Leq = Straight pipe length + equivalent length of all pipe fittings.
In most average plant situations, the Process design will require that a specific tonnage rate of solids be transported from a hopper, to a point at a level and distance away from the pump site. The transport medium is water at near ambient temperature. The process will most probably dictate that the slurry must be pumped at a certain pulp density. Thus, the required input data is:
The flow rate can be evaluated in numerous ways, but is usually established by the volume of solids to be pumped and the proposed concentration of solids and liquid.
The static head (vertical height on both the intake and discharge side of the pump) must be established, and the difference calculated to determine the net static head to be overcome by the pump.
The total static head can be calculated by taking eye of impeller of pump as datum.
Total Static Head = Total Discharge Head (Hd) - Total Suction Head (Hs)
Note: Total static head is usually positive but total Suction head may be positive, or negative.
Total Static Head (When Suction Head is Positive):
Total Static Head = Total Discharge Head (Hd) - Total Suction Head (Hs)
Total Static Head (When Suction Head is Negative):
Total Static Head = Total Discharge Head (Hd) + Total Suction Head (Hs)
It is also necessary to determine the effect of the slurry on the performance of the pump. It will be necessary to know:
These three values can now be entered into the nomograph shown in Figure (a), to determine the Head and Efficiency correcting ratio (HR and ER).
The pump head ratio (HR) is the ratio of slurry head produced to the head produced for water at the pump best-efficiency point (BEP) measured for water.
The pump efficiency ratio (ER) is the ratio of slurry efficiency to the efficiency for water at the pump BEP measured for water.
Figure (a) has been developed, from test and field results, to enable a reasonable estimation of HR and ER in most practical cases.
Figure (a): Performance of centrifugal pumps on slurry
Note: This chart applies to simple mixtures of solids and water only.
Limiting settling velocity can be calculated using Durand Formula:
Where, the parameter FL is dependent upon particle sizing and solids concentration.
Figure (b) represents the results of field tests on slurries of widely-graded sizing.
The particle sizing is simply expressed by the d50 term.
Note: FL increases with increasing Cv to about Cv = 30%, and beyond Cv = 30%, FL decreases with increasing Cv due to increasing interference of particles with each other.
Figure (b): Modified Durand’s limiting settling velocity parameter
(For particles of widely graded sizing)
The selection of the optimum pipe diameter is also of critical importance in any slurry pumping system. The use of a pipe that is too small can result in either insufficient flow rate or excessively high power requirements.
First, we choose a trial pipe internal diameter.
Note: If a pipe diameter has not been specified, the best way to arrive at one is to select the first pipe size giving a velocity above 3 m/s. This pipe size should be checked to ensure that the actual velocity is greater than the limiting settling velocity.
Velocity of slurry can be calculated as
When slurry flows through the pipe, it experiences some resistance due to which the flow loses some of its energy. The head loss is broadly classified into major and minor losses.
Slurry passing through a pipeline creates friction (or drag), against the pipe walls. The longer the pipeline, the greater the friction forces to be overcome by the slurry pump. Prior to any pump selection, it is therefore imperative that the actual length of the pipeline and details of any bends or other pipe variations be established, as accurately as possible.
Friction head loss can now be calculated by using Darcy’s formula:
Calculation of f
Here, k is the pipe internal surface roughness measured in meters in SI system.
Alternatively, Darcy Friction Factor, f can be calculated by using Warman Pipe Friction Chart shown in figure (c).
NOTE: For convenience, this chart is entered at values of Inside Diameter of Pipe: expressed in mm.
All the energy losses which are quite small in comparison with the energy losses due to friction come under minor head loss. These occur in the flowing fluid due to change in velocity of the flowing fluid.
Some of the minor head losses are:
a ) Loss at inlet to suction pipe
b)Loss at exit (pipe discharge)
c) Head Losses due to Contractions and Enlargements
These additional head losses are calculated by the use of formula provided in figure (d).
d) Loss of energy in various pipe fittings
e) Loss of energy in bends
Note: Here, v is used to indicate the upstream velocity and v1 is used for downstream velocity.
Hence, Total Head Loss = Friction head loss (hf) +Sum of all minor head losses (hL)
|Total Dynamic Head (Hm)
|= Total static head (Hd+Hs)+ Total head Loss ()
|(m. of slurry mixture)
This is the Total Dynamic Head calculated in terms of m. of slurry mixture.
By using the head ratio (HR) from figure (a), we are able to convert the calculated slurry total dynamic head to the equivalent water total dynamic head.
Total Dynamic Head(Hw) =
(m of water) Head Ratio(HR)
This is the Total Dynamic Head calculated in terms of m. of water.
Prior to the selection of a specific pump size, it is necessary to determine the pump type and material required.
Now we have to select the right type of pump by considering the operating costs, taking into account wear, maintenance and energy. Depending on the application it can be a horizontal, vertical or submersible Slurry Pump. It can also be a pump for extreme, heavy or normal wear conditions.
Selection of the type of materials to be used for slurry pumping applications is not a precise procedure. The procedure must first account for all the factors (variable characteristics) of the particular slurry.
The choice of wear parts is a balance between resistance to wear and cost of wear parts. There are two strategies for resisting wear:
The wear material has to be hard to resist cutting action of impinging solids!
The wear material has to be elastic to be able to absorb the shocks and rebound of particles!
The basic parameters required to make a selection of the type of material is:
Table (1): Classification of pumps according to solid particle size (sand hardness particles)
The material selection for the pump liners and impellers is made from two basic types of materials:
Metal is generally more tolerant to abuse than rubber and is the best choice for coarse material. Wear resistant cast alloys are used for slurry pump liners and impellers where conditions are not suited to rubber, such as with coarse or sharp edged particles, or on duties having high impeller peripheral velocities or high operating temperatures.
Elastomers are normally rubber in various qualities or polyurethane. Natural rubber is by far the major elastomers in slurry pumping and is the most cost effective for fine solids. Generally, depending on their sharpness and density, particle sizes of up to 5-8 mm can be pumped.
But, remember that oversize scrap and sharp particles can destroy the wear parts, especially the impeller.
Polyurethane is available for most pump ranges and offers excellent wear resistance for finer particles (< 0.15 mm), but is less sensitive to oversized scrap than rubber. It has its peak performance in low angular impact and sliding wear.
For slurry pumps, impellers are generally constructed in hard metal alloys or metal reinforced elastomers.
Let us look at different types of material used by Warman. A major advantage of the Warman slurry pump is the number of optional materials available. This enables a pump to be constructed with the most appropriate materials specifically to meet the duty requirements. It also allows existing pumps to be adapted in service to meet changed duty conditions, merely by changing individual parts.
A general description of some of the more common materials used in Warman slurry pump construction is listed in table (2) below.
|Alloy A03 is a maternsitic white iron which offers reasonable performance in mildly erosive duties, and where low impact levels are experienced. It is generally heat treated to stress relieve or reduce the amount of residual austenite in the matrix. The alloy is sensitive to section thickness, and the composition requires adjustment to prevent the formation of undesirable phases.
|Alloy A04 is a white iron having a hardness of 375HB in the annealed state. This low hardness allows A04 to be more readily machined than alloy A05. The alloy can be subsequently hardened to increase the wear resistance. A04 is not as erosive resistant as A05 and A12, and is not generally corrosion resistant.
|Alloy A05 is a wear resistant white iron that offers excellent performance under erosive conditions. The alloy can be effectively used in a wide range of slurry types. The high wear resistance of alloy A05 is provided by the presence of hard carbides within its microstructure. Alloy A05 is particularly suited to applications where mild corrosion resistance, as well as erosion resistance is required.
|Martensitic wear resistant alloy
|Martensitic white iron with moderate erosion resistance.
|HYPERCHROME® alloy is a hypereutectic white iron suitable for high wear duties, where corrosion is not considered a problem. It should be used in applications where A05 and A04 do not provide an adequate wear life. Alloy A12 can be used in mild alkaline slurries, between pH ranges of 8 to 14. The alloy may provide up to three times the wear life of A05 and A03 parts in some severe applications.
Tough 27% Cr
|Alloy A14 is a high chromium white cast iron offering high impact resistance and moderate erosion wear resistance. Alloy A14 is suitable for gravel pump applications where large slurry particles are present. A14 is much tougher than A05 but also exhibits a lower erosion wear resistance.
|Ni – Cr – Mo Steel
|Cast Steel Alloy
|A25 is an alloy steel having moderate wear resistance and high mechanical properties. The alloy is used for large castings where toughness is of primary importance.
28% Cr, Low C
|Alloy A49 is a corrosion resistant white iron suitable for low pH corrosion duties, where erosive wear is also a problem. The alloy is particularly suitable for Flu Gas Desulphurization (FGD) and other corrosive applications, where the pH is less than 4. The alloy can also be used in other mildly acidic environments. A49 has an erosion resistance similar to that of Ni-Hard 1.
36% Cr, Low C
|ULTRACHOME A51 is a premium erosion/corrosion alloy to be used where excellent erosion and corrosion resistance is required. The alloy has much improved corrosion resistance compared to alloy A49, whilst the erosion resistance is similar to Ni-Hard type alloy irons. The alloy is suitable for phosphoric acid duties, FGD duties, sulphuric acid, and other moderately corrosive applications.
|27 Cr-0.4 C5
|Alloy C14 is a corrosion resistant stainless steel suitable for use in acidic environments. The alloy is particularly suitable for Flue Gas Desulphurization (FGD) applications, where the pH is between 3 and 7. The alloy offers moderate erosion-corrosion resistance.
|Type 420C Stainless
|Martensitic Stainless Steel
|Alloy C21 is a martensitic stainless steel having a combination of high hardness and good general corrosion resistance. The alloy is machined in the annealed, or as cast condition and is subsequently hardened for service.
|Type 316 Stainless
|Austenitic Stainless Steel
|Alloy 23 (316SS) is an austenitic stainless steel having excellent corrosion resistance in reducing media. The molybdenum present in C23 increases its resistance to pitting corrosion. The alloy has good mechanical properties; however its low hardness gives it a low erosion resistance.
|Alloy C25 was specifically developed for sulphuric acid applications. The alloy can be used successfully in up to 85% Sulphuric acid. Alloy C25 also offers excellent corrosion resistance to a wide range of acids, and some strong alkalis. The alloy has poor resistance to erosive wear.
|26 Cr 5 Ni Stainless
Steel (CD-4M Cu)
|Duplex Stainless Steel
|Alloy C26 is a corrosion resistant stainless steel suitable for use in acidic environments. The alloy offers moderate erosion-corrosion resistance.
|Austenitic Corrosion Resistant Alloy
|Alloy C27 is an austenitic corrosion resistant alloy suitable for strong acid duties.
|27 Cr 31 Ni Stainless
|Austenitic Stainless Steel
|Alloy C30 is an all purpose austenitic stainless alloy for service in high corrosive conditions. C30 has excellent resistance to general corrosion, pitting, crevice corrosion, intergranular corrosion and stress corrosion cracking. The alloy was developed originally for use in phosphoric acid.
|Duplex Austenitic/ Ferritic Stainless Steel
|Alloy C55 is a duplex ferritic – austenitic stainless steel. It combines high strength and physical properties with excellent corrosion resistance. Alloy C55 offers improved resistance to stress corrosion cracking, pitting and crevice corrosion over C22, C23 and C25 grades of stainless steel.
|Ductile Grey Iron
|Alloy D21 is a ductile grade of grey iron used where higher physical properties and greater shock resistance are required compared to alloy G01
|Zinc Plated D21
|Alloy D81 is zinc plated ductile iron which is used for duties where higher physical properties and greater shock resistance are required in comparison to G01. D21 has a better atmospheric corrosion resistance than D21.
|Alloy G01 is an inexpensive alloy used where high physical strength and erosion resistance are not required.
|Tungsten Carbide V21 coated C21
|Ceramic Coated Stainless Steel
|J21 is a ceramic coating (V21) applied over a C21 substrate. The combination of these two materials provides high abrasive wear resistance together with high toughness. The tungsten carbide layer is deposited onto the C21 substrate using a special spray technique which yields minimal porosity and excellent interlayer adhesion. J21 is unaffected by differential thermal expansion and will not “spall”.
|Tungsten Carbide V21 coated C23
|Ceramic Coated Austenitic Stainless Steel
|J24 consists of a V21 ceramic coating deposited onto a C23 substrate using a special spray technique. The coating is very hard and offers excellent abrasive wear resistance. The spray technique gives a coating with minimal porosity and excellent interlayer bond strength. J24 is unaffected by differential thermal expansion and will not “space”.
|Chrome Oxide (Y03) coated C26
|Ceramic Coated Stainless Steel
|J26 consists of Y03 Ceramic Coating deposited onto a C26 substrate using a special spray technique. The coating is very hard and offers excellent abrasive wear resistance. The spray technique gives a coating with minimal porosity and excellent interlayer bond strength. J26 is unaffected by differential thermal expansion and will not spall.
|WC/Chromium/ Nickel Coated C26
|Tungsten Carbide V23 Coated C26
|J27 consists of a WC/Cr/Ni (V23) coating deposited onto a duplex stainless steel (C26) substrate using a thermal spray technique. The coating offers both abrasive wear resistance and corrosion resistance exhibiting minimal porosity.
|63 Ni 30 Cu Alloy
|Corrosion Resistant Alloy
|Alloy N02 is a nickel based corrosion resistant alloy for use in reducing acids and chlorides. It is used extensively in pickling and marine applications.
|58 Ni 16 Cr 16 Mo
|Alloy N04 is a nickel based corrosion resistant alloy specially resistant to oxidizing acids and reducing chlorides based solutions.
|55 Ni 22 Mo Alloy
|Corrosion Resistant Alloy
|Alloy N05 is a chemical resistant alloy which can be used in non-oxidizing environments. It has high physical properties and can be used successfully in high temperature environments.
|55 Ni 22 Cr 13 Mo
|Corrosion Resistant Alloy
|Alloy N22 is a nickel based corrosion resistant alloy especially resistant to extreme oxidizing acids and reducing chloride based solutions. Its resistance to pitting in these solutions is superior to that of N04 and N05.
|55 Ni 22 Cr 13 Mo
|Alloy N23 is a nickel based corrosion resistant alloy especially resistant to extreme oxidizing acids and reducing chloride based solutions. Its resistance to pitting in these solutions is superior to that of N04 and N05.
|Reinforced Structural Polymer
|P09 is a reinforced polyester resin used for structural pump parts as a replacement for heavier grey and ductile iron parts. The combination of glass fibers and a crystalline resin provides a material with excellent mechanical properties.
|Polyphenylene Sulphide (Ryton*) * Ryton is a trade name of the Phillips Chemical Company)
|Reinforced Structural Polymer
|P50 is a high-strength plastic suitable for parts requiring high-dimensional stability.
|Standard Impeller Rubber
|R08 is a black natural rubber, of low to medium hardness. R08 is used for impellers where superior erosive resistance is required in fine particle slurries. The hardness of R08 makes it more resistant to both chunking wear and dilation (ie, expansion caused by centrifugal forces) as compared to R26. R08 is generally only used for impellers.
|Anti Thermal Breakdown Rubber
|Anti Thermal Breakdown Rubber (ATB) is a soft natural rubber based on R26, but with improved thermal conductivity. It is intended for use as a liner material in slurry pumping applications where high impeller peripheral speeds are required.
|Standard Liner Rubber
|R26 is a black, soft natural rubber. It has superior erosion resistance to all other materials in fine particle slurry applications. The antioxidants and anti-degradents used in R26 have been optimized to improve storage life and reduce degradation during use. The high erosion resistance of R26 is provided by the combination of its high resilience, high tensile strength and low short hardness.
|Natural Rubber –
|R33 is a premium grade material for use where R26 does not provide sufficient wear life. It is a black natural rubber, of low hardness and is used for cyclone and pump liners and impellers where its superior physical properties give increased cut resistance to hard, sharp slurries.
|Natural Rubber Reinforced
|R38 is a black natural rubber, of medium hardness. R38 is used for impellers where superior erosive and tear resistance is required in fine particle slurries. The hardness and tear resistance of R38 makes it more resistant to both chunking wear and dilation (i.e., expansion caused by centrifugal forces) as compared to R26 and R08. R38 is generally only used for impellers.
|60 Duro Natural Rubber
|This is a hard (60 Duro) natural rubber product used for FGD duties primarily in GSL Pumps.
|S01 is an acid and ozone resistant rubber which is of low abrasion resistance. EPDM is non polar and difficult to bond to metal, therefore it is used typically in lip seals and volute seal applications.
|EPDM General Rubber
|S02 is an acid and ozone resistant rubber which is of medium abrasion resistance. EPDM is non polar giving it special chemical resistance. S02 is a specialty elastomer for use only in applications that require the properties of EPDM.
|High Temperature EPDM
|S03 is a high temperature and chemical resistant EPDM elastomer. It has been compounded so as to have a very low compression set and is therefore designed for use in sealing applications. This material is not designed for general use in parts subjects to erosive wear.
|Elastomer S12 is a synthetic rubber which is generally used in applications involving fats, oils and waxes. S12 has moderate erosion resistance.
|Butyl rubber is a highly saturated elastomer which has excellent chemical stability, and good resistance to heat and oxidation. The high saturation reduces the elastomeric properties of S21, and hence reduces its erosion resistance. In general S21 is used in acidic environments.
|Polychloroprene (Neoprene*) * Neoprene is the trademark of the Dupont Company
|Synthetic Elastomer (CR)
|Polychloroprene (Neoprene) is a high strength synthetic elastomer with dynamic properties only slightly inferior to natural rubber. It is less affected by temperature than natural rubber, and has excellent weathering and ozone resistance. It also exhibits excellent oil resistance.
|S45 is an erosion resistant synthetic rubber with excellent chemical resistance to hydrocarbons at elevated temperatures.
|Fluoroelastomer (Viton*) * Viton is the trademark of the Supon Company
|Synthetic Elastomer (FPM)
|S51 has exceptional resistance to oils and chemicals at elevated temperatures. Limited erosion resistance.
|Wear Resistant Polyurethane
|U01 is an erosion resistant material that performs well in elastomer applications where ‘tramp’ is a problem. This is attributed to the high tear and tensile strength of U01. However, its general erosion resistance is inferior to that of natural rubber (R26, R08).
|Z12 is the combination of Y11 Nitride
bonded Silicon Carbide and A12
Ultrachrome 27% Cr White Iron. It is
application for parts that require
resistance to low angle erosion and sliding
abrasion for particle sizes up to 5mm.
|Z13 is the combination of Y11 Nitrided bonded Silicon Carbide and A05 Ultrachrome 27% Cr White Iron. It is applicable for parts that require resistance to low angle erosion and sliding abrasion for particle sizes up to 5mm.
|Reaction Bonded Silicon Carbide/Foam
|Ceramic/ Polyurethane Foam Combination
|Z14 is used in cyclone spigot liners. The ceramic Y14 is coated in polyurethane foam. This foam provides protection and a light weight coating to seat the thin walled ceramic in position in the DMC casing.
|Nitride Bonded Silicon Carbide / Polyurethane
|Ceramic / Polyurethane Combination
|Z15 is a useful material for applications requiring low angle erosion and abrasion resistance. The Y08 Nitride bonded Silicon Carbide tiles provide a very hard, wear resistance surface with the U01 polyurethane providing support. The polyurethane backing allows the ‘brittle’ ceramic tile to float and absorb higher angle and large particle impacts.
|Nitride Bonded Silicon Carbide / UltrachromeTM 27% Cr
|Z16 is the combination of Y08 Nitrided bonded Silicon Carbide and A05 UltrachromeTM 27% Cr White Iron. It is applicable for parts that require resistance to low angle erosion and sliding abrasion for particle sizes up to 1000µm.
Table (2): Material specifications and descriptions
Pump charts are provided by the manufacturer. Pump charts differ from one manufacturer to the next and between different types of pumps. Here, we will learn how to select a pump from the charts provided by the manufacturer.
A selection chart as shown in Figure (e) makes it possible to do a preliminary pump selection by looking at a wide range of pump casing sizes for a specific impeller speed. This chart helps narrow down the choice of pumps that will satisfy the system requirements.
Figure (e): Pump family selection chart
For example, if the application called for a pump running at a nominal 1,800 revolutions per minute (rpm), that could provide 1,000 gallons per minute (gpm) at 100 feet of total head, the chart shows that 5 × 6 × 11 and 6 × 8 × 11 size pumps overlap on the selection chart and will likely be the two best sizes to evaluate further.
The following figure shows a typical pump performance chart for a given model, casing size, and impeller rotational speed. A great deal of information is crammed into one chart and this can be confusing at first.
Figure (f): Performance Curve Chart
Here, the Y axis (vertical) on this curve is the total dynamic head in feet and meters, and the X axis (horizontal) is the capacity (flow rate) in m3/hr and gpm.
Using the selection chart to narrow down the appropriate pump’s size for the duty point of 1,000 gpm and 100 feet of head, the manufacturer’s published curves can be referenced to help
determine the best pump for an application. Figure (f) shows the performance curve for a 5 × 6 × 11 pump running at 1,770 rpm. Information can be derived from the manufacturer’s pump curve for this application, including the following:
Note that data displayed on a manufacturer’s pump curve is based on 68 F or 20 C water. If a liquid other than water will be pumped, information on the manufacturer’s published curve must be adjusted for the liquid density and viscosity, which affects the head, flow, efficiency and pump input power.
It is necessary to understand the chart in detail.
A performance curve, also called head capacity curve, is a plot of Total Head vs. flow rate for a specific impeller diameter and speed. It is represented by downward sloping blue line in the above figure. The plot starts at zero flow. The head at this point corresponds to the shut-off head of the pump. Starting at this point, the head decreases until it reaches its minimum. This point is sometimes called the run-out point and represents the maximum flow of the pump. Beyond this, the pump cannot operate.
Each number above the head capacity curves to the right of the Y axis represents different impeller diameters.
For a new pump, our calculations of Total Head for a given flow rate will help determine the impeller diameter to be selected according to the performance curve. At flow rate of 1,000 gallons per minute (gpm) and total dynamic head of 100, the impeller diameter that meets the duty point falls between 10 and 10.5 inches.
Quite often, the operating point is located between two curves on the performance chart. We can calculate the impeller size required by linear interpolation. For example, if the operating point falls between the 10 inch and 10.5 inch impeller curve (see Figure (g)), the following equation will give the correct size:
Where, DOP is the required impeller diameter.
∆HOP is the pump total head at the operating point;
∆H10 is the pump total head at the intersection of the 10 inch impeller curve and flow rate;
∆H10.5 is the pump total head at the intersection of the 10.5 inch impeller curve and the flow rate.
Figure (g): Example for calculation of impeller diameter by linear interpolation
The B.E.P. (best efficiency point) is the point of highest efficiency of the pump. The numbers in the circles above the topmost head capacity curve are the pump efficiency, and the lines stemming from these circles are lines of constant efficiency. All points to the right or left of the B.E.P have a lower efficiency.
In the given example, at flow rate of 1,000 gallons per minute (gpm) and total dynamic head of 100 feet, the pump is 85 percent efficient at the rated point and 86 percent efficient at the best efficiency point (BEP).
In selecting a pump, one of the concerns is to optimize pumping efficiency. It is good practice to examine several performance charts at different speeds to see if one model satisfies the requirements more efficiently than another. Whenever possible the lowest pump speed should be selected, as this will save wear and tear on the rotating parts.
The horsepower curves give the power required to operate the pump within a certain range. For example (see Figure (f)), all points on the performance curve to the left of the 10 hp curve will be attainable with a 10 hp motor. All points to the left of 15 hp curve and to the right of the 10 hp curve will be attainable with a 15 hp motor. The horsepower can be calculated with the Total Dynamic Head, flow and efficiency at the operating point.
In the given figure, it is represented by somewhat greenish lines that run through the head capacity curves. It signifies lines of constant pump input power.
In the given example, the shaft power will be between 25 horsepower (hp) and 30 hp at the rated point. To ensure a non-overloading condition at the end of the curve, a 40-hp motor may be required.
The NPSH required by a centrifugal pump, at any given point on the Head/Quantity (H/Q) curve, is the minimum net amount of energy, that the fluid must have at the entrance to the impeller, to avoid cavitation. The pump manufacturer specifies a minimum requirement on the NPSH in order for the pump to operate at its design capacity.
The minimum NPSH required to avoid cavitation is shown on pump performance curves as “NPSH required” indicated by the vertical dashed lines with a triangle at the base and contains a number and word “NPSH”. The dashed lines are constant lines of NPSH (in feet) that the system must supply for the pump to operate with a 3 percent head loss. NPSH margin above this value is required for the pump to operate at the published head
In the given example, the value of NPSH3 is between 9 and 10 feet at the duty point.
The power required can now be calculated using formula:
Calculate and choose the next highest kilowatt motor frame size.
Cv Concentration of solids in mixture, by volume (percent)
Cw Concentration of solids in mixture, by weight (percent)
D Inside diameter of pipe (m)
D50 Average particle size of solids in a given dry sample. This size is equal to the screen aperture which would retain exactly 50% by weight of the total sample (mm or µm)
ER Efficiency Ratio
f Darcy Friction Factor (dimensionless)
FL Limiting Settling Velocity Factory (dimensionless)
g Gravitational constant (9.81 m/s2)
Hm Total Dynamic Head Developed by Pump when Pumping Mixture: Head of mixture (m)
Hw Total Dynamic Head developed by pump when pumping water: Head of mixture (m)
Hd Total Discharge Head: Head of Mixture (m)
Hs Total Suction Head: Head of Mixture (m)
hf Friction Head Loss: Head of mixture (m)
hL Minor Head Loss: Head of mixture (m)
k Pipe Material internal roughness
Leq Total Equivalent Length of Pipe
NPSH Net Positive Suction Head
P Power consumed at pump shaft (kW)
Q Mixture flow rate (m3/sec)
S Specific Gravity of Dry Solids
Sm Specific Gravity of Mixture
v Average Velocity of slurry (m/s)
vL Limiting Settling Velocity of mixture (m/s)
Z Net Static Head
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