Final answer:
To solve the engineering question, the hydraulic gradient is calculated as 0.2, the average velocity is 2 x 10⁻² m/s, the seepage velocity is 1.25 x 10⁻² m/s, and the hydraulic conductivity is 4 x 10⁻³ m/s.
Step-by-step explanation:
The student's question involves the calculation of various parameters related to the flow of water through soil, which is a typical topic in geotechnical engineering. Let's address each part of the question step by step.
Hydraulic Gradient
The hydraulic gradient (i) can be calculated by dividing the head difference by the length of the soil sample through which water flows:
i = head difference / length
i = 60 mm / 300 mm = 0.2
Average Velocity
The average velocity (V) is determined by dividing the flow rate (Q) by the cross-sectional area (A):
V = Q / A
To calculate V, we need to convert the cross-sectional area to m²:
A = 2500 mm² * (1m² / 10⁶mm²) = 2.5 x 10⁻³ m²
Now:
V = 0.05 * 10⁻⁶ m³/s / 2.5 x 10⁻³ m² = 2 x 10⁻² m/s
Seepage Velocity
The seepage velocity (Vs) is the actual velocity at which water moves through the pore spaces within the soil and is calculated using the void ratio (e) as follows:
Vs = V / (1 + e)
Vs = 2 x 10⁻² m/s / (1 + 0.6) = 1.25 x 10⁻² m/s
Hydraulic Conductivity
The hydraulic conductivity (K) is obtained by multiplying the average velocity by the hydraulic gradient:
K = V * i
K = 2 x 10⁻² m/s * 0.2 = 4 x 10⁻³ m/s