8.10 Head loss calculation paper pulp
Head loss calculation for paper pulp
The head loss calculation for paper pulp require special considerations since the behavior of pulp suspensions when flowing through a pipe is unusual from several aspects. The loss of head for chemical pulps goes through a maximum and a minimum value when the flow velocity increases from zero, and the head loss is finally less than the value for pure water.
Figure 8.10a Loss of head for chemical pulp in pipe flow.
For velocities up to point D, after the intersection of the two curves, the suspension flows like a plug surrounded by a thin boundary layer in which the whole of the viscous flow occurs. The character of the boundary layer varies according to the position of the working point on the curve:
- A to B The surface of the plug is disturbed by intermittent contact with the pipe wall.
- B to C The boundary layer consists mainly of pure water in laminar flow.
- C to E The flow in the boundary layer is turbulent.
Plug flow can be regarded as ended when the stress at the edge of the plug is equal to the ultimate shear stress of the network of fibres which form the plug. When the velocity increases beyond this point the plug breaks up and finally the whole cross section flows turbulently.
The friction loss curves for mechanical pulps do not usually have any maximum or minimum. The flow characteristics are modified by the relatively low strength of the network and the high proportion of non-fibrous solid material.
Calculation of pipe flow losses
The following symbols are used.
hL = head loss (m)
ρ = density of the suspension (kg/m³)
g = acceleration due to gravity (m/s²)
l = length of pipe (m)
d = diameter of pipe (m)
τ = shear stress (N/m²)
k = surface roughness of pipe (m)
v = flow velocity (m/s)
μ = dynamic viscosity (Ns/m²)
DS = proportion of weight of fiber (absolutely dry) (%)
Fk = length/diameter ratio of fibre
The pipe flow losses can be determined with the help of a number of diagrams, as reproduced below.
Figure 8.10b Pipe flow characteristics of chemical pulp
The non-dimensional flow parameter S is defined as:
and similarly the non-dimensional loss parameter F
The shear stress is a measure of the strength of the plug
of plaited fibres which occurs at most flow velocities in
practical operations.
τD = τ¹D * fF * fR * fM * fD (Equ. 8.10c)
If the pulp never dries out, fD = 1. If it has dried out and is absorbed again, fD = 0 75.
The diagrams, especially figure 8.10b, apply to chemical pulps. The different characteristics of mechanical pulps (fibres, networks, etc.) give the loss curve another shape and generally bigger losses. Correction factors should therefore be used. Approximate values can be obtained, however, using the above method provided that:
- the loss parameter F never assumes a value lower than the maximum point in figure 8.10b for the section of the curve S > 0,6.
- Fk = 1
- a safety factor of 1,2 should be used.
The guideline values for head losses in bends and fittings are given below in the form of equivalent pipe lengths.
It is typical of pulp suspensions, as for all plastic non-Newtonian liquids, that a certain yield shear stress (stiction) has to be overcome before a flow will be made to start up at all. This stiction can be reduced considerably by dilution.
Figure 8.10c Properties of chemical pulps
Example: Calculating loss of head for paper pulp
A chemical pulp, 281 m3/h, has to be pumped through a 70 m long pipe conduit made of stainless steel, diameter 300 mm. The pulp has never been dried and has a fineness grading 600 C.s.f., the temperature is 30°C and the concentration 2.7% (absolutely dry). The average fibre length is 2.4 mm and mean diameter 40 μm. Determine the loss of head in the conduit.
Fibre ratio Fk =2.4/0.040 = 60 → fF = 0.89
Stainless steel pipe k/d = 0.045/300 = 1.5 x 10-4 → fR = 1,11
Fineness grading 600 Csf → fM = 0,98
Undried chemical pulp → fD = 1
DS content 2.7% = 27 N/m²
Shear stress τD = 27 * 0.89 1.11 * 0.98 * 1 = 26.1 N/m³
Water at 30°C → μ = 0,8 x 10-3 Ns/m², ρ ≅ 1000 kg/m³
Flow velocity
The flow parameter
Read off loss parameter F = 1.05
hL = 2,4 m