Silo internal state monitoring method and adjustable experimental device
By using acoustic emission devices and pressure sensors to monitor the internal state of the silo in a coordinated manner, the shortcomings of existing technologies in detecting light, vibration, and temperature are overcome. This enables accurate monitoring of the material flow state inside the silo and judgment of arching phenomena, reducing costs and improving applicability.
Patent Information
- Application Number
- CN202311547186.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-20
- Publication Date
- 2026-01-16
AI Technical Summary
Existing methods for monitoring the internal condition of silos suffer from problems such as blurred camera images due to light interference, susceptibility of vibration detection to external interference, susceptibility of temperature detection to material properties, and large errors in manual measurement, resulting in poor monitoring performance.
Acoustic emission devices and pressure sensors are used to monitor the internal state of the silo. By collecting the fluctuation differences between acoustic and pressure signals, the signal characteristics are analyzed to characterize the material flow state. Combined with R/S analysis and pressure calculation formula, it is determined whether arching occurs during the unloading process.
It enables precise monitoring of the material flow state inside the silo, reduces monitoring costs, and improves monitoring effectiveness, especially its applicability to silos made of non-transparent materials, and its adjustable conical silo bottom structure can adapt to different needs.
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Figure CN121346879A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of radio station communication, in particular to a silo internal state monitoring method and an adjustable experimental device. BACKGROUND
[0002] In the industrial field, vertical silos are widely used, not only for storing materials, but also for ensuring stable material supply. The relatively closed internal environment can also well protect the quality of the materials, and the overall design of the silo body can greatly improve the space utilization, better utilize the vertical space, and save the horizontal space occupation, which helps to effectively plan the factory layout and improve the site utilization efficiency. However, the energy-driven equipment added during the unloading process consumes a lot of energy and has a high cost of regular inspection and maintenance. Most importantly, the internal material accumulation problem may cause poor flow or blockage, and even more, the wall may be structurally damaged due to overpressure.
[0003] Therefore, monitoring the internal state of the silo is the key to preventing arching, ensuring smooth material unloading, and preventing damage to the silo structure. Modern vertical silos usually use a variety of methods to monitor the internal state of the silo. First, camera monitoring: a camera is installed inside the silo to monitor the movement of the material during unloading, or to monitor the changes on the surface of the material to determine whether arching occurs. Second, vibration detection: the vibration during the silo unloading process can also be used to monitor the movement of the material in the silo. By measuring the vibration signals around the silo, it can be determined whether the material flow is blocked, and whether arching or other problems exist. Third, temperature monitoring: changes in the internal temperature of the silo can also reflect the unloading and flow conditions of the material. These monitoring methods can be achieved by installing sensors and instruments to monitor the state of the material in the silo at any time and generate data to quickly determine whether there are abnormal phenomena. Finally, silo part stress monitoring: by measuring the displacement, strain, deformation, and other information of the silo parts, the stress condition of the silo can be understood, and whether the silo is affected by arching or other problems can be monitored to prevent and solve problems in a timely manner.
[0004] However, the above methods have some shortcomings. First, the installation position of the built-in camera is difficult to determine, which may cause the picture to be blurred due to light reasons, and the replacement and maintenance cost is high. The vibration detection signal is difficult to exclude external interference and is prone to deviation. The temperature detection signal is easily affected by the properties of some materials, such as heating of the material. Finally, the silo part stress monitoring method considers the error of manual measurement and the position selection of the measured parts, which will affect the monitoring effect.
[0005] Therefore, it is necessary to provide a silo internal state monitoring method and an adjustable experimental device to solve the above problems. SUMMARY
[0006] The purpose of the present application is to provide a silo internal state monitoring method and an adjustable experimental device, a method for monitoring the internal state of a silo by arranging an acoustic emission device and a pressure sensor, aiming to analyze the signal characteristics by collecting the fluctuation differences of the acoustic signals and the pressure signals, to characterize the material flow state in the adjustable silo, thereby playing a monitoring role.
[0007] To achieve the above-mentioned purpose, the present application provides a silo internal state monitoring adjustable experimental device, characterized in that: it comprises a silo body and a silo bottom, the silo body and the silo bottom are connected through a flange plate, a tray is arranged inside the silo body, a weight is arranged above the tray, the lower part of the tray is in contact with the bulk material placed inside the silo body, and a circular groove is arranged on the wall surface of the silo body and the silo bottom.
[0008] Preferably, the silo body is arranged in a cylindrical structure, the silo bottom is arranged in a spliced conical structure, and the silo bottom comprises upper, middle and lower parts, wherein the lower end inner diameter of the upper part is equal to the upper end inner diameter of the middle part, the lower end inner diameter of the middle part is equal to the upper end inner diameter of the lower part, and the upper, middle and lower parts are connected through flange plates.
[0009] Preferably, the circular grooves are symmetrically installed at the four side edges of the wall surfaces of the silo body and the silo bottom, six circular grooves are arranged on each side of the silo body, and four circular grooves are arranged on each side of the silo bottom, wherein the acoustic emission devices are arranged in the circular grooves symmetrically arranged on the left and right, the pressure sensors are arranged in the circular grooves symmetrically arranged on the front and back, and the connecting lines of the circular grooves symmetrically arranged on the front and back pass through the central axis of the silo body and are perpendicular to the connecting lines of the circular grooves symmetrically arranged on the left and right.
[0010] A silo internal state monitoring method, specifically comprising the following steps:
[0011] S1: close the bottom opening of the conical silo bottom, and make the bulk material enter the silo through the upper opening of the silo body and accumulate, and place the tray on the top surface of the material;
[0012] S2: after the material is accumulated, the computer opens the acoustic emission collection device and the pressure collector to start collecting signals;
[0013] S3: open the bottom opening of the conical silo bottom, start collecting acoustic signals and pressure signals, and continue until the unloading is completed;
[0014] S4: after the unloading is completed, the computer closes the collection of acoustic signals and pressure signals.
[0015] Preferably, in step S3, the collection of acoustic signals is as follows:
[0016] S31: The acoustic emission probes arranged on the left and right sides of the bin body and the bin bottom wall receive signals generated by the movement between materials and between materials and the wall during the unloading process in the bin body and the bin bottom. The signals received by the probes are collected by the acoustic emission device and finally transmitted to the computer for waveform display;
[0017] S32: The flow conditions of materials at different times and different height positions inside are determined by the fluctuations or static differences of the signal states;
[0018] When the materials in the bin are smoothly unloaded, the signal is in a stable and regular fluctuation state;
[0019] When the materials in the bin are blocked to form an arch phenomenon, the signal is in a suspended or slight fluctuation state.
[0020] Preferably, in step S32, the step of determining the corresponding relationship between the acoustic signal and the state in the bin is as follows:
[0021] S321: The collected original signal P(t) is filtered;
[0022] S322: The filtered signal P'(t) is subjected to discrete wavelet transform using db2 of the Daubechies series as the mother wavelet, W i,j =∑ t P'(t)ψ(2 i t-j);
[0023] Where W i,j is the wavelet function after discrete wavelet transform, t is time, ψ is the mother wavelet function, i and j are 0, ±1, ±2, … to obtain the decomposition signal at different scales, and the complex signal composed of different frequencies is decomposed into sub-signals at different frequency bands;
[0024] S323: The Hurst index of the wavelet function W i,j after the discrete transform is calculated using the R / S analysis method, where δ(t) = W i,j (t+dt)-W i,j (t) represents its increment, dt is the sampling interval, and for a time window length τ, the cumulative deviation is:
[0025]
[0026] Then:
[0027]
[0028]
[0029] S324: According to the Hurst analysis principle Judging the change trend of the signal characteristics, wherein H is the Hurst index;
[0030] When the Hurst index is greater than 0.5, the past trend is positively correlated with the future trend, and at this time, the unloading is smooth;
[0031] When the Hurst index is less than 0.5, the past trend is negatively correlated with the future trend, and at this time, the unloading is blocked;
[0032] S325: Correlate the signal characteristics with the evolution of the flow state in the bin body, and use the signal characteristics to represent the change trend of the material flow state in the bin body.
[0033] Preferably, in step S3, the collection of the pressure signal is as follows:
[0034] S311: Receive the pressure signal generated by the material on the wall surface during the unloading process in the bin body and the bin bottom through the pressure sensors arranged on the front and back sides of the bin body and the bin bottom wall;
[0035] S312: Transmit it to the computer through the pressure signal collector for waveform analysis, and judge whether the arching phenomenon occurs during the unloading process by analyzing the change of the wall surface pressure value at different time nodes and different position heights;
[0036] S313: When the material in the bin is smoothly discharged, the amplitude of the wall surface pressure is stable within the allowable range of the calculated value, and when the material in the bin is blocked to form an arching phenomenon, the amplitude of the wall surface pressure will appear overpressure fluctuation in the blocked area, exceeding the allowable range of the calculated value;
[0037] Wherein the calculated value is the allowable range of the horizontal pressure P h of the bin wall, and the formula is: And the formula for calculating the normal pressure Pn acting on the funnel wall is: n =(cos 2 α+ksin 2 α)P v Theoretical data is obtained;
[0038] In the formula: P v is the standard value of static vertical pressure, C h and C v are dynamic pressure correction coefficients, γ is the gravity density of the material, ρ is the hydraulic radius of the net cross section of the silo, for a cylindrical silo with an inner diameter of d n , ρ=d n / 4, μ is the friction coefficient of the material on the bin wall, e is the base of natural logarithm, s is the material depth, α is the inclination angle of the bin bottom inclined wall to the horizontal plane, and k is the lateral pressure coefficient of the material.
[0039] Therefore, the application adopts the above-mentioned silo internal state monitoring method and adjustable experimental device, and has the following beneficial effects.
[0040] (1) The method for monitoring the internal state of the silo by arranging the acoustic emission device and the pressure sensor in the application aims to collect the fluctuation difference of the acoustic signal and the pressure signal, analyze the signal characteristics to represent the material flow state in the adjustable silo, and thus play a monitoring role.
[0041] (2) In the application, the pressure sensor arranged in the wall circular groove collects the dynamic pressure signal during the unloading process, collects it into the pressure transmitter, and finally transmits it to the computer for analysis and processing, so as to realize the purpose of monitoring the flow state in the silo, and judge whether the arching phenomenon occurs in the silo according to the numerical value and the actual material flow state, and obtain the critical value of the wall pressure of the arching.
[0042] (3) In the application, the signals collected by the pressure sensor and the acoustic emission device are processed into image data for comparison and verification, and the current internal state change of the silo is comprehensively judged, which is a good monitoring method for silos with non-transparent materials.
[0043] (4) The spliced conical bottom in the application is more convenient and cost-saving compared with the traditional conical bottom, and for the comparison experiment of the opening diameter and the half-cone angle, the traditional conical bottom needs more models to meet the requirements, while the spliced conical bottom can change the opening diameter by disassembling different parts, and can meet the requirements by replacing conical bottoms with different half-cone angles.
[0044] The technical solutions of the application will be further described in detail below with reference to the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS
[0045] Figure 1 is a flow chart of a silo internal state monitoring method of the application;
[0046] Figure 2 is a circular groove schematic diagram of the application;
[0047] Figure 3 is a tray schematic diagram of the application;
[0048] Figure 4 is a spliced conical bottom schematic diagram of the application;
[0049] Figure 5 is a whole adjustable silo schematic diagram of the application;
[0050] Figure 6 is a working section schematic diagram of the application;
[0051] Figure 7is a schematic diagram of the working principle of the present application;
[0052] Reference signs
[0053] 1, bin body; 2, circular groove; 3, bin bottom; 4, flange plate; 5, weight; 6, tray; 7, bulk material; 8, acoustic emission device; 9, pressure sensor. DETAILED DESCRIPTION
[0054] The technical solutions of the present application are further described below through the drawings and examples.
[0055] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meanings understood by those skilled in the art to which the present application belongs.
[0056] The terms such as "comprise" or "include" and the like used in the present application mean that the elements before the terms encompass the elements listed after the terms, and do not exclude the possibility of also encompassing other elements. The orientations or positional relationships indicated by the terms "in", "on", "upper", "lower", etc. are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In the present application, unless otherwise explicitly specified and limited, the term "attached" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be a connection or interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.
[0057] Embodiment
[0058] As Figures 1-7 shown, the present application provides a silo internal state monitoring adjustable experimental device, characterized by: comprising a bin body 1 and a bin bottom 3, the bin body 1 and the bin bottom 3 are connected through a flange plate 4, the bin body 1 is internally provided with a tray 6, the upper portion of the tray 6 is provided with a weight 5, the lower portion of the tray 6 is in contact with bulk material 7 placed inside the bin body 1, and the wall surface of the bin body 1 and the bin bottom 3 is provided with a circular groove 2.
[0059] The bin body 1 is provided in a cylindrical structure, the bin bottom 3 is provided in a spliced conical structure, the bin bottom 3 comprises upper, middle and lower portions, wherein the lower end inner diameter of the upper portion of the upper portion is equal to the upper end inner diameter of the middle portion, the lower end inner diameter of the middle portion is equal to the upper end inner diameter of the lower portion, and the upper, middle and lower portions are connected through the flange plate 4.
[0060] The circular grooves 2 are symmetrically installed on the four sides of the walls of the chamber body 1 and the bottom of the chamber 3. There are six circular grooves 2 on each side of the chamber body 1 and four circular grooves 2 on each side of the bottom of the chamber 3. The circular grooves 2 symmetrically arranged on the left and right are equipped with acoustic emission devices 8, and the circular grooves symmetrically arranged in front and back are equipped with pressure sensors 9. The connecting line of the circular grooves symmetrically arranged in front and back passes through the central axis of the chamber body 1 and is perpendicular to the connecting line of the circular grooves symmetrically arranged on the left and right.
[0061] A method for monitoring the internal condition of a silo, specifically including the following steps:
[0062] S1: Close the bottom opening of the conical silo bottom, and allow bulk materials to enter the silo through the upper opening for stacking. Place the pallet on top of the material.
[0063] S2: After the material has been piled up, the computer turns on the acoustic emission acquisition device and pressure acquisition device to prepare to start acquiring signals.
[0064] S3: Open the bottom opening of the conical silo and begin collecting acoustic and pressure signals until unloading is complete;
[0065] In step S3, the acquisition of the acoustic signal is as follows:
[0066] S31: Acoustic emission probes arranged on the left and right sides of the silo body and bottom wall receive signals generated by the movement of materials between materials and between materials and walls during the unloading process in the silo body and bottom wall. The signals received by the probes are collected by the acoustic emission device and finally transmitted to the computer for waveform display.
[0067] S32: By utilizing the fluctuation or static difference in signal status, determine the material flow at different times and heights within the interior;
[0068] When the material in the warehouse is discharged smoothly, the signal is a stable, continuous and regular fluctuation.
[0069] When materials in the warehouse become blocked, forming an arch-like structure, the signal indicates a halt or slight fluctuation.
[0070] In step S32, the steps for determining the correspondence between the acoustic signal and the state inside the chamber are as follows:
[0071] S321: Filter the acquired raw signal P(t);
[0072] S322: The filtered signal P′(t) is subjected to discrete wavelet transform using the Daubechies db2 wavelet as the mother wavelet, W i,j =∑ t P′(t)ψ(2 i tj);
[0073] Among them Wi,j For the discrete wavelet transform of the wavelet function, t is time, ψ is the mother wavelet function, i, j are 0, ±1, ±2…, the decomposition signals at different scales are obtained, and the complex signal composed of different frequencies is decomposed into sub-signals at different frequency bands;
[0074] S323: using R / S analysis method, the Hurst index of the wavelet function W i,j after the discrete transform is calculated, where δ(t) = W i,j (t+dt)-W i,j (t) represents its increment, dt is the sampling interval, and for the time window length τ, the cumulative deviation is:
[0075]
[0076] Then:
[0077]
[0078]
[0079] S324: according to the Hurst analysis principle to determine the change trend of the signal characteristics, where H is the Hurst index;
[0080] When the Hurst index is greater than 0.5, the past trend and the future trend are positively correlated, and at this time, the unloading is smooth;
[0081] When the Hurst index is less than 0.5, the past trend and the future trend are negatively correlated, and at this time, the state is blocked;
[0082] S325: correlate the signal characteristics with the evolution of the flow state in the bin body, and use the signal characteristics to represent the change trend of the material flow state in the bin body.
[0083] In step S3, the collection of the pressure signal is as follows:
[0084] S311: receiving the pressure signal generated by the material on the wall surface during the unloading process in the bin body and the bin bottom through the pressure sensor arranged on the front and back sides of the bin body and the bin bottom wall surface;
[0085] S312: transmitting it to the computer through the pressure signal collector for waveform analysis, and judging whether the arching phenomenon occurs during the unloading process by analyzing the change of the wall surface pressure value at different time nodes and different position heights;
[0086] S313: When the material in the bin is smoothly discharged, the amplitude of the wall pressure is stable in the allowable range of the calculated value, and when the material in the bin is blocked to form an arch phenomenon, the amplitude of the wall pressure will appear overpressure fluctuation in the blocked area, exceeding the allowable range of the calculated value;
[0087] Wherein the calculated value is according to the horizontal pressure P h The calculation formula is: And the normal pressure Pn acting on the funnel wall is calculated as: P n =(cos 2 α+ksin 2 α)P v Theoretical data is obtained;
[0088] In the formula: P v is the standard value of static vertical pressure, C h and C v are dynamic pressure correction coefficients, γ is the gravity density of the material, ρ is the hydraulic radius of the net cross section of the silo, for a cylindrical silo with an inner diameter of d n , ρ=d n / 4, μ is the friction coefficient of the material to the silo wall, e is the base of natural logarithm, s is the material depth, α is the inclination angle of the inclined wall of the silo bottom to the horizontal plane, and k is the lateral pressure coefficient of the material.
[0089] S4: After the discharge is completed, the computer turns off the sound signal and the collection of the pressure signal.
[0090] In the application, the acoustic emission device is an acoustic emission probe, and the installation positions of the acoustic emission probe and the pressure sensor can be changed: one acoustic emission probe is alternately installed with one pressure sensor.
[0091] Therefore, the application adopts the above-mentioned silo internal state monitoring method and adjustable experimental device to cooperatively act by the pressure transmitter and the acoustic emission device, to jointly determine the arching phenomenon in the silo through the cooperative corresponding changes of the pressure signal and the acoustic signal, to represent the state in the silo by the signal characteristics, and to realize the monitoring of the material flow state in the silo.
[0092] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the application but not to limit them, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the application.
Claims
1. A silo internal condition monitoring adjustable experimental device, characterized in that: The silo body and the silo bottom are connected by flanges, the silo body is internally provided with a tray, the tray is provided with a weight above, and the tray is in contact with bulk materials placed inside the silo body below, and the wall surface of the silo body and the silo bottom is provided with a circular groove.
2. The adjustable experimental device for monitoring the internal state of a silo according to claim 1, characterized in that: The silo body is provided in a cylindrical structure, the silo bottom is provided in a spliced conical structure, and the silo bottom comprises upper, middle and lower parts, wherein the lower end inner diameter of the upper part is equal to the upper end inner diameter of the middle part, the lower end inner diameter of the middle part is equal to the upper end inner diameter of the lower part, and the upper, middle and lower parts are connected by flanges.
3. The adjustable experimental device for monitoring the internal state of a silo according to claim 1, characterized in that: The circular grooves are symmetrically installed at the four side edges of the wall surface of the silo body and the silo bottom, six circular grooves are provided on each side of the silo body, and four circular grooves are provided on each side of the silo bottom, wherein the sound emission devices are arranged in the circular grooves symmetrically arranged on the left and right, the pressure sensors are arranged in the circular grooves symmetrically arranged on the front and back, and the connecting lines of the circular grooves symmetrically arranged on the front and back pass through the central axis of the silo body and are perpendicular to the connecting lines of the circular grooves symmetrically arranged on the left and right.
4. A method of monitoring the internal state of a silo, characterised by: Specifically comprising the following steps: S1: closing the bottom opening of the conical silo bottom, bulk materials enter the silo through the upper opening of the silo and are accumulated, and the tray is placed on the material top surface; S2: after the material is accumulated, the computer opens the sound emission collection device and the pressure collector to start collecting signals; S3: opening the bottom opening of the conical silo bottom, starting the collection of sound signals and pressure signals until the unloading is completed; S4: after unloading, the computer closes the collection of sound signals and pressure signals.
5. A method of detecting the internal state of a silo according to claim 4, characterized in that: In step S3, the collection of sound signals is as follows: S31: the sound emission probes arranged on the left and right sides of the wall surface of the silo body and the silo bottom receive the signals generated by the movement between the materials and the wall surface in the unloading process inside the silo body and the silo bottom, the signals received by the probes are collected by the sound emission device, and finally transmitted to the computer for waveform display; S32: using the difference between the fluctuation and the static state of the signal to judge the flow condition of the materials at different time and height positions inside; When the materials in the silo are smoothly discharged, the signal is a stable and continuous fluctuation state; When the materials in the silo are blocked to form an arch phenomenon, the signal is in a suspended or slight fluctuation state.
6. A method of detecting the internal state of a silo according to claim 5, characterized in that: In step S32, the steps of judging the corresponding relationship between the sound signal and the state in the silo are as follows: S321: filtering the collected original signal P(t); S322: The filtered signal P'(t) is subjected to discrete wavelet transform using db2 of Daubechies series as a mother wavelet, W i,j =∑ t P'(t)ψ(2 i t-j) where W i,j is the wavelet function after discrete wavelet transform, t is time, ψ is the mother wavelet function, i, j are 0, ±1, ±2… to obtain the decomposition signals at different scales, and realize the decomposition of the complex signal composed of different frequencies into sub-signals at different frequency bands; S323: Calculate the Hurst exponent of the wavelet function W i,j after the discrete transformation by using the R / S analysis method, where δ(t) = W i,j (t+dt) - W i,j (t) represents the increment, dt is the sampling interval, and the cumulative deviation for the time window length τ is: Then: S324: According to the Hurst analysis principle determines the change trend of the signal characteristics, wherein H is the Hurst index. When the Hurst index is greater than 0.5, the past trend and the future trend are positively correlated, and at this time, the unloading is smooth; When the Hurst index is less than 0.5, the past trend and the future trend are negatively correlated, and at this time, the unloading is blocked; S325: correlating the signal characteristics with the evolution of the flow state in the silo to represent the change trend of the flow state of the materials in the silo by the signal characteristics.
7. A method of detecting the internal state of a silo according to claim 4, characterized in that: In step S3, the collection of pressure signals is as follows: S311: receiving the pressure signals generated by the materials on the wall surface in the unloading process inside the silo body and the silo bottom through the pressure sensors arranged on the front and back sides of the wall surface of the silo body and the silo bottom; S312: Transmits it to the computer through the pressure signal collector for waveform analysis. By analyzing the changes of wall pressure values at different time nodes and different position heights, it is determined whether the arching phenomenon occurs during the unloading process; S313: When the material in the bin is smoothly discharged, the amplitude of the wall pressure is stable within the allowed range of the calculated value. When the material in the bin is blocked to form an arching phenomenon, the amplitude of the wall pressure will have an overpressure fluctuation in the blocked area, exceeding the allowed range of the calculated value. where the calculated values are in terms of the horizontal pressure P h Calculation formula: and the normal pressure Pn acting on the funnel wall is calculated as: n = (cos 2 α + k sin 2 α) P v Theoretical data obtained; wherein: P v is the static vertical pressure standard value, C h and C v is the dynamic pressure correction coefficient, γ is the gravity density of the material; ρ is the hydraulic radius of the net cross section of the silo, for a cylindrical silo with an internal diameter d n ρ = d n / 4, μ is the friction coefficient of the material against the walls of the silo, e is the base of the natural logarithm, s is the depth of the material, α is the angle of inclination of the inclined walls of the bottom of the silo to the horizontal, and k is the lateral pressure coefficient of the material.
Citation Information
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