Selection and technological calculation of equipment for pulp pumping. Influence of pulp density on flotation results How to calculate pulp specific gravity
Pulp (suspension) parameters
Definitions and formulas for calculation
Pulp is usually called a mixture of mineral particles and water. In which solid particles are in suspension and evenly distributed in the volume of water.
If such a mixture is used as a medium for separation by density, then it is customary to call it not a pulp, but a suspension.
The pulp (or suspension) is characterized by the following parameters: solids content in the pulp by mass or volume, liquefaction by mass or volume, density.
P \u003d Q / (Q + W)
λ \u003d V T / (V T + V g),
Where V T \u003d Q / ρ; V f = F /Δ ; ρ and Δ – density respectively solid and liquid, kg/m 3 , if the liquid phase is water Δ=1000 kg/m 3 .
With highly liquefied pulps, the solid content in it is characterized by the mass of solids, ĸᴏᴛᴏᴩᴏᴇ is contained in the unit volume of the pulp, ᴛ.ᴇ. indicate how many grams or milligrams of solid matter per 1 m 3 or 1 liter of such liquefied pulp. This is how they characterize, for example, thickener overflows, filtrates and centrates. In this case, the conversion to the usual solids content by weight or volume is carried out in accordance with the formulas () according to the following formulas:
where Q 1 is the mass of solid per unit volume of the pulp (for example, in 1 l), g; V T 1 - volume of solid per unit volume of the pulp, l, V T 1 \u003d Q 1 / ρ.
When calculating the values of P and λ it is extremely important to carefully monitor the units of solid mass, pulp volume, and solid and water densities.
Pulp liquefaction by mass R is the ratio of the mass of liquid F to the mass of solid Q in a certain amount of pulp:
R \u003d W / Q \u003d (1-P) / R.
R = 1 / (R + 1).
Pulp liquefaction by weight can be calculated from its moisture content:
R = M / (100-M),
where M is pulp moisture content, %.
Pulp liquefaction by volume R 0 - the ratio of the volume of liquid to the volume of solid: R 0 \u003d V w / V T \u003d (1-λ) / λ; solid content by volume λ = 1 / (1 + R 0).
Pulp liquefaction by mass and volume are related to each other, as well as the solids content in the pulp by mass and volume:
pulp volume V is determined through liquefaction according to the formulas:
V = Q ( + ) or
In the formulas () and (), the units of volume will be determined by the units of density of the solid and liquid ( and Δ), which, of course, must be the same and correspond to the unit mass of the solid. For example, if the values and Δ are measured in kg/m 3 . then the value of Q should be expressed in kg, then the pulp volume V will be obtained in cubic meters.
The density of the pulp (or suspension) n is the mass per unit volume of the pulp. It is determined by directly weighing a certain volume of pulp (most often 1 liter) or calculated using the formulas below, if the solid content (mass or volume) or its liquefaction in the pulp is known, as well as the density of solid and liquid:
where p and Δ are defined in kilograms per cubic meter, P and λ - in fractions of a unit.
If the density of the pulp is determined by directly weighing a certain volume of the pulp (usually 1 liter), then it is possible to calculate the density of the solid (knowing its mass and volume content in the pulp) or, on the contrary, knowing the density of the solid, its mass or volume content in the pulp and liquefaction:
Here the pulp density is q·10 3 , kg/m 3 ; q is the mass of 1 l. Pulp, kg, obtained by direct weighing.
By the density of the pulp and the density of the solid, one can determine both the mass and volumetric liquefaction of the pulp:
In the formulas () - () the values \u200b\u200bof ρ p (ρ c), ρ, Δ, are determined in kilograms per cubic meter; P and λ are in fractions of a unit.
According to the parameters of the pulp (or suspension), you can directly calculate the mass of solid and water in 1 m 3 of pulp (suspension) or in 1 ton of pulp (suspension):
where Q is the mass of solid (for a suspension, the weight of the weighting agent) in 1 m 3 of pulp (suspension), kg; Q T - mass of solid (for a suspension of weighting agent) in 1 ton of pulp (suspension), tons;
W is the mass of water in 1 m 3 of pulp (suspension), kg; W T - mass of water in 1 ton of pulp (suspension), t.
5. Control questions on disciplines:
1. Basic concepts and types of screening for technological purposes: independent, preparatory, auxiliary, selective, dehydrating.
2. Screening surface of screens: grates, sheet screens with punched holes, rubber screens, wire meshes, spalt screens, jet screens. Clear area of screening surfaces (live area factor).
3. Granulometric composition of bulk material, size classes. The average diameter of an individual particle and a mixture of particles. Types of screening according to the size of the material: large, medium, fine, thin.
4. Sieve analysis, standard sieve scales. Apparatus for the production of sieve analysis. Characteristics of bulk material size by private and total yields of size classes. Forms of the total (cumulative) size characteristic: by ʼʼplusʼʼ and ʼʼminusʼʼ, semi-logarithmic, logarithmic.
5. Equations of material size characteristics (Godin–Andreev, Rozin–Rammler). Distribution curves. Calculation of the surface and the number of grains according to the equation of the total size characteristic. Calculation of the average grain diameter of bulk material.
6. Efficiency of screening - overall and for individual size classes. ʼʼLightʼʼ, ʼʼdifficultʼʼ and ʼʼhinderingʼʼ grains. The probability of grains passing through the sieve holes.
7. Influence on the screening process of various factors: material humidity, the shape and size of its particles, the shape of the holes and the inclination of the screening surface, the speed of the screened material, the amplitude and frequency of vibrations of the box of inertial screens. The sequence of separation of size classes: from large to small, from small to large, combined.
8.. Dependence of screening efficiency on screening duration, screen load and particle size distribution of screened material. Extraction of the fine class into the undersize product. ʼʼCrushingʼʼ oversize product.
9. General classification of screens. Fixed grate screens. Roller screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
10. Drum screens. Flat oscillating screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
11. Vibrating (inertial) screens with circular and elliptical vibrations, self-centering screens. Amplitude-frequency characteristic of inertial screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
12. Vibrating screens with linear vibrations. Types of vibrators. Screens with a self-balancing vibrator, self-synchronizing, self-balancing screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
13. Resonant horizontal screens. Electrovibrating inclined screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
14. Conditions affecting the performance and efficiency of vibrating screens. Technological calculation of inclined inertial screens. Hydraulic screens: arc screens, flat screens for fine screening.
15. Operation of screens. Ways of fastening sieves, replacement of sieves. Balancing of vibrating screens. Fight against sticking of the working surface and dust emission. Basic techniques for safe maintenance of screens.
16. Basic concepts and purpose of crushing processes. The degree of crushing and grinding. Stages and schemes of crushing and grinding. Specific surface area of loose material.
17. Modern ideas about the process of destruction of elastic-brittle and brittle solids under mechanical action. Physical and mechanical properties of rocks: strength, hardness, viscosity, plasticity, elasticity, their significance in the destruction processes. The scale of the fortress of rocks according to M.M. Protodyakonov.
18. Structure of rocks, porosity, defects, fracturing. Formation and propagation in a stressed elastic-brittle body of a bursting crack of ʼʼcriticalʼʼ length as a criterion for the stress of atomic-molecular bonds at the mouth of the crack. The physical essence of stress and its maximum possible value.
19. Laws of crushing rocks (Rittinger, Kirpichev-Kick, Rebinder, Bond), their essence, advantages and disadvantages, scope. The dependence of the specific energy consumption of the destruction of a piece or particle of a solid body on their size, a general expression for the energy consumption for reducing the size. Bond crushing work index, the possibility of its practical use. crushing selectivity, physical basis process, criteria and indicators characterizing selectivity. The role of defects and cracks in the separation of intergrowths of various minerals and their relationship with selectivity indicators.
20. Granulometric composition of the rock mass supplied to the crushing and screening plant. crushing methods. Crushing coarse, medium and fine. The degree of crushing, its definition. Schemes of crushing, stages of crushing. Open and closed crushing cycles. Operation of fine crushers in closed loop with a roar.
21. Technological efficiency of crushing. Energy indicators of crushing. Circulating load in crushing cycles. Technological features crushing in the processing of various mineral raw materials: ores of metallic and non-metallic minerals, coal.
22. Operation of crushing departments, requirements of technological mode maps for the final product of crushing. Optimum size of the crushed product ͵ entering the subsequent grinding operations. Pre-concentration operations in crushing cycles: dry magnetic separation, enrichment in heavy suspensions, etc.
23. Classification of crushing machines. Jaw crushers with simple and complex jaw movement. Device diagrams and principle of operation, formulas for determining the angle of grip, theoretical performance, swing frequency (for cone and jaw), crushing degree, power and metal consumption for crushing, advantages and disadvantages, applications.
24. Cone crushers for coarse crushing with upper suspension and lower crushing cone support. Cone reduction crushers. Cone crushers of medium and fine crushing. Crushers with hydraulic damping and adjustment of the loading gap. Eccentric free impact crusher. Device diagrams and principle of operation, formulas for determining the angle of grip, theoretical performance, swing frequency (for cone and jaw), crushing degree, power and metal consumption for crushing, advantages and disadvantages, applications.
25. Roll crushers, devices, peripheral speed of rolls, scope. The dependence of the diameter of the rolls on the size of crushed pieces. Crushers with smooth, corrugated and toothed rolls. Device diagrams and principle of operation, formulas for determining the angle of grip, theoretical performance, swing frequency (for cone and jaw), crushing degree, power and metal consumption for crushing, advantages and disadvantages, applications.
26. New types of crushing machines. Physical methods crushing: electro-hydraulic, cavitation, Snyder process, etc.
27. Machines for medium and fine crushing of soft and brittle rocks. Roll crushers for coal. Hammer and impact crushers, disintegrators. Schemes of the device and the principle of operation, degree of crushing, productivity, consumption of electricity and metal, control methods.
28. Selection of the type and size of crushers for medium and fine crushing to work in given conditions. Advantages of impact crushers Methods for automatic control of crushing units.
29. Features of destruction of mineral particles and grains in grinding processes. The size of the initial and final products. The concept of ʼʼscale factorʼʼ and its influence on the energy intensity of the grinding process based on the fineness of grinding.
30. Opening of ore and non-metallic minerals in the process of grinding, determination of opening parameters, selectivity of grinding, ways to increase it. The relationship between the processes of grinding and enrichment in the processing of ores with different sizes of disseminated minerals.
31. Grindability of minerals. Methods for determining grindability.
32. Kinetics of grinding, equations of the kinetics of grinding, the value of the parameters of the equation, their definition. Technological dependencies arising from the equation of grinding kinetics.
33. Types of mills, their classification. Rotary drum mills as the main grinding equipment at concentrating plants: ball mills with central discharge and through a grate, rod mills, ore-pebble mills. Design features, modes of operation, feeders, drive.
34. Speed modes of grinding in ball mills: waterfall, cascade, mixed, supercritical. Ball break angle. Critical and relative frequency of rotation of mills. Equations of circular and parabolic trajectory of balls in a mill. Coordinates of the characteristics of the points of the parabolic trajectory of the balls in the mill. Turnover of balls in the mill, cycles of movement of the grinding load.
35. The degree of filling the volume of the mill drum with grinding medium. Bulk mass of balls of rods, ore haul in a mill. Determination of the degree of filling the volume of the mill drum with grinding load.
36. The power consumed by the mill in cascade and waterfall modes of its operation. The dependence of useful power on the frequency of rotation of the mill and the degree of filling of its volume with grinding medium. Useful power formulas.
37. Patterns of wear of balls in a mill, equations for the characteristics of the size of balls in a mill with their regular additional loading. Rational loading of balls. Factors affecting the consumption of balls in the grinding process.
38. Drum mills of dry and wet self-grinding, features of the grinding process, its advantages. Formation of "critical size" classes in self-grinding mills and ways to reduce their accumulation. Semi-self-grinding mills. Ore-pebble mills, size and density of ore pebble, its consumption. design features, operating modes, feeders, drive. Design features, modes of operation, feeders, drive. Mill lining, lining types, service life. Areas of use. Operation of drum mills.
39. Vibrating, planetary, centrifugal, jet mills. The principle of operation, device diagrams. Areas of use.
40. Open and closed grinding cycles. The process of formation and establishment of a circulating load in a closed grinding cycle, the relationship with the productivity of the mill. Determination of the circulating load. throughput of the mill.
41. Technological schemes of grinding, stages of grinding. The number of stages and their connection with enrichment processes. Features of the use of rod, ball and ore-pebble mills in technological schemes staged grinding. Combination of ore-pebble grinding with primary ore self-grinding. Classifiers and hydrocyclones in grinding schemes. Features of interface nodes ʼʼmill - classifierʼʼ. Effect of classification efficiency on mill performance. Pulp, indicators of its composition, pulp properties.
42. Performance of mills by initial feed and design class, factors affecting performance. Determination of the productivity of mills. Calculation of mills by specific productivity.
43. Automation of grinding cycles, features of regulation of these cycles.
44. Technical and economic indicators of grinding. The cost of grinding for individual items of expenditure.
Main literature:
Perov V.A., Andreev E.E., Bilenko L.F. Crushing, grinding and screening of minerals: A textbook for universities. - M.: Nedra, 1990. - 301 p.
Additional literature:
1. Handbook of ore dressing. Preparatory processes / Ed. O.S. Bogdanova, V.A. Olevsky. 2nd edition. – M.: Nedra, 1982. – 366 p.
2. Donchenko A.A., Donchenko V.A. Handbook of an ore-dressing plant mechanic. – M.: Nedra, 1986. S. 4-130.
3. Magazines ʼʼEnrichment of oreʼʼ, ʼʼMining magazineʼʼ.
4. M.N. Kell. Enrichment of minerals. Collection of tasks. - L.: LGI, 1986. - 64 p.
Pulp (suspension) parameters - concept and types. Classification and features of the category "Pulp (suspension) parameters" 2017, 2018.
Pulp is a mixture of mineral particles and water. In which solid particles are in suspension and evenly distributed in the volume of water.
If such a mixture is used as a density separation medium, then it is not called a pulp, but a suspension.
The pulp (or suspension) is characterized by the following parameters: solids content in the pulp by mass or volume, liquefaction by mass or volume, density.
P \u003d Q / (Q + W)
λ \u003d V T / (V T + V W),
Where V T \u003d Q / ρ; V f = F /Δ ; ρ and Δ - the density of the solid and liquid, respectively, kg/m3, if the liquid phase is water Δ = 1000 kg/m3.
With highly liquefied pulps, the solid content in it is characterized by the mass of solid, which is contained in a unit volume of the pulp, i.e. indicate how many grams or milligrams of solid matter per 1 m 3 or 1 liter of such liquefied pulp. This characterizes, for example, thickener overflows, filtrates and centrates.
In this case, the conversion to the usual solid content by weight or volume is carried out in accordance with the formulas () according to the following formulas:
where Q 1 is the mass of solid per unit volume of the pulp (for example, in 1 l), g; V T 1 - volume of solid per unit volume of pulp, l, V T 1 = Q 1 /ρ.
When calculating the values of P and λ it is necessary to carefully monitor the units of solid mass, pulp volume and solid and water densities.
Pulp liquefaction by mass R is the ratio of the mass of liquid W to the mass of solid Q in a certain amount of pulp:
R \u003d W / Q \u003d (1-P) / R.
R = 1 / (R + 1).
Pulp liquefaction by weight can be calculated from its moisture content:
R = M / (100-M),
where M is pulp moisture content, %.
Liquefaction of the pulp by volume R 0 - the ratio of the volume of liquid to the volume of solid: R 0 \u003d V W / V T \u003d (1-λ) / λ; solid content by volume λ = 1 / (1 + R 0).
Pulp liquefaction by mass and volume are related to each other, as well as solids content in the pulp by mass and volume:
pulp volume V is determined through liquefaction according to the formulas:
V = Q ( + ) or
In the formulas () and (), the units of volume will be determined by the units of density of the solid and liquid ( and Δ), which, of course, must be the same and correspond to the unit mass of the solid. For example, if the values and Δ are measured in kg/m 3 . then the value of Q should be expressed in kg, then the pulp volume V will be obtained in cubic meters.
The density of the pulp (or suspension) n is the mass per unit volume of the pulp. It is determined by directly weighing a certain volume of pulp (most often 1 l) or calculated using the formulas below, if the solid content (mass or volume) or its liquefaction in the pulp is known, as well as the density of solid and liquid:
where p and Δ are defined in kilograms per cubic meter, P and λ - in fractions of a unit.
If the density of the pulp is determined by directly weighing a certain volume of the pulp (usually 1 liter), then it is possible to calculate the density of the solid (knowing its mass and volume content in the pulp) or, conversely, knowing the density of the solid, its mass or volume content in the pulp and liquefaction:
Here the pulp density is q·10 3 , kg/m 3 ; q - weight of 1 l. Pulp, kg, obtained by direct weighing.
By the density of the pulp and the density of the solid, one can determine both the mass and volumetric liquefaction of the pulp:
In the formulas () - () the values of ρ p (ρ c), ρ, Δ, are determined in kilograms per cubic meter; P and λ - in fractions of a unit.
According to the parameters of the pulp (or suspension), you can directly calculate the mass of solid and water in 1 m 3 of pulp (suspension) or in 1 ton of pulp (suspension):
where Q is the mass of solid (for a suspension, the weight of the weighting agent) in 1 m 3 of pulp (suspension), kg; Q T - mass of solid (for weighting agent suspension) in 1 ton of pulp (suspension), tons;
W is the mass of water in 1 m 3 of pulp (suspension), kg; W T - mass of water in 1 ton of pulp (suspension), t.
Control questions on the discipline:
1. Basic concepts and types of screening for technological purposes: independent, preparatory, auxiliary, selective, dehydrating.
2. Screening surface of screens: grates, sheet sieves with stamped holes, rubber sieves, wire mesh, spalt, jet sieves. Living section of screening surfaces (live section coefficient).
3. Granulometric composition of bulk material, size classes. The average diameter of an individual particle and a mixture of particles. Types of screening according to the size of the material: large, medium, fine, thin.
4. Sieve analysis, standard sieve scales. Apparatus for the production of sieve analysis. Characteristics of bulk material size by private and total yields of size classes. Forms of the total (cumulative) size characteristic: by "plus" and "minus", semi-logarithmic, logarithmic.
5. Equations of material size characteristics (Godin-Andreev, Rozin-Rammler). Distribution curves. Calculation of the surface and the number of grains according to the equation of the total size characteristic. Calculation of the average grain diameter of bulk material.
6. Efficiency of screening - overall and for individual size classes. "Easy", "difficult" and "obstructive" grains. The probability of grains passing through the sieve holes.
7. Influence on the screening process of various factors: moisture content of the material, the shape and size of its particles, the shape of the holes and the inclination of the screening surface, the speed of the screened material, the amplitude and frequency of vibrations of the box of inertial screens. The sequence of separation of size classes: from large to small, from small to large, combined.
Fig. 8. Dependence of the screening efficiency on the duration of screening, the load of the screen and the granulometric composition of the screened material. Extraction of the fine class into the undersize product. "Crushing" of the oversize product.
9. General classification of screens. Fixed grate screens. Roller screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
10. Drum screens. Flat oscillating screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
11. Vibrating (inertial) screens with circular and elliptical oscillations, self-centering screens. Amplitude-frequency characteristic of inertial screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
12. Vibrating screens with linear vibrations. Types of vibrators. Screens with a self-balancing vibrator, self-synchronizing, self-balancing screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
13. Resonant horizontal screens. Electrovibrating inclined screens. Scheme of the device, principle of operation, dimensions, scope, performance, performance indicators. Advantages and disadvantages.
14. Conditions affecting the performance and efficiency of vibrating screens. Technological calculation of inclined inertial screens. Hydraulic screens: arc screens, flat screens for fine screening.
15. Operation of screens. Ways of fastening sieves, replacement of sieves. Balancing of vibrating screens. Fight against sticking of a working surface and dust emission. Basic techniques for safe maintenance of screens.
16. Basic concepts and purpose of crushing processes. The degree of crushing and grinding. Stages and schemes of crushing and grinding. Specific surface area of loose material.
17. Modern ideas about the process of destruction of elastic-brittle and brittle solids under mechanical action. Physical and mechanical properties of rocks: strength, hardness, viscosity, plasticity, elasticity, their significance in the destruction processes. The scale of the fortress of rocks according to M.M. Protodyakonov.
18. Structure of rocks, porosity, defects, fracturing. Formation and propagation in a stressed elastic-brittle body of a rupturing crack of a "critical" length as a criterion for the resulting stress of atomic-molecular bonds at the mouth of the crack. The physical essence of stress and its maximum possible value.
19. Laws of crushing rocks (Rittinger, Kirpichev-Kik, Rebinder, Bond), their essence, advantages and disadvantages, scope. The dependence of the specific energy consumption of the destruction of a piece or particle of a solid body on their size, a general expression for the energy consumption for reducing the size. Bond crushing work index, the possibility of its practical use. Selectivity of crushing, the physical basis of the process, criteria and indicators characterizing the selectivity. The role of defects and cracks in the separation of intergrowths of various minerals and their relationship with selectivity indicators.
20. Granulometric composition of the rock mass supplied to the crushing and screening plant. crushing methods. Crushing coarse, medium and fine. The degree of crushing, its definition. Schemes of crushing, stages of crushing. Open and closed crushing cycles. The operation of fine crushers in a closed cycle with a screen.
21. Technological efficiency of crushing. Energy indicators of crushing. Circulating load in crushing cycles. Technological features of crushing in the processing of various mineral raw materials: ores of metallic and non-metallic minerals, coal.
22. Operation of crushing departments, requirements of technological mode maps for the final product of crushing. Optimum size of the crushed product entering the subsequent crushing operations. Pre-concentration operations in crushing cycles: dry magnetic separation, enrichment in heavy suspensions, etc.
23. Classification of crushing machines. Jaw crushers with simple and complex jaw movement. Schemes of the device and the principle of operation, formulas for determining the angle of capture, theoretical performance, swing frequency (for cone and jaw), crushing degree, electricity and metal consumption for crushing, advantages and disadvantages, applications.
24. Cone crushers for coarse crushing with upper suspension and lower crushing cone support. Cone reduction crushers. Cone crushers of medium and fine crushing. Crushers with hydraulic damping and adjustment of the loading gap. Non-eccentric inertial crusher. Schemes of the device and the principle of operation, formulas for determining the angle of capture, theoretical performance, swing frequency (for cone and jaw), crushing degree, electricity and metal consumption for crushing, advantages and disadvantages, applications.
25. Roll crushers, devices, peripheral speed of rolls, scope. The dependence of the diameter of the rolls on the size of crushed pieces. Crushers with smooth, corrugated and toothed rolls. Schemes of the device and the principle of operation, formulas for determining the angle of capture, theoretical performance, swing frequency (for cone and jaw), crushing degree, electricity and metal consumption for crushing, advantages and disadvantages, applications.
26. New types of crushing machines. Physical methods of crushing: electro-hydraulic, cavitation, Snyder process, etc.
27. Machines for medium and fine crushing of soft and brittle rocks. Roll crushers for coal. Hammer and impact crushers, disintegrators. Schemes of the device and the principle of operation, degree of crushing, productivity, consumption of electricity and metal, control methods.
28. Selection of the type and size of crushers for medium and fine crushing to work in given conditions. Advantages of impact crushers Methods for automatic control of crushing units.
29. Features of destruction of mineral particles and grains in grinding processes. The size of the initial and final products. The concept of "scale factor" and its influence on the energy intensity of the grinding process, depending on the fineness of grinding.
30. Opening of ore and non-metallic minerals in the process of grinding, determination of opening parameters, grinding selectivity, ways to increase it. The relationship between the processes of grinding and enrichment during the processing of ores with different sizes of disseminated minerals.
31. Grindability of minerals. Methods for determining grindability.
32. Kinetics of grinding, equations of kinetics of grinding, the value of the parameters of the equation, their definition. Technological dependencies arising from the equation of grinding kinetics.
33. Types of mills, their classification. Rotary drum mills as the main grinding equipment at concentrating plants: ball mills with central discharge and through a grate, rod mills, ore-pebble mills. Design features, modes of operation, feeders, drive.
34. Speed modes of grinding in ball mills: waterfall, cascade, mixed, supercritical. Ball break angle. Critical and relative frequency of rotation of mills. Equations of circular and parabolic trajectory of balls in a mill. Coordinates of the characteristics of the points of the parabolic trajectory of the balls in the mill. Turnover of balls in the mill, cycles of movement of the grinding load.
35. The degree of filling the volume of the mill drum with grinding medium. Bulk mass of balls of rods, ore haul in a mill. Determination of the degree of filling the volume of the mill drum with grinding load.
36. The power consumed by the mill in cascade and waterfall modes of its operation. The dependence of useful power on the frequency of rotation of the mill and the degree of filling of its volume with grinding medium. Useful power formulas.
37. Patterns of wear of balls in a mill, equations for the characteristics of the size of balls in a mill with their regular additional loading. Rational loading of balls. Factors affecting the consumption of balls in the grinding process.
38. Drum mills of dry and wet self-grinding, features of the grinding process, its advantages. Formation of "critical size" classes in self-grinding mills and ways to reduce their accumulation. Semi-self-grinding mills. Ore-pebble mills, size and density of ore pebble, its consumption. design features, operating modes, feeders, drive. Design features, modes of operation, feeders, drive. Mill lining, lining types, service life. Areas of use. Operation of drum mills.
39. Vibrating, planetary, centrifugal, jet mills. The principle of operation, device diagrams. Areas of use.
40. Open and closed grinding cycles. The process of formation and establishment of a circulating load in a closed grinding cycle, the relationship with the productivity of the mill. Determination of the circulating load. throughput of the mill.
41. Technological schemes of grinding, stages of grinding. The number of stages and their connection with enrichment processes. Features of the use of rod, ball and ore-pebble mills in technological schemes of staged grinding. Combination of ore-pebble grinding with primary ore self-grinding. Classifiers and hydrocyclones in grinding schemes. Features of interface nodes "mill - classifier". Effect of classification efficiency on mill performance. Pulp, indicators of its composition, pulp properties.
42. Performance of mills by initial feed and design class, factors affecting performance. Determination of the productivity of mills. Calculation of mills by specific productivity.
43. Automation of grinding cycles, features of regulation of these cycles.
44. Technical and economic indicators of grinding. The cost of grinding for individual items of expenditure.
Main literature:
Perov V.A., Andreev E.E., Bilenko L.F. Crushing, grinding and screening of minerals: A textbook for universities. - M.: Nedra, 1990. - 301 p.
Additional literature:
1. Handbook of ore dressing. Preparatory processes / Ed. O.S. Bogdanova, V.A. Olevsky. 2nd edition. - M.: Nedra, 1982. - 366 p.
2. Donchenko A.A., Donchenko V.A. Handbook of an ore-dressing plant mechanic. - M.: Nedra, 1986. S. 4-130.
3. Magazines "Ore enrichment", "Mining magazine".
4. M.N. Kell. Enrichment of minerals. Collection of tasks. - L.: LGI, 1986. - 64 p.
The invention relates to the automation of the technological process of flotation and can be used to automatically control the technological parameters of the flotation process - density, pulp aeration and mass concentration solid in the pulp. The device contains a measuring buoy placed in a damper, which is equipped with a damper in its lower part. The measuring buoy is suspended from a strain gauge force sensor, the output of which is connected to the input of the microcontroller. A movement mechanism is introduced into the device, connected by means of a rod to the damper damper. The movement mechanism is controlled by a microcontroller. The device operates cyclically. The cycle of work begins with the measurement of the weight of the displacer with the lower part of the damper open. At the same time, the density of the aerated pulp is calculated, after which the damper, under the action of the movement mechanism, closes the lower part of the damper, leaving a gap for the precipitated solid to exit. Air bubbles exit the damper and the weight of the displacer in the deaerated slurry is measured and the density of the deaerated slurry is calculated. Based on the density values of the aerated and deaerated pulp, the microcontroller calculates the degree of aeration of the pulp - the volumetric amount of air in percent in the pulp. Similarly, according to the appropriate formula, the microcontroller calculates the mass concentration of solids in the pulp. Information about the values of the density of aerated and deaerated pulp, as well as the degree of aeration of the pulp and the mass concentration of solids in the pulp is transmitted via a digital communication channel of the microcontroller to the upper level automated system control, as well as in the form of output analog signals of the microcontroller to external control devices. Device management (viewing current values, setting, entering constants) is carried out by means of the display and keyboard according to the graph in the "Menu" mode. The technical result is the creation of a device for measuring the density, the degree of aeration of the pulp and the mass concentration of solids in the pulp. 2 ill.
Drawings to the RF patent 2518153
The invention relates to automation, in particular to devices for monitoring and controlling flotation parameters. The most important flotation parameters are the density of the pulp, the volumetric percentage of air (degree of aeration) in the pulp and the mass percentage of solids (solid) in the pulp. A device for measuring density is known, containing as a sensitive element a displacer completely immersed in the pulp, the measuring element is a strain gauge. The disadvantage of the device is the control of only one pulp parameter - density, which in some specific cases is insufficient to control the flotation process.
A device is known that provides measurement of pulp aeration. The device contains channels for measuring the weight of the buoys in the pulp. One channel measures the weight of the displacer placed in the aerated pulp, the second channel measures the weight of the displacer placed in the deaerated (without air) pulp.
The conditions for measuring aerated and deaerated pulp are created in two special devices - dampers dispersed in the chamber of the flotation machine.
The disadvantages of the device include the variance in the change in the weight of the buoys due to sticking of solid pulp fractions and measurement channels for the buoy of aerated and deaerated pulp, the need to adjust two channels for measuring the weight of the buoys, and also the fact that the places for measuring the parameters of aerated and deaerated pulp are spaced apart in the volume of the flotation machine . The prototype of the invention is a device. The proposed device eliminates the listed disadvantages of the device.
This is achieved by introducing a damper with a damper, a movement mechanism connected by means of a connecting rod to the damper damper, a microcontroller equipped with a display and keyboard, input and output modules, digital channel communication, software blocks that implement the control of the movement mechanism, the calculation of the density of aerated and deaerated pulp, the degree of aeration of the pulp and the mass concentration of solids in the pulp. The proposed device is shown in Fig. 1, where the following are indicated:
1 - flotation machine,
3 - pulp,
4 - aerator,
5 - strain gauge force sensor,
6 - measuring thrust of the buoy,
7 - calmer,
7.1 - damper damper,
8 - measuring buoy,
9 - damper,
10 - movement mechanism,
11 - damper connecting rod,
12 - microcontroller,
12.1 - display of the microcontroller,
12.2 - microcontroller keyboard,
12.3 - input signal of the microcontroller,
12.4 - output control signal of the microcontroller,
12.5 - digital communication channel of the microcontroller,
13 - output signal of pulp aeration degree,
14 - output signal of the mass concentration of the solid.
The proposed device operates cyclically. Before commissioning the proposed device, the following procedures are carried out:
calibration of the measuring channel - the output signal of the strain gauge force sensor 5 with the measuring rod 6 suspended from it and the displacer 8 removed by pressing a specially dedicated keyboard button 12.2 is assigned (stored in the microcontroller 12) a conditional zero signal;
calibration of the measuring channel - when suspended from the measuring rod 6 of the reference weight, the output signal of the strain gauge force sensor 5 is assigned (stored in the microcontroller 12) a signal corresponding to the value of the weight of the reference weight by pressing a dedicated keyboard button 12.2;
determination of the weight P of the measuring buoy 8 - when the measuring buoy 8 is suspended from the measuring rod 6 while in the air, the buoy 8 is weighed, and by pressing a dedicated keyboard button 12.2 in the microcontroller 12, the weight of the buoy 8 is stored, and this weight is used when calculating the density aerated and deaerated pulp.
determination of the volume V6 of the measuring buoy 8 - for this purpose, the buoy 8 is lowered into the water and the weight of the buoy 8 in the water is weighed and stored in a manner similar to determining the weight of the measuring buoy 8 in the air. The measured weight of the buoy 8 in water is used to calculate its volume.
the input of constants into the microcontroller 12 is intended to use their values when calculating the measured parameters, cyclic control of the movement mechanism 10 and setting the data transfer rate via the digital communication channel 12.5 of the microcontroller 12.
Constants entered into the microcontroller:
device operation cycle - T, s
solid density - TV, g / cm 3
liquid density - w, g / cm 3
gravitational acceleration (world constant) - g, m/s 2 density measurement delay after connecting rod lowering - o, s
density measurement delay after lifting the connecting rod - n, s
device number - N, (0-255)
data transfer rate over a digital communication channel - baud
Formula for calculating the density a(d) of aerated (deaerated) pulp
where F T is the tension force of the measuring rod 6 of the measuring buoy 8 is the output signal of the strain gauge force sensor 5, P is the weight of the measuring buoy 8, V b is the volume of the measuring buoy 8 when it is immersed in water:
where water is the density of water;
After entering all the constants into the microcontroller 12, the proposed device is ready for use. The device works as follows.
In the initial state, the connecting rod 11 is in the upper position, and the lower part of the damper 7 is open. The damper is in a vertical position. The pacifier 7 is filled with aerated pulp. When the supply voltage is turned on, the microcontroller 12 measures the density of the aerated pulp with a set time delay. After the measurement of the density of the aerated pulp, the microcontroller 12 issues a control signal to the movement mechanism 10, the connecting rod 11 is lowered and, by means of the damper 9, closes the lower part of the damper 7, leaving a gap for the release of the settling solid fraction. The air bubbles in the damper 7 rise up and the deaerated pulp remains in the damper 7. After that, with a set delay, the density of the deaerated pulp is measured. Then, from the output of the microcontroller 12, a control signal is sent to the movement mechanism 10 to raise the connecting rod 11 to the upper position, which causes the lower part of the damper 7 to open, release the deaerated pulp from it and fill its volume with aerated pulp. This completes the control cycle of the movement mechanism 10, and the degree of aeration of the pulp and the mass concentration C of solids in the pulp are calculated.
The degree of aeration of the pulp is carried out according to the formula:
A is the density of the aerated pulp, d is the density of the deaerated pulp. The mass concentration of a solid is calculated by the formula:
TV is the density of the solid phase of the pulp in the pulp, w is the density of the liquid phase of the pulp.
To transfer information about the measured parameters to the upper level of the automated control system, it is necessary to set the device number via digital communication channel 12.5. In response to this request of the upper level system, the proposed device includes a digital communication channel 12.5 and provides information about the measured parameters (density of aerated and deaerated pulp, degree of pulp aeration and mass concentration of solids in the pulp). To transmit information to external control devices, the microcontroller 12 is equipped with outputs 13 and 14, to which the signals of the pulp aeration degree and mass concentration, respectively, are fed from the microcontroller 12.
Technological programming and intended use of the PAT Meter is carried out in accordance with the graph presented in Fig. 2, in the MENU mode. The graph contains branches: "VIEW CURRENT VALUES", "SETTINGS" and "INPUT CONSTANTS". Moving along the column "down" is carried out by pressing the first dedicated key of the keyboard 12.2 of the microcontroller 12, moving "to the right" is carried out by pressing the second dedicated button of the keyboard 12.2. Return to the top of the branch of the graph or to the top of the graph is carried out by pressing the third dedicated button on the keyboard 12.2 of the microcontroller 12.
In the branch "VIEW CURRENT VALUES" of the graph, by successively pressing the first dedicated button of the keyboard 12.2 on the display 12.1 of the microcontroller 12, the values of the density of aerated and deaerated pulp, the degree of aeration of the pulp in percent and the mass concentration of solids in the pulp in percent are viewed.
In the “SETTINGS” branch of the graph, by pressing the first dedicated button of the keyboard 12.2, calibration and calibration are sequentially performed and the weight and volume of the displacer 8 are entered into the microcontroller 12 in the manner indicated in this text of the description.
In the branch "INPUT CONSTANTS" of the graph, by moving along this branch, typing the input constant and pressing the first dedicated button of the keyboard 12.2 of the microcontroller 12, the following is entered: the cycle T of the device, the density of the solid, the density of the liquid phase of the pulp, the acceleration of free fall, the time delay o for measurement density after lowering the connecting rod 11, time delay n for measuring the density after raising the connecting rod 11, device number (one of 0-255), data transfer rate over a digital communication channel 12.5 (baud) of the microcontroller 12.
Thus, new elements are introduced into the proposed device - a damper 7 equipped with a damper 9, a connecting rod 11 and a movement mechanism 10; microcontroller 12, equipped with a display 12.1, a keyboard 12.2, an analog input 12.3, a discrete output 12.4, a digital communication channel 12.5 and analog outputs 13 and 14 for displaying the values of the measured parameters, as well as software tools that include software blocks: Viewing current values, Setting, Entering constants, Calculation of the density of aerated and deaerated pulp, Calculation of the degree of aeration of the pulp, Calculation of the mass concentration of solids in the pulp, Control of the movement mechanism, Input of an analog signal, Output of analog signals, Output of a discrete control signal, Control of a digital communication channel.
The proposed device is new, useful, technically feasible and meets the criteria of the invention.
Literature
1. Soroker L.V. etc. Management of flotation parameters. - M.: Nedra, 1979, p.53-59.
2. Density microprocessor weight "Density meter TM-1A", 2E2.843.017.RE, Moscow, JSC "Soyuztsvetmetavtomatika", 2004
3. RU 2432208 C1, January 29, 2010
CLAIM
A device for measuring the density, the degree of aeration of the pulp and the mass concentration of solids in the pulp, containing a measuring displacer placed in a damper located in the pulp; strain gauge force sensor connected to the measuring displacer by a rod, a computing device, to the input of which the output of the strain gauge force sensor is connected, characterized in that the damper is equipped with a damper and a movement mechanism is introduced; connecting rod connected at one end to the damper, and at the other end to the movement mechanism; a microcontroller is introduced into the device, equipped with a display and a keyboard, an analog input, a control output, analog outputs and a digital communication channel, and the analog input of the microcontroller is connected to the output of the strain gauge force sensor, the control output is connected to the control input of the movement mechanism, and the analog outputs of the microcontroller are connected to external control devices; the digital communication channel is connected to the upper level of the automation system, while the microcontroller is equipped with software blocks: Viewing current values, Setting, Entering constants, Calculating the density of aerated and deaerated pulp, Calculating the degree of pulp aeration, Calculating the mass concentration of solids in the pulp, Controlling the movement mechanism, Entering analog signal output, analog signal output, discrete control signal output, digital communication channel control.
Note: When solving these problems, one should pay attention to the units of quantities included in one or another formula for calculation. Units must correspond to those indicated in formulas (4.14) - (4.42).
Tasks 186-201. For given conditions (Table 4.5), determine the solid content in the pulp by mass and volume and the liquefaction of the pulp by mass and volume.
Tasks 202-207. For given conditions (Table 4.6) determine the volume of the pulp.
Tasks 208-217. For given conditions (Table 4.7), determine the solid content in the pulp by weight and volume and the liquefaction of the pulp by weight and volume.
Task 218-227. Based on the known density of the solid and liquid phases of the pulp and the content of solids in it by weight, determine the liquefaction of the pulp by weight and volume. Calculate also the density of the pulp. The conditions of the tasks are given in Table 4.8.
Tasks 228-240. Based on the known densities of the solid and liquid phases and the content of solids in the pulp by volume, calculate the liquefaction of the pulp by volume and mass. Calculate also the density of the pulp. The conditions of the tasks are given in Table. 4.9.
Tasks 241-253. Based on the known densities of the solid and liquid phases of the pulp and the volumetric liquefaction of the pulp, determine the solid content in the pulp by weight. Calculate also the density of the pulp. The conditions of the tasks are given in Table 4.10.
Tasks 254-266. Based on the known densities of the solid and liquid phases and the liquefaction of the pulp by mass, determine the solid content in the pulp by volume. Calculate also the density of the pulp. The conditions of the tasks are given in Table 4.11.
Tasks 267-279. Based on the known densities of the solid and liquid phases of the pulp and the content of solids in it by volume, determine the content of solids in the pulp by weight. Calculate also the density of the pulp. The conditions of the tasks are given in Table. 4.12.
Tasks 280-289. Based on the known densities of the solid and liquid phase of the pulp and the content of solids in it by weight, determine the content of solids in the pulp by volume. Calculate also the density of the pulp. The conditions of the tasks are given in Table 4.13.
Task 290-303. According to the known parameters of the pulp (density of the solid and liquid phases, solid content in the pulp by mass or volume), calculate the density of the pulp. The conditions of the tasks are given in Table 4.14.
According to the calculated density of the pulp, determine: in tasks 290-296, the solid content in the pulp by volume; in tasks 297-303 - solids content in the pulp by mass P. In addition, in each task, determine the amount of solid and liquid for 1 m 3 of pulp and the amount of solid and water for 1 ton of pulp. Similar calculations are carried out for suspensions.
Tasks 304-317. From the density of the solid and liquid phases and from the liquefaction of the pulp by mass or by volume, calculate the density of the pulp. The conditions of the tasks are given in Table 4.15.
According to the calculated density of the pulp, in tasks 304-310 determine the liquefaction of the pulp by volume, in tasks 311-317 - the liquefaction of the pulp by mass. In addition, in each task, determine the amount of solid and liquid for 1 m 3 of pulp and the amount of solid and water for 1 ton of pulp. Similar calculations are carried out for suspensions.
Tasks 318-330. Based on the mass of 1 liter of pulp (this value is obtained by testing by directly weighing a liter cup with pulp), calculate the solid content in the pulp and its liquefaction by mass, knowing the density of the solid and liquid phases. Calculate also the solids content in the pulp and its liquefaction by volume. The conditions of the tasks are given in Table 4.16.
Tasks 331-344. Based on the mass of 1 liter of pulp, determine the density of the solid, if the density of the liquid phase and the solid content in the pulp are known either by mass or by volume. The conditions of the tasks are given in Table 4.17.
Tasks 345-359. Determine the required amount of a weighting agent of known density and water to obtain 1 m 3 of an aqueous mineral suspension of a given density. The same is calculated to obtain 1 ton of suspension. The density of water is 1,000 kg/m3. The conditions of the tasks are given in Table 4.18.
Table 4.5
Task Conditions 186-201
| Task number | Initial data | Answers | ||||||
| Density | Weight, t | |||||||
| solid | liquid phase | hard dogo | kike | |||||
| 4.5 kg/l 5000 kg/m3 2.7 g/cm3 2.9 g/cm3 3.5 t/cm3 4000 kg/m3 5 g/cm3 4000 kg/m3 3.8 t/m 3 6.5 g/cm 3 5.5 g/cm 3 3000 kg/m 3 2.2 g/cm 3 3400 kg/m 3 4.8 kg/l 5.0 t/m 3 | 1 g/cm3 1 kg/l 1000 kg/m3 1.0 g/cm3 1200 kg/m3 1 g/cm3 1000 kg/m3 1.1 g/cm3 1.3 g/cm3 1 g/cm3 1000 kg/m3 1.1 g/cm3 1000 kg/m3 1 g/cm3 1200 kg/m3 1.0 g/cm3 | 0,29 0,66 0,26 0,27 0,40 0,40 0,24 0,20 0,29 0,30 0,33 0,23 0,16 0,23 0,25 0,22 | 0,085 0,26 0,11 0,11 0,16 0,14 0,06 0,06 0,10 0,06 0,083 0,097 0,08 0,08 0,06 0,053 | 2,45 0,5 2,8 2,7 1,5 1,5 3,2 4,0 2,45 2,3 2,0 3,3 5,2 3,3 3,0 3,54 | 10,8 2,8 7,56 8,0 5,23 6,0 15,8 16,0 9,0 15,0 11,0 9,8 11,4 11,4 14,6 17,8 |
Table 4.6
Task Conditions 202-2077
| Task number | Initial data | Answer:, m 3 | ||||
| Density | Solid mass, t | Pulp Liquefaction | ||||
| solid | liquid phase | by weight | by volume | |||
| 5000 kg/m3 3.2 g/cm3 4000 g/l 6200 kg/m3 2.8 g/cm3 1.6 kg/l | - 1000 kg/m 3 1.1 g/cm 3 1.0 kg/l - - | - 1,5 - - | - - - 4,5 | 174,6 141,6 321,4 |
Table 4.7
Task Conditions 208-217
| Task number | Initial data | Answers | |||||
| Density | Solid content in pulp, g/l | ||||||
| solid | liquid phase | ||||||
| 2950 kg/m 3 5.0 t/m 3 3.0 t/m 3 2400 kg/m 3 4000 kg/m 3 3.2 g/cm 3 2.85 g/cm 3 5730 kg/m 3 3, 3 t/m 3 4.1 t/m 3 | 1.0 g/cm3 1000 kg/m3 1000 g/l 1.1 g/cm3 1.2 g/cm3 1200 kg/m3 1000 kg/m3 1.0 t/m3 1.0 kg/l 1.0 kg/cm 3 | 0,25 0,21 0,14 0,32 0,24 0,26 0,12 0,22 0,21 0,26 | 0,1 0,05 0,05 0,16 0,087 0,12 0,044 0,048 0,075 0,079 | 3,0 3,8 6,3 2,2 3,0 2,8 7,6 3,5 3,7 2,8 | 9,0 19,0 19,0 5,23 10,5 7,5 21,7 19,8 12,3 11,5 |
Table 4.8
Conditions of tasks 218-227
| Task number | Initial data | Answers | ||||
| Density | Solids content in the pulp by weight | , kg / m 3 | ||||
| solid | liquid phase | |||||
| 2700 kg/m3 3.2 g/cm3 5.0 t/m3 4200 g/l 5500 kg/m3 4.3 t/m3 2.65 g/cm3 2900 kg/m3 3550 kg/ m 3 6.0 kg/l | 1.0 g/cm 3 1000 kg/m 3 1.0 g/cm 3 1.2 g/cm 3 1.0 g/cm 3 1000 g/l 1.0 t/m 3 1000 g/l 1, 2 g/cm 3 1.0 g/cm 3 | 0,2 0,15 0,45 0,35 0,6 0,1 0,4 0,5 0,65 0,3 | 4,0 5,7 1,2 1,85 0,67 1,5 1,0 0,57 2,33 | 10,8 18,1 6,0 6,5 3,68 38,7 4,0 2,9 1,68 14,0 |
Table 4.9
Task conditions 228-240
| Task number | Initial data | Answers | ||||
| Density | Pulp solids content by volume | , kg / m 3 | ||||
| solid | liquid phase | |||||
| 2700 kg/m3 3200 kg/l 4300 kg/m3 5.0 g/cm3 3.1 g/m3 2850 kg/m3 5.0 t/m3 5000 kg/m3 6.0 g/ cm 3 2750 kg/m 3 2.9 g/cm 3 3.8 kg/l 4200 g/l | 1.0 t/m 3 1.0 kg/l 1.0 g/cm 3 1000 kg/m 3 1000 g/l 1.2 kg/l 1500 kg/m 3 1.0 g/cm 3 1000 kg/ m 3 1.0 kg/l 1100 g/l 1100 kg/m 3 1.0 t/m 3 | 0,1 0,15 0,35 0,40 0,05 0,2 0,15 0,08 0,25 0,03 0,6 0,45 0,5 | 5,7 1,86 1,5 19,0 4,0 5,7 11,5 3,0 32,3 0,67 1,2 1,0 | 3,3 1,78 0,44 0,3 6,1 1,4 1,7 2,75 0,5 11,7 0,25 0,35 0,24 |
Table 4.10
Conditionstasks 241-253
| Task number | Initial data | Answers | |||
| Density | Pulp liquefaction by volume | , kg / m 3 | |||
| solid | liquid phase | ||||
| 2650 kg/m3 4000 kg/m3 3.2 t/m3 3100 kg/m3 4100 kg/m3 5.0 t/m3 2900 kg/m3 4600 kg/m3 4000 kg/m3 3 .5 t/m 3 2800 kg/m 3 4800 kg/m 3 5500 g/l | 1 g/cm 3 1.0 t/m 3 1000 kg/m 3 1.0 g/cm 3 1.2 g/cm 3 1200 kg/m 3 1.0 t/m 3 1.0 g/cm 3 1.0 g/cm 3 1000 kg/m 3 1.1 g/cm 3 1.2 t/m 3 1.0 g/cm 3 | 5,25 3,2 4,5 3,0 2,5 6,0 5,0 3,5 2,0 7,0 5,5 12,0 10,0 | 0,3 0,56 0,42 0,5 0,62 0,41 0,37 0,57 0,67 0,33 0,32 0,25 0,35 |
Table 4.11
Task Conditions 254-266
| Task number | Initial data | Answers | |||
| Density | Pulp liquefaction by weight | , kg / m 3 | |||
| solid | liquid phase | ||||
| 3.5 g/cm3 3800 kg/m3 4.0 g/cm3 5.0 g/cm3 5.5 t/m3 4300 kg/m3 3.0 g/cm3 2900 kg/m3 4.5 t/m3 3000 kg/m3 2.65 g/cm3 2900 kg/m3 4350 kg/m3 | 1000 kg/m3 1.0 t/m3 1.0 t/m3 1000 kg/m3 1000 kg/m3 1.0 t/m3 1200 kg/m3 1.0 g/cm3 1000 kg /m 3 1.0 g/cm 3 1000 kg/m 3 1.0 t/m 3 1.0 t/m 3 | 4,0 2,5 1,0 3,5 1,5 1,25 4,5 6,0 4,75 7,0 8,0 6,0 2,0 | 0,067 0,095 0,2 0,05 0,108 0,157 0,08 0,054 0,045 0,045 0,045 0,054 0,10 |
Table 4.12
Task Conditions 267-279
| Task number | Initial data | Answers | |||
| Density | Solid content by volume | , kg / m 3 | |||
| solid | liquid phase | ||||
| 3.5 g/cm3 3300 kg/m3 4000 kg/m3 5.0 t/m3 4.3 t/m3 2800 kg/m3 3100 kg/m3 4.5 g/cm3 2900 kg /m3 5750 kg/m3 3.8 t/m3 5.0 t/m3 2800 kg/m3 | 1000 kg/m 3 1.0 g/cm 3 1.0 t/m 3 1.0 kg/l 1000 kg/m 3 1.0 g/cm 3 1100 kg/m 3 1.2 t/m 3 1000 kg/m3 1.0 g/cm3 1000 g/l 1250 kg/m3 1.0 g/cm3 | 0,2 0,3 0,15 0,09 0,4 0,25 0,1 0,5 0,35 0,45 0,06 0,18 0,23 | 0,47 0,68 0,61 0,33 0,74 0,48 0,22 0,79 0,65 0,82 0,19 0,47 0,46 |
Table 4.13
Task Conditions 280-289
| Task number | Initial data | Answers | |||
| Density | Solids content in the pulp by weight | , kg / m 3 | |||
| solid | liquid phase | ||||
| 4.1 t/m 3 3.1 g/cm 3 2900 kg/m 3 3000 kg/m 3 4.8 g/cm 3 1900 kg/m 3 6.2 t/m 3 3600 kg/m 3 4, 0 t/m 3 2900 kg/m 3 | 1000 kg/m 3 1.0 t/m 3 1.0 g/cm 3 1.1 g/cm 3 1.0 t/m 3 1.0 kg/l 1000 kg/m 3 1.0 t/m 3 1.0 g/cm 3 1.1 g/cm 3 | 0,75 0,15 0,40 0,55 0,6 0,3 0,25 0,15 0,20 0,16 | 0,42 0,054 0,19 0,31 0,24 0,18 0,05 0,047 0,06 0,067 |
Table 4.14
Problem conditions 290 – 303
| Task number | Initial data | Answers | |||||||||||
| Density | , kg / m 3 | , t/m 3 | , t/m 3 | , t/t | , t/t | ||||||||
| solid | liquid phase | by weight | by volume | ||||||||||
| 5 t/m 3 3500 kg/m 3 4500 kg/m 3 2750 kg/m 3 2.9 t/m 3 5.0 t/m 3 2.65 g/cm 3 2200 kg/m 3 1800 g/l 4300 kg/m3 4.5 t/m3 3.3 g/cm3 2900 kg/m3 1.9 t/m3 | 1000 kg/m 3 1100 kg/m 3 1.0 t/m 3 1.0 t/m 3 1000 kg/m 3 1.2 t/m 3 1000 kg/m 3 1.0 t/m 3 1, 0 t/m 3 1.0 kg/l 1000 kg/m 3 1100 kg/l 1.0 t/m 3 1.0 kg/l | - - - - - - - | - - - - - - - | 0,05 0,15 0,18 0,27 0,06 0,227 0,38 - - - - - - - | - - - - - - - 0,10 0,49 0,32 0,44 0,67 0,6 0,43 | 0,24 0,51 0,63 0,74 0,17 1,13 1,0 0,11 0,63 0,43 0,68 1,32 0,99 0,53 | 0,95 0,94 0,85 0,73 0,93 0,93 0,62 0,85 0,65 0,9 0,85 0,66 0,66 0,72 | 0,2 0,35 0,45 0,5 0,15 0,55 0,62 0,1 0,49 0,32 0,44 0,67 0,6 0,43 | 0,8 0,65 0,55 0,5 0,85 0,45 0,38 0,9 0,51 0,68 0,56 0,33 0,4 0,57 |
Table 4.15
Task Conditions 304 – 317
| Task number | Initial data | Answers | ||||||||||
| Solid content in pulp, % | , kg / m 3 | , t/m 3 | , t/m 3 | , t/t | , t/t | ||||||
| solid | liquid phase | by weight | by volume | |||||||||
| 3.5 g/cm3 2800 kg/m3 4200 kg/m3 4.5 t/m3 2.65 g/cm3 3800 kg/m3 6200 kg/m3 2750 kg/m3 3.5 t /m3 2000 kg/m3 3 t/m3 6800 kg/m3 3.5 t/m3 5300 kg/m3 | 1000 kg/m3 1.0 g/cm3 1.1 g/cm3 1.0 t/m3 1000 kg/m3 1.2 t/m3 1.0 g/cm3 1.0 t/ m 3 1000 kg/m 3 1.0 t/m 3 1000 kg/m 3 1.1 t/m 3 1200 kg/m 3 1.0 g/cm 3 | 1,5 2,5 4,0 3,75 2,25 - - - - - - - | - - - - - - - 2,5 1,5 4,5 | 7,0 4,2 11,5 11,25 10,6 12,0 14,0 - - - - - - - | - - - - - - - 1,1 1,7 1,25 1,3 1,6 0,51 0,85 | 0,43 0,54 30,34 0,35 30,23 0,25 30,42 0,43 0,5 0,57 0,6 0,61 1,4 0,95 | 0,88 0,81 1,01 0,94 0,91 1,11 0,93 1,01 0,86 0,72 0,8 1,01 0,72 0,83 | 0,33 0,4 0,25 0,27 0,2 0,2 0,3 0,48 0,37 0,44 0,43 0,38 0,66 0,54 | 0,67 0,6 0,75 0,73 0,8 0,8 0,7 0,52 0,63 0,56 0,57 0,62 0,34 0,46 | |||
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