**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.

V_{max} = K' C^{o} (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 V_{max}, 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 V ^{a} C^{b} D^{y} (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 V_{max}. The upper limit of the correlation equation (Equation [2]) is also given by Equation . In this case, the upper velocity is actually V_{w}.

**Region 2: **The lower limit of Region 2 in Figure 3 (Point B) is V_{max} and the upper limit (Point D) is V_{w}. The velocity of the stock at the onset of drag reduction is determined using Equation [3] V_{w} = 4.00 C^{1.40} (ft/s),

where C = consistency (oven-dried, expressed as a percentage, not decimally). If V is between V_{max} and V_{w}, Equation 2 may be used to determine AHIL at the maximum point (V_{max}). Because the system must cope with the worst flow condition, AH/L at the maximum point (V_{max}) can be used for all design velocities between V_{max} and V_{w}.

**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).