What is the linear flow form of Darcy's Law?

What is the linear flow form of Darcy's Law?

• A. q = μ L / (k a (p1 - p2))
• B. q = k a (p1 - p2) / μ L
• C. q = k a (p1 + p2) / μ L
• D. q = (p1 - p2) / (k a μ L)

Answer: (B)

Darcy's Law in its linear form shows that the flow rate increases with the driving pressure difference and with the medium's ability to transmit flow (permeability and cross-sectional area) and decreases with how long the path is and how thick the fluid is. Expressed cleanly, the volumetric flow rate q equals the permeability k times the cross-sectional area a, divided by the fluid viscosity μ and the length L, all multiplied by the pressure drop (p1 − p2). In formula form: q = (k a / μ L) (p1 − p2), which is equivalent to q = k a (p1 − p2) / (μ L). The other forms either invert the fraction, use a sum of pressures, or mix terms in a way that doesn’t reflect the direct proportionality to the pressure difference and the inverse proportionality to μ and L.

Darcy's Law in its linear form shows that the flow rate increases with the driving pressure difference and with the medium's ability to transmit flow (permeability and cross-sectional area) and decreases with how long the path is and how thick the fluid is. Expressed cleanly, the volumetric flow rate q equals the permeability k times the cross-sectional area a, divided by the fluid viscosity μ and the length L, all multiplied by the pressure drop (p1 − p2). In formula form: q = (k a / μ L) (p1 − p2), which is equivalent to q = k a (p1 − p2) / (μ L). The other forms either invert the fraction, use a sum of pressures, or mix terms in a way that doesn’t reflect the direct proportionality to the pressure difference and the inverse proportionality to μ and L.