Drawdown at a 0.20 m diameter, fully penetrating well, which has been pumping at

Question

Drawdown at a 0.20 m diameter, fully penetrating well, which has been pumping at the rate of 1000 m^3/day for a long enough time that steady state conditions have been reached, is determined to be 0.70 m. The aquifer is undefined and 10.0 m thick. An onservation well 10 m away has been drawn down by 0.20 m.

Determine the hydraulic conductivity of the aquifer?

the formula for the unconfined aquifer: Q= piK(h_c,1-h_c,2/ ln(r1/r2)

please help solve I have two answers 153.494 and 176.63

I seen the problem worked both ways I am confused with the 153.494 way do someone know how to work this problem in detailed steps it would really be appreciated

Explanation / Answer

Here

Q = 1000 m^3/day

r2 = 0.20/2 = 0.10 m

r1 = 10 m

h1 = 10 - 0.20

h2 = 10-0.70

As we know

Q = pi*K*(h1^2 - h2^2)/ln(r1/r2)

1000 = pi*K*((10-0.20)^2 - (10-0.70)^2)/ln(10/0.10)

K = 153.494 m/day

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