# Existing methods of calculation of key parametres of pneumochamber pumps

At pneumatic transportation the pressure air should overcome own resistance, and also resistance of a material in the pipeline and resistance of elements of transport system. Thereof there is a pressure drop in a direction of a current of transporting gas which the corresponding pressure-blowing car should overcome.

Pressure losses occur also at expansion of gas and at other local resistance of the pipeline. All these resistance should be overcome to the transporting environment [5, 37, 107].For calculation of pressure losses at pneumatic transportation of loose materials the expressions offered by a number of authors [5, 36, 37, 97, 107, 108] are widely used. The general dependence defining pressure losses at transportation of a material in the horizontal pipeline, looks like

Where ΔP _{} - a pressure loss at movement of the transporting environment, the Pas; K - factor Gastershtadta; μ - concentration of a material.

The pressure loss at movement of the transporting environment is defined from expression [127]

Where ζ - a coefficient of friction at air movement in the pipeline; L - length of the pipeline, m; D - a pipeline interior diameter, m; r - density of the transporting environment, kg/m^{3}; U_{В} - an average speed of the transporting environment, km/s.

On experimental data of some authors [36, 48, 70] factor Gastershtadta kдля each material can vary in a certain range, even at low concentration of a material in a mix.

Proceeding from some data received by practical consideration, dependences by definition of factor Gastershtadta have been deduced. So, for example, Strahovich K.I. [36] specifies in return proportionality of factor Gastershtadta kот diameter of transport path Dв expression

Numerical value of factor Gastershtadta thus makes 1,253 both 0,213 in initial and final sectional view of a transporting path accordingly.

On Dzjadzio A.M.'s researches of [48] factor Gastershtadta k directly proportional to diameter of transport path Dи is defined by expression

Where - speed vitanija material particles, km/s; d_{3} - diameter of particles of a material, m; η - factor of dynamic viscosity, the Pas-with; Re - Reynolds's number.

Numerical value of factor Gastershtadta thus makes 4,043 both 1,115 in initial and final sectional view of a transporting path accordingly.

It is necessary to consider, that factor Gastershtadta to has no certain geometrical sense, and dependences available in the literature for its definition have been received by generalisation of experimental data. Despite the simple formula (1.1), all complexity by calculation of pressure losses is necessary on definition of factor Gastershtadta to which depends in various cases on various factors.

At transportation of loose materials factor Gastershtadta can accept various values (from 0,17 to 3,43), therefore it is expedient to define it only by practical consideration.The general pressure loss in the pipeline of installation of pneumatic transportation of loose materials is defined under the formula [5, 77]

Where ^_{rt} - the pressure losses arising at movement of the transporting environment, the Pas; _{ARJA} - pressure losses on ascending gradient of a cement aeromix, the Pas; ∆^{p}_{д} - pressure losses on dispersal of transported particles, the Pas; _{an automated workplace} - the additional pressure losses arising at interaction of particles of a material with walls of the transport pipeline and among themselves, the Pas.

The parity of these components can vary depending on geometry of a transport path, a mode of transportation and from properties of a transported material.

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The pressure losses arising at movement of the transporting environment are considered by many authors [4, 77, 127]. The formula (1.2) is In most cases applicable, results of calculations are relatives with the data received experimental by.

The additional pressure losses arising at interaction of particles of a material with walls of the transport pipeline also are among themselves caused by reduction of axial speed of particles of a material after their impacts with pipeline walls.

Segal I.S. has offered the dependence depending on concentration of a material in a mix [77]

Where λ the-factor of resistance in this case depending on number Fruda; μ - concentration of a material, kg/kg; L_{np} - the resulted length of transportation, m; D - diameter of the pipeline, m; U_{В} - speed of movement of air, km/s.

Numerous experiences of various researchers have shown, that the resistance factor dlja a case of movement of a material in the transport pipeline is not function from Reynolds's Re number. V.Bart's experiences which has established dependence between factor i number Fruda [5] are In this respect indicative

In the work [37] Velshof G has resulted the following general dependence for definition of the pressure losses arising at interaction of particles of a material with walls of the transport pipeline

Where G _{} - productivity of pneumotransport installation, kg/with; F - a pipeline area of cut, м^{2}; L - length of the pipeline, m; l_{c } - length of jump of a particle, m; U_{1}, U_{2} - speeds of particles of a material before blow about a wall of the transport pipeline accordingly, km/s.

Some scientific pressure losses at interaction of particles of a material among themselves allocate in separate group. Velshof G [37] has resulted some expressions for calculation by a pressure loss at interaction of particles of a material among themselves. One of them are proportional to a coefficient of friction and the forces operating in bulk mass of a material. At researches at many materials the internal friction always surpassed a friction about pipeline walls, therefore a material slid on pipeline walls, representing compact mass. Babuha G. L [9] asserts, that at pneumotransport of materials special influence on character of interaction of particles among themselves influences rotation of particles of a material. Also in work [9] transportation of polydisperse materials has been considered. It has been revealed, that the essential difference in speeds of particles of a material of different size is not present. Small particles gives a part of the energy to larger, therefore there is a growth of speed of large particles of a material and decrease in speed small therefore speeds of particles are levelled.

At movement pylevozdushnoj the mix on vertical or slope pipelines should add to general pressure losses the pressure created in weight of a column of a material, or pressure losses equal to it for the purpose of maintenance of a transported material in a suspension on a vertical lot.

There are expressions which are fair for materials with rather narrow grain size distribution with a small particles at which speed vitanija is much less than speed of transporting air.

Speed of movement of large particles in a riser always is less than speed of transporting air [36].

The formula of definition of a pressure loss on maintenance of a transported material in a suspension on a vertical lot will become

Where N - length of a vertical pipe run, m; U_{m} - speed of movement of large particles, km/s.

Olejnik V. N [84] has offered dependence for a pressure loss on maintenance of a transported material in a suspension on the vertical lot, considering interaction of particles of a material with riser walls

Pressure losses on dispersal of transported particles _{ARd} are caused by a difference between a full pressure loss on razgonnom a lot and a pressure loss at transportation of particles to the established mode of movement pylevozdushnoj mixes [5, 94]. Razumov I.M. has considered [94] dependence of these parametres in the work and has come to expression

Where U_{koh}, U_{НАЧ} - final and initial speeds of a particle, accordingly, km/s.

The structure of the formula for head loss definition on a lot of the message of speed to material particles can be theoretically defined [27] if to apply the theorem of linear momentum change

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To a thalweg of the mix, limited to the sectional views coinciding with the beginning and the end razgonnogo of a lot, boundary conditions in which are known [5,35]. The estimation of an additional pressure loss on razgonnom a lot ^rd is defined by expression

Where ξ_{p} - resistance factor razgonnogo a lot.

Values of factor of resistance fluctuates in rather narrow limits. On operational experiences of many scientists (Uspensky Century A, Dogin M. E, Karpov A.I., Dzjadzio A.M., Kostyuk G. F) [48-52, 108] the resistance factor is equal ζ_{p} = 1^{_}2,1.

From the analysis of results of experimental works follows, that:

- At vertical lots of pipelines the resistance factor should be increased by 15-20 %;

- The resistance factor essentially does not depend on airspeed change;

- The increase in diameter of particles influences reduction of factor of resistance as value of final speed of particles thus decreases;

- With increase in diameter of the pipeline this factor increases.

Besides considered above the basic making general pressure losses at transportation of loose materials (cement) there are still pressure losses which in some cases essentially influence total losses. These are losses in local resistance of a transport path (corners, bending downs, narrowings, etc.), the structures of a stream caused by infringement.

Representing a transported material as compact mass, in pipeline knees this dense grain-growing mass at movement changes the form [37]. Owing to the big internal friction a pressure loss

In such places considerably increases. If in long pipelines pressure is great, at the big pressure loss material moving can become practically impossible.

There is a set of sources of the literature in which the two-phase environment as incompressible is considered that guides to errors in calculation by a pressure loss. But is a few works which are devoted calculation of movement of the compressed two-phase environment and which consider change of density of a stream on length of the pipeline [37, 38, 64, 92, 117]. Shvab V. A in work [117] considered movement of a two-phase stream in its two various conditions. In the first variant uniform distribution of particles of a material in section the pipeline is supposed, and in the second movement of a material in the form of timber connectors or stoppers when speeds of the transporting environment and a transported material are approximately equal is supposed. Velshof G [37] results a design procedure of pressure losses at isothermal expansion of an air stream and transportation of a material of the big concentration. But this technique does not consider change of concentration of a material on all length of a transporting path.

Pashchatskij N.V. in article [92] considers movement of the compressed two-phase environment in the conditions of equality of speeds of a material phase and an air phase. However, at any various speeds of an air phase because of hydraulic resistance of particles of a material there will be a backlog of a material phase from the air.

Authors of works [37, 38, 64, 84, 92], considering movement of the compressed environment, take in attention contractibility of environment because of high speeds of the air environment. But at pneumotransport of loose materials change of density of the air environment depends, first of all, on pressure losses on pneumotransport of loose materials.

Urban JA, Kalinushkin M. P [60, 61, 107] result a design procedure of the expense of transporting gas (pressure air) through productivity of the pneumochamber pump.

The given formula gives only approached value of the weight expense of air as does not consider pump chamber volume, and also pressure of a submitted pressure air.

A number of authors [37, 38, 64, 84, 92, 117] use for definition of productivity of pneumochamber pumps the relation of mass of the loaded material to time of discharge of a pump chamber. At designing this relation to use difficult enough as dependence of productivity on pressure of air in a pump chamber and from the chamber sizes does not undertake in attention.

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