Understanding Aquifer Transmissivity Calculation
The question asks for the transmissivity ($T$) of a confined aquifer, given its saturated thickness ($b$) and hydraulic conductivity ($K$). The calculation requires converting units to match the desired output ($m^2/day$).
Aquifer Parameters
- Saturated Thickness, $b = 10$ m
- Hydraulic Conductivity, $K = 10^{-2}$ cm/s
- Desired Transmissivity Unit: $m^2/day$
Converting Hydraulic Conductivity (K)
First, convert the hydraulic conductivity from cm/s to m/day:
- Convert cm to m: $1 \text{ cm} = 10^{-2} \text{ m}$
- Convert seconds to days: $1 \text{ day} = 24 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 86400 \text{ s}$
- Apply the conversions: $K = 10^{-2} \frac{\text{cm}}{\text{s}} \times \frac{10^{-2} \text{ m}}{1 \text{ cm}} \times \frac{86400 \text{ s}}{1 \text{ day}}$ $K = 10^{-2} \times 10^{-2} \times 86400 \frac{\text{m}}{\text{day}}$ $K = 8.64 \frac{\text{m}}{\text{day}}$
Calculating Transmissivity (T)
Transmissivity ($T$) is the product of hydraulic conductivity ($K$) and aquifer saturated thickness ($b$).
- Formula: $T = K \times b$
- Substitute the values: $T = 8.64 \frac{\text{m}}{\text{day}} \times 10 \text{ m}$ $T = 86.4 \text{ m}^2/\text{day}$
Final Answer
The calculated transmissivity is $86.4 \text{ m}^2/\text{day}$. Rounded to one decimal place, the value is 86.4.
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 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 ________.
- The dimension of transmissivity of an aquifer is
