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Chapter 1: Problem 31

Porous rock through which groundwater can move is called an aquifer. The volume \(V\) of water that, in time \(t\), moves through a cross section of area \(A\) of the aquifer is given by $$ V / t=K A H / L $$ where \(H\) is the vertical drop of the aquifer over the horizontal distance \(L\); see Fig. \(1-5 .\) This relation is called Darcy's law. The quantity \(K\) is the hydraulic conductivity of the aquifer. What are the SI units of \(K ?\)

Short Answer

Expert verified
The SI units for the hydraulic conductivity \(K\) are meters per second (\(m/s\)).

Step by step solution

01

Identify the variables and their SI units

Identify the variables in Darcy's law and their respective SI units. Here, \(V\) (volume) has SI units of cubic meter (\(m^3\)), \(t\) (time) has SI units of seconds (s), \(A\) (cross-sectional area) has SI units of square meter (\(m^2\)), and \(H\) and \(L\) (vertical drop of the aquifer and horizontal distance) have SI units of meter (m).
02

Deduce the SI units of \(K\)

Substitute the variables in Darcy's law with their corresponding SI units. As per the equation \(V / t=K A H / L\), replace \(V\) with \(m^3\), \(t\) with \(s\), \(A\) with \(m^2\), \(H\) with \(m\) and \(L\) with \(m\), giving us the equation \(m^3/s = K m^2 m/m\). Solving this equation for \(K\) gives us the SI units of \(K\).
03

Simplify the units of \(K\)

Simplify the units on the right hand side of the equation. Multiplying and cancelling the units, we get \(K = m/s\).

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Most popular questions from this chapter

Antarctica is roughly semicircular in shape with a radius of \(2000 \mathrm{~km}\). The average thickness of the ice cover is \(3000 \mathrm{~m}\). How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature of the Earth.)

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