Understanding Transmissivity Dimensions
Transmissivity (T) is a key property in groundwater hydrology, representing the rate at which water can be transmitted through a unit width of an aquifer under a unit hydraulic gradient.
It is defined as the product of the aquifer's hydraulic conductivity (K) and its saturated thickness (b).
Formula: \( T = K \times b \)
Calculating Transmissivity Dimensions
To find the dimensions of transmissivity, we need the dimensions of hydraulic conductivity and saturated thickness.
- Hydraulic Conductivity (K): This represents a fluid flow rate through a porous medium and has dimensions of velocity. Dimensions of K = $[L][T]^{-1}$ = \( M^0L^1T^{-1} \)
- Saturated Thickness (b): This is a measure of length. Dimensions of b = $[L]$ = \( M^0L^1T^0 \)
Now, multiply the dimensions:
Dimensions of T = (Dimensions of K) \(\times\) (Dimensions of b)
Dimensions of T = \( (M^0L^1T^{-1}) \times (M^0L^1T^0) \)
Dimensions of T = \( M^{0+0}L^{1+1}T^{-1+0} \)
Dimensions of T = \( M^0L^2T^{-1} \)
Result
The calculated dimensions for transmissivity are \( M^0L^2T^{-1} \). This matches Option 4.
Important Questions from Aquifer Properties
- An aquifer has a surface area of 100 km$^2$. With no recharge, assume that pumping out 2 $\times$ 10$^7$ m$^3$ of ground water resulted in a drop of the water table by 6 m. If the aquifer has a specific retention of 15 %, then the porosity of the aquifer is _____ % (rounded off to one decimal place).
- A well penetrates an unconfined aquifer. The water level (i.e., head) in the well prior to pumping is 25 m. After a long period of pumping at a constant rate of 0.05 m$^3$/s, the drawdowns at distances of 50 m and 150 m from the well are observed to be 3 m and 1.2 m, respectively.
The hydraulic conductivity of the unconfined aquifer is ______ $\times 10^{-4}$ m/s (rounded off to two decimal places).
Consider $\pi$ = 3.14. - A confined aquifer with a uniform saturated thickness of 10 m has hydraulic conductivity of $10^{-2}$ cm/s. Considering a steady flow, the transmissivity of the aquifer in $m^2/day$ is _______ (rounded off to one decimal place).
- A stratified confined aquifer consists of three parallel homogeneous and isotropic horizontal layers with thickness of 10 m, 5 m and 5 m. The layers have the same width. The hydraulic conductivities of the strata are 15 m/day, 20 m/day and 30 m/day, respectively. The water flow follows Darcy's law and is parallel to the strata. Considering the same hydraulic gradient for all the layers, the effective hydraulic conductivity of the aquifer is ________ m/day. [in integer]
If $d$ is the depth of an aquifer through which water is flowing, then the relationship between permeability $K$ and transmissibility (also known as transmissivity) $T$ is given by ________.
