Question

The hydraulic conductivity of a 100cm long cylindrical core is estimated as 1.2cm/min when hydraulic head difference is 20cm in an experimental setup. If the effective porosity of the core is 20%, then, assuming steady state Darcy flow, the average interstitial velocity of groundwater through the core is _____m/day. (Round off to two decimal places)

Answer 1

Correct Answer: 17.2

To find the average interstitial velocity of groundwater through the core, we start by using the formula for interstitial velocity, \( v_i \):

\( v_i = \frac{K \cdot i}{n_e} \)

Where:
\( K \) = hydraulic conductivity = 1.2 cm/min
\( i \) = hydraulic gradient = \(\frac{20}{100}\) = 0.2 (since head difference is 20 cm and length of core is 100 cm)
\( n_e \) = effective porosity = 0.2

Now, converting hydraulic conductivity from cm/min to m/day:

\( K \) (m/day) = 1.2 cm/min × 60 min/hour × 24 hour/day × 0.01 m/cm = 17.28 m/day

Substitute the values into the formula for interstitial velocity:

\( v_i = \frac{17.28 \cdot 0.2}{0.2} = 17.28 \text{ m/day} \)

This confirms that the calculated interstitial velocity is 17.28 m/day,