Q1 Estimate the discharge in literminute from fully penetrat

Q1. Estimate the discharge (in liter/minute) from fully penetrating pumping well in a confined aquifer of thickness 20 m with following data: Distance of observation well from pumping well = 100 m Drawdown at the observation well after 4 hours of pumping = 15 m Drawdown at the observation well after 16 hours of pumping is 2.0 m Storage coefficient of aquifer 0.0003.

Solution

Solution:-

Given

Thickness of aquifer (b) = 20 meter

Distance of observation well from pumping well (r ) = 100 meter

Storage coefficient of aquifer(S) = 0.0003

Time(t₁) = 4 hours = 4 * 3600 = 14400 second

t₂ = 16 hours = 57600 seconds

drawdown (s₁) = 1.5 m

drawdown(s₂) = 2 m

Let Coefficient of permeability = 35 m/day

Transmissibility(T) = b *k = 20 * 35 m²/day = 0.0081 m²/second

Let discharge = Q

Case I

When t₁ = 14400 seconds

s₁ = 1.5 m

Jacob’s equation

s₁ = Q₁/(4 *pi *T) *(log_e(4T t₁/(r² S)) – 0.5772)

1.5 = Q₁/(4 * pi *0.0081) * (log_e((4*0.0081*14400)/(100² *0.0003)) - 0.5772)

Discharge(Q₁) = 0.0946 m³/second

Discharge(Q₁) = 0.0946 *1000*60

= 5676 litre/minute      Answer

Where pi = 3.1415

Case 2

When

t₂ = 57600 seconds

s₂ = 2 meter

2 = Q₂/(4 * pi *0.0081) *(log((4*0.0081*57600)/(100² * 0.0003)) - 0.5772)

Discharge(Q₂) = 0.0918 m³/second

= 0.0918*1000*60

= 5508 litre/minute   Answer