In the Darcy's Law expression, which statement describes how flow rate relates to pressure difference?

In the Darcy's Law expression, which statement describes how flow rate relates to pressure difference?

• A. Flow rate is proportional to the pressure difference
• B. Flow rate is proportional to the square of the pressure difference
• C. Flow rate is independent of pressure difference
• D. Flow rate is inversely proportional to pressure difference

Answer: (D)

Flow through a porous medium under Darcy's law is driven by the pressure difference, and the flow rate increases linearly with that difference when permeability, viscosity, cross-sectional area, and path length are fixed. The relationship is captured by Q = - (k A / μ) (ΔP/ΔL) (or q = - (k/μ) ∇P), where the magnitude of flow rate is directly proportional to ΔP. The negative sign indicates flow from high to low pressure, not the magnitude itself. This linear dependence holds for laminar flow in a homogeneous medium. So the best statement is that flow rate is proportional to the pressure difference.

Flow through a porous medium under Darcy's law is driven by the pressure difference, and the flow rate increases linearly with that difference when permeability, viscosity, cross-sectional area, and path length are fixed. The relationship is captured by Q = - (k A / μ) (ΔP/ΔL) (or q = - (k/μ) ∇P), where the magnitude of flow rate is directly proportional to ΔP. The negative sign indicates flow from high to low pressure, not the magnitude itself. This linear dependence holds for laminar flow in a homogeneous medium. So the best statement is that flow rate is proportional to the pressure difference.