In a laboratory experiment using Darcy's law, if the cross-sectional area of the sample is doubled and the hydraulic gradient is halved, how is the discharge (Q) affected?

Effect on Discharge (Q) Using Darcy's Law

According to Darcy's law, the discharge (Q) through a porous medium is given by the equation:

Q = K * A * (Δh / L), where:

• Q is the discharge.
• K is the hydraulic conductivity.
• A is the cross-sectional area of the sample.
• Δh / L is the hydraulic gradient (Δh is the difference in hydraulic head, and L is the length of the sample).

Analyzing the Given Scenario

1. Doubling the Cross-Sectional Area (A):

   • When the cross-sectional area (A) is doubled, Q is directly proportional to A. Therefore, doubling A will double Q.

2. Halving the Hydraulic Gradient (Δh / L):

   • When the hydraulic gradient (Δh / L) is halved, Q is directly proportional to the hydraulic gradient. Therefore, halving the hydraulic gradient will halve Q.

3. Combining Both Effects:

   • The effect of doubling the cross-sectional area (A) is to double Q, and the effect of halving the hydraulic gradient (Δh / L) is to halve Q.

   • Therefore, the two effects will cancel each other out, and the discharge (Q) will remain the same.