Water from a confined aquifer having transmissivity of 1000 $m^2 day^{-1}$ is pumped through a fully penetrating well of 300 mm diameter at a rate of 1200 $m^3 day^{-1}$. If the radius of influence is 400 m, the drawdown in the well under steady-state flow condition in meter is __________ [round off to two decimal places]
(Take $\pi = 3.14$)
Confined Aquifer Drawdown Calculation
This section details the calculation of drawdown in a confined aquifer under steady-state pumping, utilizing the Thiem equation.
Given Aquifer Parameters
- Transmissivity ($T$): 1000 $m^2 day^{-1}$
- Pumping Rate ($Q$): 1200 $m^3 day^{-1}$
- Well Diameter: 300 mm
- Radius of Influence ($R$): 400 m
- Constant $\pi$: 3.14
Well Radius Determination
The radius of the pumping well ($r_w$) is half of its given diameter.
Well Radius ($r_w$) = Diameter / 2 = 300 mm / 2 = 150 mm = 0.15 m
Steady-State Drawdown Formula
For steady-state radial flow to a well in a confined aquifer, the drawdown ($s$) is calculated using the Thiem equation:
$ s = \frac{Q}{2 \pi T} \ln\left(\frac{R}{r_w}\right) $
Calculation Steps for Drawdown
- Substitute values into the Thiem equation:
$ s = \frac{1200 \, m^3 \, day^{-1}}{2 \times 3.14 \times 1000 \, m^2 \, day^{-1}} \ln\left(\frac{400 \, m}{0.15 \, m}\right) $
- Simplify the discharge and radius ratio terms:
$ s = \frac{1200}{6280} \ln\left(\frac{400}{0.15}\right) $
$ s \approx 0.19108 \times \ln(2666.67) $
- Evaluate the natural logarithm:
$ \ln(2666.67) \approx 7.8882 $
- Compute the drawdown:
$ s \approx 0.19108 \times 7.8882 $
$ s \approx 1.5070 \, m $
- Round to two decimal places:
The calculated drawdown is approximately 1.51 m.
Final Drawdown Result
The drawdown in the well under steady-state flow conditions is approximately 1.51 meters, which falls within the provided range of 1.48 m to 1.53 m.
Important Questions from Steady Flow Through Wells
- A well fully penetrates a $30\text{ m}$ thick confined aquifer. After a long period of pumping at a constant rate of $0.06\text{ m}^3\text{.s}^{-1}$, drawdowns of $3.6\text{ m}$ and $2.0\text{ m}$ are found at distances $60\text{ m}$ and $120\text{ m}$ away from the well, respectively. The hydraulic conductivity of the aquifer is $n \times 10^{-4}\text{ m.s}^{-1}$. The value of $n$ is ________ (Rounded off to two decimal places)
- A $40$ cm diameter tubewell is constructed in a $10$ m thick confined aquifer having hydraulic conductivity of $25$ m day$^{-1}$. The peizometric surface is observed to be $40$ m high from the impervious stratum at the radius of influence of $500$ m. The drawdown in the tubewell is $30$ m. If the thickness of aquifer is doubled and diameter of tubewell is reduced to half, keeping all other parameters and conditions same, the change in discharge from the well is [Take $ \pi = 3.14$]
- In an area, one tubewell of 15 cm diameter was operating such that groundwater table is 40 m above the bottom of screen. The groundwater formation has permeability (K) as 20 m.d$^{-1}$ and well has radius of influence of 980 m with a maximum drawdown of 12 m. After some time, a second tubewell of same size was installed at a distance of 500 m from the first tubewell. If both the tubewells are running simultaneously and have equal discharge, the loss of discharge in the first tubewell due to installation of the second tubewell, in %, is _________. (Rounded off to 2 decimal places)
- A $0.30$ m diameter well penetrates an unconfined aquifer with a saturated depth of $40$ m. After $8$ hours of pumping at a steady rate of $0.03$ $m^3$ $s^{-1}$, the drawdown in two observation wells located at $20$ m and $50$ m away from the pumping well are found to be $3$ m and $2$ m, respectively. The drawdown in the pumping well in m is ________ (rounded off to $1$ decimal place, Consider $\pi = 3.14$).
- The drawdown at the well face of a 30 cm diameter fully penetrating well in a confined aquifer is 3 m. The radius of influence of this well is 3 km. For the same discharge and aquifer condition, the drawdown at 300 m away from the centre of the well is ________ m.
