Question

An unconfined aquifer made up of silt loam has an initial piezometric surface of 40 m. If wells 28 m and 15 m away from the pumping well have drawdowns of 4 m and 8 m, respectively, what is the pumping rate (m3/d) of the well?

Based on this, if you wanted to keep the same drawdowns at the observation wells, but needed a drawdown of 10 m in your pumping well, what diameter would the pumping well casing need to be?

Answer 1

Answer 1) Pumping rate of the well from an unconfined aquifer in (m3/d) is given by Dupit's equation

Q=

where k= permeability of aquifer =1m/d (assumed)

h1 and h2 are the depths of water in the observation wells at radial distances of r1=15m and r2=28m(given)

as shown in figure below

Now to get h1 =H-s1

H = depth of aquifer or thickness of aquifer = 40m (given)

s1 and s2 are drawdowns 8 and 4 m respectively(given)

h1= 40-8=32m

h2=40-4 = 36m

now on substituting the values we get

Q =

Q=1369.07m3/d

Answer 2) Diameter of the pumping well by keeping the same drawdown

let r,s and h be the radius,drawdown,and depth of water respectively of pumping well as shown in the figure above

h=H-s=40-10=30m

By dupit's equation we have

Q=

Q=1369.07m3/d h2=36m k=1m/d r2=28m

now on substituting the values we get

1369.07=

r= 11.28m

d=22.56m