Better CE Practice Test

Which of the following statements correctly reflects Darcy's law for groundwater flow?

Flow is proportional to the gradient of hydraulic head with a positive sign. Flow is proportional to the gradient of hydraulic head with a negative sign. Flow is independent of hydraulic conductivity. Flow is proportional to the square of the gradient.

Correct Answer:

Flow is proportional to the gradient of hydraulic head with a negative sign.

Explanation:

The main idea is that groundwater flow follows gradients in hydraulic head, but moves from high head to low head, so the flow is opposite the gradient. Darcy's law expresses this as q = -K ∇h, where q is the Darcy flux (per unit area), K is the hydraulic conductivity (a positive property of the medium), and h is the hydraulic head (h = pressure head plus elevation head). The negative sign ensures flow goes toward lower head, with its magnitude set by how strong the head gradient is and by how permeable the material is (K). The other statements don’t fit because flow does depend on hydraulic conductivity, it isn’t proportional to the square of the gradient, and it isn’t directed along the gradient but opposite to it.

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