Present a step by step annotated derivation of the advective velocity equation relating the standard relationships of water flow and velocity in a pipe to the velocity of water through soil pore space pathways. You are required to provide your own annotations and any additional interim steps you see fit to demonstrate your understanding of the pipe flow to groundwater flow analogy involved.  The derivation does not require calculus and can be developed with algebraic expressions and consistency with flow, area and velocity relationships of water flow in a pipe, and water flow through an aquifer.

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Groundwater Flow

The term groundwater refers to the water which is found beneath the earth's surface. Pores present in the soil and rocks with fractures make a passage for rainwater to enter the earth's surface and deposit as groundwater. The flow nature and direction of groundwater under the earth's surface directly impacts the strength and compressibility of the soil, which reflects its ability to support structural loads.