Deduccion Formulas Explotacion Aguas Subterraneas

DEDUCCIÓN DE FÓRMULAS PARA UN PIEZÓMETRO Y UN POZO UBICADO EN UN ACUÍFERO SEMICONFINADO Y UN ACUÍFERO LIBRE

ACUÍFERO LIBRE
ACUÍFERO LIBRE EN RÉGIMEN PERMANENTE (RECARGA)
N

+Q
r2
r1
-Q

Z
Z
2
1


∆hr - ∆h²r2D = Q2πKDln ( rir )
Descenso en el piezómetro N:
∆hN1- ∆h²N12D = Q2πKDln ( rir1 )
∆hN2 - ∆h²N22D = - Q2πKDln ( rir2 )
∆hN - ∆h²N2D = ( ∆hN1 - ∆h²N12D )+ ( ∆hN2 -∆h²N22D )
∆hN - ∆h²N2D = Q2πKDln ( rir1 ) - Q2πKDln ( rir2 )
∆hN- ∆h²N2D = Q2πKD ((ln ( rir1 ) - ln ( rir2 ))
∆hN - ∆h²N2D = Q2πKD ln ( r2r1 )

Descenso en el pozo 1:
∆h11 - ∆h²112D = Q2πKDln ( rirw ) = ∆hw =∆f
∆h12 - ∆h²122D = - Q2πKDln ( ri2z ) =- ∆r
∆hT - ∆h²T2D = (∆h11 - ∆h²112D ) + (∆h12 - ∆h²122D )
∆hT - ∆h²T2D = Q2πKDln ( rirw ) - Q2πKDln ( ri2z )
∆hT - ∆h²T2D = Q2πKD ((ln ( rirw) - ln ( ri2z ))
∆hT - ∆h²T2D = Q2πKDln ( 2zrw )


ACUÍFERO LIBRE EN RÉGIMEN VARIABLE (RECARGA)

N

+Q
r2
r1
-Q

Z
Z
2
1

∆h- ∆h²2D= Q4πKD W (u); u = Sy.r²4KDt
Descenso en el piezómetro N:
∆hN1- ∆h²N12D= Q4πKD W (u)…………………………………………. u = Sy.r²14KDt
∆hN2 - ∆h²N22D= - Q4πKD W (u')……………………………………… u' = Sy.r²24KDt
β=r2 r1 ……… r2=r1.βr²2=r²1.β²
u' = Sy.r²1.β²4KDt
u' = β². u
∆hN2 - ∆h²N22D = - Q4πKD W (β². u)
∆hN - ∆h²N2D = ( ∆hN1 - ∆h²N12D) + ( ∆hN2 - ∆h²N22D )
∆hN - ∆h²N2D = Q4πKD W (u) - Q4πKD W (β². u)
∆hN - ∆h²N2D =Q4πKD (W (u) - W (β². u))
W (u) Ver anexo I o II
W (β². u) Ver anexo IV A
Descenso en el pozo 1:
∆h11- ∆h²112D= Q4πKD W (u)…………………………………………. u = Sy.r²W4KDt
∆h12 - ∆h²122D= - Q4πKD W (u')……………………………………... u' = Sy.(2Z)²4KDt
β=2Z rw ……… 2z=rw.β(2z)²=r²w.β²
u' = Sy.r²w.β²4KDt
u' = β². u
∆h12 - ∆h²122D = - Q4πKD W (β². u)
∆hT - ∆h²T2D = (∆h11 - ∆h²112D) + (∆h12 - ∆h²122D )
∆hT - ∆h²T2D = Q4πKD W (u) - Q4πKD W (β². u)
∆hT - ∆h²T2D = Q4πKD (W (u) - W (β². u))W (u) Ver anexo I o II
W (β². u) Ver anexo IV A






∆h - ∆h²2D = 2.3Q4πKDlog ( 2.25kDtSy.r² )
Descenso en el piezómetro N:
∆hN1- ∆h²N12D = 2.3Q4πKDlog ( 2.25kDtSy.r²1 )
∆hN2 - ∆h²N22D =- 2.3Q4πKDlog ( 2.25kDtSy.r²2 )
∆hN - ∆h²N2D = ( ∆hN1 - ∆h²N12D) + ( ∆hN2 - ∆h²N22D )
∆hN - ∆h²N2D = 2.3Q4πKDlog ( 2.25kDtSy.r²1 ) - 2.3Q4πKDlog (2.25kDtSy.r²2 )
∆hN - ∆h²N2D = 2.3Q4πKD (log ( 2.25kDtSy.r²1 ) - log ( 2.25kDtSy.r²2 ))
∆hN - ∆h²N2D = 2.3Q4πKD log ( r2r1 )²
∆hN = 2.3Q2πKD log ( r2r1 )

Descenso en el pozo 1:
∆h11- ∆h²112D = 2.3Q4πKDlog ( 2.25kDtSy.r²w ) = ∆hw =∆f
∆h12 - ∆h²122D =- 2.3Q4πKDlog ( 2.25kDtSy.(2z)² )=- ∆r
∆hT - ∆h²T2D = (∆h11 - ∆h²112D) + (∆h12 - ∆h²122D )
∆hT - ∆h²T2D = 2.3Q4πKDlog (2.25kDtSy.r²w ) - 2.3Q4πKDlog ( 2.25kDtSy.(2z)² )
∆hT - ∆h²T2D = 2.3Q4πKD (log ( 2.25kDtSy.r²w ) - log ( 2.25kDtSy.(2z)² ))
∆hT - ∆h²T2D = 2.3Q4πKDlog ( 2zrwrw ) ²
∆hN - ∆h²T2D = 2.3Q2πKD log ( 2zrw )
ACUÍFERO LIBRE (BARRERA)
ACUÍFERO LIBRE EN RÉGIMEN PERMANENTE (BARRERA)
N

+Q
r2
r1
-Q

Z
Z
2
1


∆hr- ∆h²r2D = Q2πKDln ( rir )
Descenso en el piezómetro N:
∆hN1- ∆h²N12D = Q2πKDln (rir1 )
∆hN2 - ∆h²N22D = Q2πKDln rir2 )
∆hN - ∆h²N2D = ( ∆hN1 - ∆h²N12D )+ ( ∆hN2 - ∆h²N22D )
∆hN - ∆h²N2D = Q2πKDln ( rir1 ) + Q2πKDln ( rir2 )
∆hN - ∆h²N2D = Q2πKD ((ln ( rir1 ) + ln ( rir2 ))
∆hN - ∆h²N2D = Q2πKD ln ( ri²r1.r2 )
Descenso en el pozo 1:
∆h11 - ∆h²112D = Q2πKDln ( rirw ) =∆f
∆h12 - ∆h²122D = Q2πKDln ( ri2z ) = ∆b
∆hT - ∆h²T2D = (∆h11 - ∆h²112D ) + (∆h12 -...