Environmental Engineering Reference
In-Depth Information
Alas, because the flow has been decreased, the total power dissipation from
the turbine will remain constant. Using the correlation between Ohm's law
and equations governing the flow, head, and hydraulic resistance, design
trade-offs can be calculated (Figure 4.6 and Equation [4.5]). The basic equa-
tions governing the linear behavior of an electric circuit (Ohm's Law) are
HEAD
=
HEAD
+
HEAD
Total
Turbine
Injection
HEAD
=
Q
*
R
Turb
ine
Total
Turbine
(4.5)
HEAD
=
Q
*
R
Injection
Total
I
njection
POWER
=
Q
*
HEAD
Turbine
Total
Turbine
Given the resistances associated with turbine piping and aquifer hydraulics,
the relative trade-off among flow, head, and power output can be modeled
using Equation (4.5). Also, a correlation can be derived relating the trans-
missivity in the hydraulic circuit to the resistance in the equivalent electric
circuit. The allowable flow (current) through the circuit is proportional to
the transmissivity (resistance) in the circuit. The equations to determine the
resistance and conductance in an electrical circuit are
l
1
σ
⋅
A
R
=
;
G
=
=
(4.6)
σ
⋅
A
R
l
where R = resistance [Ω], G = conductance [S], l = length [m], σ = conductivity
[S/m], and A = area [m
2
]. The analogous equation in hydraulics for transmis-
sivity is
T
k A
r
T k b
⋅
=
= ⋅
(4.7)
κ γ
µ
⋅
⋅
b
T
=
where T = transmissivity [m
2
/s] or [ft
2
/min], k = hydraulic conductivity [m/s]
or [ft/min], A = area [m
2
] or [ft
2
], r = radius [m] or [ft], b = aquifer thick-
ness [m] or [ft], κ = intrinsic permeability [m
2
] or [ft
2
], γ = specific weight
of water [1000 kg/m
3
(at 4°C)], and µ = dynamic viscosity of water, [0.00089
Pa/s]. Comparison of these two equations shows that electrical conductance
is the corollary to transmissivity, and electrical conductivity is the corollary
