Answer :
To calculate the hydraulic conductivity of soil in the capillary, we can use Darcy's law, which relates the flow rate and pressure difference across a porous medium. Here's how you can calculate it:
1. Convert the flow rate from m^3/h to m^3/s:
- Flow rate = 0.005 m^3/h = 0.005 m^3/h × (1/3600) h/s = 1.39 × 10^-6 m^3/s
2. Calculate the cross-sectional area of the capillary tube:
- The diameter of the capillary tube is given as 0.1 m, so the radius is 0.05 m.
- The cross-sectional area (A) of the capillary tube can be calculated using the formula A = πr^2:
- A = π × (0.05 m)^2 = 0.00785 m^2
3. Calculate the velocity (v) of water flow in the capillary:
- Velocity (v) can be calculated using the formula v = Q / A, where Q is the flow rate and A is the cross-sectional area.
- v = (1.39 × 10^-6 m^3/s) / 0.00785 m^2 = 1.77 × 10^-4 m/s
4. Calculate the hydraulic conductivity (K) using Darcy's law:
- Darcy's law states that the flow rate (Q) is equal to the hydraulic conductivity (K) multiplied by the cross-sectional area (A) and the pressure difference (Δh):
- Q = K × A × Δh
- Rearrange the equation to solve for K:
- K = Q / (A × Δh)
- Given that the flow rate (Q) is 1.39 × 10^-6 m^3/s and the pressure difference (Δh) is 0.02 m, we can calculate the hydraulic conductivity:
- K = (1.39 × 10^-6 m^3/s) / (0.00785 m^2 × 0.02 m)
- K ≈ 8.92 × 10^-5 m/s
Therefore, the hydraulic conductivity of the soil in the capillary is approximately 8.92 × 10^-5 m/s.
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