer. For the sand layer, ksand is 0.3 ft/day and the porosity (n) is 0.4. Elv. 180 ft Levee Elv. 170 ft 5 ft 100 ft Impervious Sand Determine the followings. (20 pts) (a) What is the flow rate? (b) How long does it take for water to flow from reservoir to the ditch?

Solution

Solution:-

a) q = k_p * i *A

q= discharge

k= coefficient of permeability/ hydraulic conductivity

i = Hydraulic gradient Change in length/ total length = (180-170) / `100 =0.1

k_p =  coefficient of percolation = k/porosity = (n) = 0.3 / 0.4 =0.75 ft /day

A= area = 100 * 2 *3.28 =656 ft²

q= 0.75 * 0.1 * 656

q = 49.2 ft³/ft/ day

b) time = volume / discharge

time = 100 * 2*3.28 *1/ 49.2

= 13.33 days