Darcy’s law: The French hydrologist Henri Darcy discovered that the velocity V of underground water is proportional to the magnitude of the slope S of the water table (see Figure 1.71). The constant...

Darcy’s law: The French hydrologist Henri Darcy discovered that the velocity V of underground water is proportional to the magnitude of the slope S of the water table (see Figure 1.71). The constant of proportionality in this case is the permeability of the medium through which the water is flowing. This proportionality relationship is known as Darcy’s law, and it is important in modern hydrology.

a. Using K as the constant of proportionality, express Darcy’s law as an equation.

b. Sandstone has a permeability of about 0.041 meter per day. If an underground aquifer is seeping through sandstone, and if the water table drops 0.03 vertical meter for each horizontal meter, what is the velocity of the water flow? Be sure to use appropriate units for velocity and keep all digits.

c. Sand has a permeability of about 41 meters per day. If the aquifer from part a were flowing through sand, what would be its velocity?