KITUI SAND DAMS

∆i = ϖ =∆xwfxf− wi− xi‘K’ is the hydraulic conductivity of the material with dimensions length over time (LT -1 ).Thus as ∆x approaches Zero, ∆ω/∆x becomes δω/δx. Thus in three dimensions Darcy’sδϖlaw becomes q = −kδxFlow in unconfined situation is usually in three dimensions. However, in practice it ishard to solve the three-dimensional flow water problem.This is countered by using the Dupits –Forchheimer approximation this assumes thepresence of vertical flow if overridden by the horizontal flow. Horizontal flow is moreactive than vertical flow.The continuity equation and Darcy’s law are combined to solve this equation. Groundwater recharge is also included denoted by N.δϖNδx =Where Q =ωq- flow in the horizontal direction.NB: The base of the aquifer is the reference level for ωδ ⎛ϖδϖ⎞ NSubstituting the Darcy’s law becomes. ⎜ ⎟ = −δx⎝ δx⎠ K2 2k ⎛ wf − wi ⎞Discharge through land mass = Q =⎜⎟2 ⎝ xf − xi ⎠CATCHMENT STORAGE AND WATER BALANCE DETERMINATION.A catchment is an area contributing to the discharge at a particular part of a river basin. Inthe case of sand dam development, this can be defined as a drainage basin of a riversystem. This is the area water flowing in the river falls. This includes the main river andits tributaries. This is usually the lowest topographic region. Water flows to the lowerareas. This includes both the surface run off and the water from the interflow water thatgets to the river through moving in the ground.Thus, the water falling in a catchment will partly be held in the catchment, and the restflows out. It is worth determining the amount of water falling in the catchment, waterheld in the catchment is referred to as the water balance. It is usually affected by theprecipitation, which is the input and the output that comprises the evapotranspiration E,and river discharge Q at the outlet of the catchment.∆SHence water balance is written as ( P − E)× A − Q =∆tWhere ∆S is change of storage with time step ∆t, A is the Surface area of the catchmentupstream of the outlet point.27