Question

The dimension of Hydraulic Conductivity is

• A. $\text{LT}^{-1}$
• B. $\text
  ^{-1}\text{T}$
• C. $\text
  ^{-1}\text{T}^{-1}$
• D. $\text{LT}$

Hint:

Because the hydraulic gradient is a ratio of two lengths and is dimensionless, hydraulic conductivity carries the same dimensions as velocity (\(\text{LT}^{-1}\)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Hydraulic conductivity (\(K\)) measures the ease with which water can move through soil pores or other porous media under a hydraulic gradient.
Key Formula or Approach:
According to Darcy's Law:
\[ v = K \cdot i \] where:
\( v \) = discharge velocity or flux (\( \frac{Q}{A \cdot t} \))
\( K \) = hydraulic conductivity
\( i \) = hydraulic gradient (\( \frac{dh}{dl} \), which is dimensionless, i.e., \( \frac{\text{length}}{\text{length}} \))

Step 2: Detailed Explanation:
Let us derive the dimensions of hydraulic conductivity using dimensional analysis:
Since the hydraulic gradient \( i \) is dimensionless (\([\text
] / [\text
] = [1]\)), the dimensions of hydraulic conductivity \( K \) must be identical to those of velocity \( v \).
The dimension of velocity is distance (Length, \(\text
\)) divided by time (\(\text{T}\)):
\[ [v] = \frac{[\text
]}{[\text{T}]} = \text{LT}^{-1} \] Thus, the dimension of hydraulic conductivity \( K \) is also \(\text{LT}^{-1}\).
Common units for hydraulic conductivity include \(\text{cm/s}\), \(\text{m/s}\), or \(\text{m/day}\).

Step 3: Final Answer:
The dimensional formula for hydraulic conductivity is \(\text{LT}^{-1}\).