Answer:
The answers to the questions are;
<em>Series flow</em>
Flow rate = cm³/s
Apparent permeability = 30/13 Darcy.
<em>Parallel flow</em>
Flow rates for each layer
q₁ =3 cm²
q₂ = 5 cm³/s
q₃ = 10 cm³/s
Total flow rate = q = 16 cm³/s
Apparent permeability = 16/3 Darcy.
Explanation:
Here we have the flow rate given by
q =
Where:
q = Flow rate
K = Permeability
dP = Potential difference = 1 atm
μ = Viscosity
Series flow
We note that the average permeability is given by
k' = = = 30/13 Darcy
P₁ - P₂ =
Therefore, q = ,
here A = 3 cm × 3 cm = 9 cm²
Hence q = = cm³/s.
Parallel flow
The apparent permeability k' = ∑(kh)/∑h = (1 + 5 + 10)/(1 + 1 + 1) = 16/3 Darcy
q =
A = W × h = 3 cm²
∴ we have q = = = 16 cm³/s.
Aliter
Therefore for each of the three layers, we have
q₁ = A₁ =3 cm²
q₁ = = cm³/s = 1 cm³/s
For q₂, we have
q₂ = = 5 cm³/s and q₃ = = 10 cm³/s
Therefore we have the total flow rate ∑q = q₁ + q₂ + q₃
= 1 cm³/s +5 cm³/s +10 cm³/s = 16 cm³/s.