Friction Loss of Pulp Suspensions in Pipe
Region 1 The upper limit of Region 1 in Figure 3 (Point B) is designated Vmax . The value of V max is determined using Equation [1] and data given in Table I or IA.
Vmax = K' Co (ft/s),
where K' = numerical coefficient (constant for a given pulp is attained from Table I or IA.
C = consistency (oven-dried, expressed as a percentage,
not decimally), and
o = exponent (constant for a given pulp), obtained from
Table I or IA.
It the proposed design velocity (V) is less than Vmax, the value of flow resistance (AH/L) may be calculated using Equation [2] and data given in Table II or IIA, and the appendices.
H/L = F K Va Cb Dy (ft/100 ft),
-
where F = factor to correct for temperature, pipe
roughness, pulp type, freeness, or safety factor (refer to Appendix D),
K = numerical coefficient (constant for a given pulp), obtained from Table II or IIA
, V = bulk velocity (ft/s),
C = consistency (oven-dried, expressed as a percentage, not decimally),
D = pipe inside diameter (in), and
For mechanical pumps, there is no true Vmax. The upper limit of the correlation equation (Equation [2]) is also given by Equation . In this case, the upper velocity is actually Vw.
Region 2
The lower limit of Region 2 in Figure 3 (Point B) is Vmax and the upper limit (Point D) is Vw. The velocity of the stock at the onset of drag reduction is determined using Equation [3]
Vw = 4.00 C1.40 (ft/s),
-
where C = consistency (oven-dried, expressed as a percentage, not decimally).
Region 3
A conservative estimate of friction loss is obtained by using the water curve. (AH/L)w can be obtained from a Friction Factor vs. Reynolds Number plot (Reference 3, for exam pie), or approximated from the following equation (based on the Blasius equation).
