Flow rate in unconfined aquifier?

[tzx9633]

Homework Statement

A 40cm well was drilled penetrating straight into unconfined aquifier at depth of 90m . The other wells were drilled at a distance of 20m and 100m from initial well have decrease in water level of 12m and 8m from groundwater level . If the aquifier has a permeability value of 200m / day , what’s the pumping rate of well ?

Homework Equations

The Attempt at a Solution

Permeability in m^3 / s = 200/24/3600
H = 90 – 8 = 82
H = 90- 12 = 78

My working is Q = πk( H^2 -h^2) / ln (R /r)= π( (200/24/3600)x (82^2 - 78^2)) / ln(100/200 = 2.89m^3 / s , But the ans provided is 1.06m^3 / s , what's wrong with my answer ? The ans provided is in m^3 /s

 

[haruspex]

H = 90 – 8 = 82
H = 90- 12 = 78

depth of 90m ... decrease in water level

 

[tzx9633]

what do you mean ? Can you explain further ?

 

[haruspex]

what do you mean ? Can you explain further ?

If the water level of an aquifer decreases, is it shallower or deeper?

 

[tzx9633]

If the water level of an aquifer decreases, is it shallower or deeper?

Shallower , am i right ?

 

[haruspex]

Shallower , am i right ?

Just realized my question was ambiguous.
I meant shallower in the sense of nearer the ground surface. If the water level falls it will be further from the ground surface, right?

 

[tzx9633]

Just realized my question was ambiguous.
I meant shallower in the sense of nearer the ground surface. If the water level falls it will be further from the ground surface, right?

yes , any part of my working is wrong ? I couldn't get the ans ...

 

[haruspex]

yes , any part of my working is wrong ? I couldn't get the ans ...

You are not getting my hints.
The first well is at a depth of 90m, i.e. its water's surface is at 90m below ground level.
The next well has a water surface 12m lower, so how far below ground level is that?

 

[tzx9633]

You are not getting my hints.
The first well is at a depth of 90m, i.e. its water's surface is at 90m below ground level.
The next well has a water surface 12m lower, so how far below ground level is that?

102 m ...

 

[tzx9633]

You are not getting my hints.
The first well is at a depth of 90m, i.e. its water's surface is at 90m below ground level.
The next well has a water surface 12m lower, so how far below ground level is that?

H = 90+ 8 = 98
H = 90 + 12 = 102

My working is Q = πk( H^2 -h^2) / ln (R /r)= π( (200/24/3600)x (102^2 - 98^2)) / ln(100/200 = 3.61m^3 / s , but the ans provided is 1.06m^3 / s , what's wrong with my answer ? Which is still wrong

 

[haruspex]

Sorry, I should have looked at the diagram sooner. I now see that the wording is misleading. Your original calculation of 82m and 78m was correct. The only error I see in your working is that you have ln(100/200) instead of ln(200/100), but that would have simply flipped the sign.
That said, if I put your numbers through my calculator I get 6.71m³/s.
The equation puzzles me. I do not understand where that π comes from, since it is not getting multiplied by a radius anywhere. The given 40cm does not seem to feature in the equation (is that radius or diameter?), but I can see why it might be irrelevant.

Edit, just noticed you had 200 instead of 20.., just a typo I guess. Now I get your 2.89.

Edit 2: I tried dividing 2.89 by 1.06. It gives a number very close to e. Perhaps a result of fat-fingering a calculator?