SAMPLE PROBLEMS Darcy’s Law for Calculating Discharge

Solve these problems and report your answers in the requested units. Show all calculation steps and account for units of measure in enough detail that anyone can follow your methods.

1a) A sand aquifer has a permeability of 10-2 cm/sec, and a porosity of 26%. In the subsurface it has a width of 5000 meters and a thickness of 10 meters. How much water will it transmit per day if it has an elevation drop of 5 meters/100 meters? Give your answer in meters3/day.1b) How fast will the water travel in cm/sec?1c) How fast is that in feet/day? (1 inch = 2.54 cm)1d) How many feet3/second of water will the aquifer transmit? (1 foot3/sec = 2450 meters3/day)1e) How does the discharge of this enormous aquifer compare to the discharge of the Tioga River?

2a) A 10 meter-thick aquifer is 2000 meters wide, measured perpendicular to the direction of ground water flow. Along the flow direction, we have installed two observation wells 100 meters apart. These wells have water table elevations of 567 meters above sea level and 564 meters above sea level. If the aquifer has a permeability of 10-3 cm/sec, and a porosity of 16%, how much water will it transmit in meters3/day.2b) How fast will the water travel in cm/sec?2c) How fast is that in inches/hour? (1 inch = 2.54 cm)2d) How many gallons/minute will the aquifer transmit? (1 gallon/minute = 5.42 meters3/day)2e) How does the discharge of this enormous aquifer compare to the discharge of the Tioga River?

The Velocity of Ground Water Flow

Henri Darcy discovered the most important method for determining the rate of ground water flow in the 1850's. It is a mathematical relationship between gradient, permeability and porosity. Later discoveries by other scientists applied Darcy's law to problems in petroleum geology and contaminant transport.

Three-Point Problems

Three-point problems are used in many types of geology and hydrology field work. They can be used to determine directions of ground water flow, depth to a subsurface rock unit and determine the strike/dip of subsurface rock units. You are to solve four three-point problems for practice and two for a grade.