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Friction Loss of Pulp Suspensions in Pipe - Section 3

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.

{DELTA}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

a, b, y = exponents (constant for a given pulp), obtained from Table II or IIA.

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). If V is between Vmax and Vw, Equation 2 may be used to determine AHIL at the maximum point (Vmax). Because the system must cope with the worst flow condition, AH/L at the maximum point (Vmax) can be used for all design velocities between Vmax and Vw.

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 example), or approximated from the following equation (based on the Blasius equation).