Nomenclature
R = Coil radius or Radius of curvature of curve
a = pipe diameter
a/R = curvature ratio
NDn = Dean number
NRe = Reynolds number
NRe’ = Modified Reynolds number
Nwe = Weissenberg number
NRe_crit = Critical Reynolds number for flow transition
from laminar to turbulent flow.
H = Coil pitch
L = original definition of Dean number
f = friction factor
K = consistency factor of power law model
\(K_{p}\) = consistency factor from pipe viscometer,\(\frac{\text{Ib}_{f}s^{n}}{\text{ft}^{2}}\)
n = behavioural index (exponent of power law fluids)
S = Slip ratio
P = Static pressure head
T = fluid relaxation time
β = inlet water fraction
Cc = dimensionless concentration defined as the ratio of
surfactant concentration to the lower critical concentration in a
straight pipe of C=250 ppm for ODEAO surfactant at which the
rod-like micelles cannot be formed and there is no drag reduction
effect.
Tc = dimensionless temperature, defined as the ratio of actual
surfactant solution to the lower critical absolute temperature of 275 K
where there is no drag reduction effect.
\(\varnothing\) is the angle of curvature measured from the inlet of the
curved tube.
\(m=\frac{1}{2}\alpha_{3}^{{}^{\prime}},\) a measure of the elasticity of the
fluid
\(r_{1}=\frac{r}{a}\)
\(\Psi=\) secondary flow stream function
\(h_{r}\) = pipe roughness projections
Subscripts
s = solvent
p = polymer
w = water