Chapt13 Unsteady Well Hydraulics Theis Cooper Jacob

8/11/2019 Chapt13 Unsteady Well Hydraulics Theis Cooper Jacob

1/4

cmutsvangwa irrigation systems design: dept. of civil and water eng., nust, 16/02/2006 15:23:35

UNSTEADY WELL HYDRAULICS

Cooper-Jacob solution (Modified Theis method)

Determining the aquifer constants, Scand T=kb from a pumping test of onesingle well and one observation well.

From Theis equations:

==u

u

o duu

e

kb

Qhhs

4 (1)

Where: ho-h = drawdown (s) at an observational well at distance rfrom the pumping well

( )uWkb

Qhhs o

4== (2)

( ) ++++= .....!4.4!3.3!2.2

ln577216.0432

uuuuuuW (3)

And u is the argument:

t

r

kb

Su c

2

4

= (4)

The argument u decreases as the pumping time increases. For large values of tand small values r, u becomes small enough so that the terms after the first twobecome negligible. Thus the drawdown (s) can be expresses as:

=

Tt

Sr

T

Qs c

4ln577216.0

4

2

(5)

Rewriting the above equation to base 10 and simplifying:

cSr

Tt

T

Qs

2

25.2log

4

3.2

= u


2/4


Where rwis the radius of the pumping well.

A plot of equation 6 on a semi-log paper gives a best fit straight line (Fig. 1) andthe drawdown difference per log cycle, s is:

TQs

43.2=

Therefore the constant T=kb can be computed.

Fig. 1

From equation 6, s=0 (at t0) when 125.22

0 =cSr

Tt

The time tois found by extending the best fit line to meet the zero drawdown line.

From this equation, 125.22

=c

Sr

Tt the storage coefficient can be determined:

2

25.2

r

TtSc =

Determining the aquifer constants, Scand T=kb from a pumping test of onesingle well and several observation wells

The pumping will done for a fixed time t and draw downs are recorded in severalobservation wells.

From

One log-cycleDrawdown,s,m

10

s

100t

t0

(0, 0)

2


3/4


c

Sr

Tt

T

Qs

2

25.2log

4

3.2

=

=

cSrTt

TQ

225.2log

43.2

+=

2

1log

25.2log

4

3.2

rS

Tt

T

Q

c

+= rS

Tt

T

Q

c

log21log25.2

log4

3.2

=

= r

S

Tt

T

Q

c

log225.2

log4

3.2

rTS

Tt

T

Q

C

log24

3.225.2log4

3.2

=

=r

TS

Tt

T

Q

C

log22

3.225.22log

4

3.2=

constant i.e t=const

Therefore above a plot of the above equation a semi-log paper gives a

straight line andTQ

23.2 is the gradient and also equal to s , which is also

equal to one log cycle.

T

Qs

2

3.2=

Therefore T can be computed as:

s

QkbT

==2

3.2

3


4/4


At s=0, r=ro (Fig. 2) and fromc

Sr

Tt

T

Qs

2

25.2log

4

3.2

=

co Sr

Tt

T

Q2

25.2log

4

3.20

= , and therefore the term 125.22

0

=cSr

Tt

Thus the storage coefficient can be computed from:

2

0

25.2

r

TtSC=

Fig.2

References

1. Raghunath H. M., (1991), Hydrology, Wiley Eastern, Bombay.2. Shaw E. M., (1988), Hydrology in Practice, Van Nostrand Reinhold,

Wokingham3. Viessman J.R., Lewis G. L., and Knapp J.W., (1989), Introduction to

hydrology, Harper Collins, USA4. Wanielista M., (1990), Hydrology and Water Quality Control, John Wiley,

Canada5. Wilson E.M., (1990), Engineering Hydrology, Macmillan Education, UK

ro at s=0cycle1-log

r m

s, m

4

Documents

Chapt13 Unsteady Well Hydraulics Theis Cooper Jacob