Groundwater flows through a sandy aquifer with a Darcy macroscopic discharge velocity of $v = 1.20\text{ m/day}$. If the effective porosity of the sand is $n = 0.30$, the actual seepage pore velocity ($v_s$) through the interconnected pore channels in meters per day ($\text{m/day}$) is ________ (round off to two decimal places).
Answer Key:
4.00
Step-by-Step Solution & Explanation
1. Relationship between Darcy velocity ($v$) and seepage pore velocity ($v_s$):
$v_s = \frac{v}{n}$
Where:
- $v = 1.20\text{ m/day}$
- $n = 0.30$
$v_s = \frac{1.20\text{ m/day}}{0.30} = 4.00\text{ m/day}$
(The microscopic velocity is $3.33$ times faster than macroscopic discharge velocity because only $30\%$ of the cross-section is available for fluid flow).