Applets are programs based on the java language that are designed to run on your computer using the Java Run Time environment.

You can also find this information in the Technical Section of the Goulds pump catalog and in the TAPPI Technical Information sheet (TIS) 408-4. This method has been developed by Dr. G.G. Duffy of the university of Auckland, New Zealand.

Pulp suspensions are a special class of non Newtonian fluids. Depending on the consistency, the friction factor can be much greater than that of water. Dr. GG. Duffy's research has established friction parameters for 21 different types of pulp. These parameters allow the calculation of the friction afctor in feet per 100 feet of pipe.

This program will help you calculate the friction factor for each type of pulp suspension. It will also rank them in order of highest friction first. This method can only be used for pulp consistency higher than 2% and less than 6%. Two percent consistency pulp is considered to have the same friction factor as water.

The applet is designed to be used in English or French.

ENJOY! This is a short description of the method:

**PIPE FRICTION LOSS**

Empirical data for wood fiber suspensions (usually referred to as stock) have been gathered and correlated for many different types of pulps. Depending on flow rate and type of stock, different characteristic regions of flow friction loss vs. velocity have been established.

The friction loss curve for chemical pulp can be conveniently divided into three regions, as illustrated by the hatched areas of the two next figures.

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Figure 3-19 Pipe friction loss vs. velocity and consistency for chemical pulp. |
Figure 3-20 Pipe friction loss vs. velocity and consistency for mechanical pulp. |

**REGION 1**

Curve AB is a linear region where friction loss for a given pulp is a function of consistency, velocity, and pipe diameter. The velocity at the upper limit of this linear region (Point B) is designated vmax.

**REGION 2**

Curve BCD shows an initial decrease in friction loss (to Point C), after which the friction loss again increases. The intersection of the pulp friction loss curve with the friction loss curve for water (Point D) is termed the onset of drag reduction. The velocity at this point is designated vw.

**REGION 3**

Curve DE shows the friction loss curve for pulp fiber suspensions below the friction loss curve for water. This is due to a phenomenon called drag reduction.

Regions 2 and 3 are separated by the friction loss curve for water, which is a straight line with a slope approximately equal to 1.75, when plotted with log-log coordinates.

The friction loss curve for mechanical pulp, as illustrated in Figure 3-19, is divided into only two regions: Region 1 and 3. For this pulp type, the friction loss curve crosses the water curve at vw. There is no true vmax.

**PIPE FRICTION ESTIMATION PROCEDURE**

The bulk velocity (v) will depend upon the mass flow rate and pipe diameter (D) selected. The final value of v can be optimized to give the lowest capital investment and operating cost with due consideration of future demands or possible system expansion. The mass flow rate of wood fiber is of particular interest in the design of pipes and pumping systems since the purpose of the solution is to convey the fiber. The mass flow rate has the following relationship between the volumetric flow and the pulp fiber consistency:

[3-23] |

where M : mass flow rate of pulp;

C : pulp dry consistency ratio expressed as a percentage.

and

[3-24] |

The bulk velocity will fall into one of the regions previously discussed. When this region is identified, the appropriate correlations for determining pipe friction loss values may be selected. The following describes the procedure to be used for estimating pipe friction loss in each of the regions.

**REGION 1**

Region 1 is delimited by the bulk velocity of the stock (v), between the ranges:

where and

K' : Numerical coefficient (constant for a given pulp)

: Exponent (constant for a given pulp)

The relationship between the friction loss and the governing parameters is:

[3-25] |

where K : numerical coefficient (constant for a given pulp);

, , : exponents (constant for a given pulp).

**REGION 2**

Region 2 is delimited by the bulk velocity of the stock v, between the ranges:

where

If v is between vmax and vw, equation [3-25] may be used to determine at the maximum point vmax. The friction loss is then estimated and can be assumed to be constant for velocities in this region.

**REGION 3**

Region 3 is delimited by the bulk velocity of the stock v for the region:

A conservative estimate of friction loss is obtained by using the water curve as determined by Blasius' equation:

[3-26] |

Here Blasius' equation is used rather than Colebrook's, because the friction values for pulps were determined using smooth pipe (notably stainless steel copper and PVC), so that pipe roughness was not a factor in the determination of pressure drop. Blasius' equation is an accurate representation of friction values for water in such a case.

Previously published methods for calculating pipe friction loss of pulp suspensions gave a very conservative estimate of head loss, whereas the method just described gives a more accurate estimate.

Wood fiber does not significantly affect the overall density of the fiber-water solution. The specific gravity of the solution is therefore the same as water.

The Goulds pump catalogue also provides more information on the pulp friction calculation procedure.