CN112540028B - Power law fluid viscosity parameter measuring and calculating method - Google Patents

Power law fluid viscosity parameter measuring and calculating method Download PDF

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CN112540028B
CN112540028B CN202011583817.8A CN202011583817A CN112540028B CN 112540028 B CN112540028 B CN 112540028B CN 202011583817 A CN202011583817 A CN 202011583817A CN 112540028 B CN112540028 B CN 112540028B
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power
law fluid
power law
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CN112540028A (en
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毕成
杨旭
鲁元
贠柯
丁勇
刘金娥
梁楠
陈梦诗
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Xian Special Equipment Inspection and Testing Institute
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G01N11/02Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material
    • G01N11/04Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material through a restricted passage, e.g. tube, aperture
    • G01N11/06Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material through a restricted passage, e.g. tube, aperture by timing the outflow of a known quantity
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G01N2011/0026Investigating specific flow properties of non-Newtonian fluids

Abstract

The invention discloses a measuring and calculating method of power law fluid viscosity parameters. The measuring and calculating method comprises the steps of firstly, carrying out measurement preparation debugging on a measuring device; secondly, measuring parameters; processing the measurement data and establishing a first binary equation of the viscosity parameter of the power law fluid; supplementing the closed condition of the binary equation, and establishing a second binary equation of the power law fluid viscosity parameter; and fifthly, calculating the viscosity parameter of the power law fluid. The method can be effectively applied to the rapid measurement of the viscosity parameters of the power law fluid under the limited condition or the crude experimental condition, and has the advantages of few measurement parameters, high measurement accuracy, remarkable effect and convenience in popularization.

Description

Power law fluid viscosity parameter measuring and calculating method
Technical Field
The invention belongs to the technical field of non-Newtonian fluid flow characteristic measurement, and particularly relates to a method for measuring and calculating power law fluid viscosity parameters.
Background
non-Newtonian complex fluids widely exist in various fields of the nature, except Newtonian fluids such as gas, pure liquid, low molecular weight solution and the like, the non-Newtonian fluids almost cover all fluid types of the earth nature and the ecosystem, and the non-Newtonian fluids are different from the Newtonian fluids in that the shear stress of the non-Newtonian fluids does not linearly change along with the shear deformation rate, so that the flow characteristics and the application research of the non-Newtonian fluids are always an important task in most fields such as oil exploitation, bio-pharmaceuticals, medical inspection, resource storage, food manufacturing, industrial manufacturing, energy power and the like.
The power law fluid is a typical non-Newtonian fluid, the shear stress and the shear deformation rate of the non-Newtonian fluid follow a power law exponential distribution law, the non-Newtonian fluid is the most common non-Newtonian fluid, the viscosity parameter of the non-Newtonian fluid can directly reflect the flow characteristics of the non-Newtonian fluid, and the non-Newtonian fluid has a very important significance for the application of the non-Newtonian fluid in various fields. In the prior art, the research and detection on the viscosity of the Newtonian fluid are very mature, for example, the viscosity of the Newtonian fluid can be simply and quickly obtained by methods such as capillary tubes, flat plate translation/rotation, falling bodies and the like, but for the power law fluid, only apparent viscosity can be obtained, the apparent viscosity can only qualitatively reflect the viscosity characteristic of the power law fluid, accurate and quantitative description cannot be realized, the efficacy of the power law fluid in an application link can be misjudged, and therefore the viscosity parameters of the power law fluid, namely the consistency coefficient and the power law index, need to be accurately detected.
The existing instrument or experimental facility capable of accurately detecting the power-law fluid viscosity parameter is complex and expensive, or the experimental condition requirement is high, and a measuring and calculating method capable of quickly, simply and accurately measuring the power-law fluid viscosity parameter under limited conditions or simple experimental conditions is also lacked in the prior art.
Disclosure of Invention
The invention aims to solve the technical problem of providing a power law fluid viscosity parameter measuring device aiming at the defects in the prior art, the device is simple in structure, reasonable in design and convenient to implement, can be effectively applied to the rapid measurement of the power law fluid viscosity parameters under limited conditions or simple and crude experimental conditions by combining with a measuring and calculating method, and is few in measurement parameters, high in measurement accuracy, remarkable in effect and convenient to popularize.
In order to solve the technical problems, the invention adopts the technical scheme that: the utility model provides a measuring device of power law fluid viscosity parameter, includes open-ended cylinder container, the spherical granule of uniform diameter is filled in the cylinder container, forms the porous region, the upper portion of porous region forms the free zone that is used for holding power law fluid, the bottom of cylinder container is connected with the discharge pipe, be provided with the valve that is used for controlling power law fluid to discharge on the discharge pipe.
The power law fluid viscosity parameter measuring device is characterized in that the ratio of the inner diameter of the cylindrical container to the diameter of the spherical particles is larger than or equal to 10, the ratio of the diameter of the discharge pipe to the diameter of the spherical particles ranges from 0.5 to 0.9, and the ratio of the length of the discharge pipe to the inner diameter of the cylindrical container ranges from 1 to 3.
The ratio of the height of the porous region to the inner diameter of the cylindrical container ranges from 1 to 2.
The invention also discloses a method for measuring and calculating the power law fluid viscosity parameter by adopting the device, which comprises the following steps:
step one, carrying out measurement preparation debugging on a measuring device;
step two, parameter measurement;
processing the measurement data, and establishing a first binary equation of the viscosity parameter of the power law fluid;
supplementing the closed condition of the binary equation, and establishing a second binary equation of the power law fluid viscosity parameter;
and step five, calculating the viscosity parameter of the power law fluid.
In the method for measuring and calculating the power law fluid viscosity parameter, in the first step, the specific process of measuring the measuring device and preparing for debugging comprises the following steps: filling power-law fluid to be detected into a cylindrical container, and enabling the ratio of the height of the power-law fluid in a free area to the height of a porous area to be more than or equal to 2; the valve is then opened to allow the power law fluid to settle out of the drain by its own weight, and closed when a continuous fluid column is formed.
In the method for measuring and calculating the power law fluid viscosity parameter, the specific process of measuring the parameter in the second step comprises the following steps: opening the valve to make the power law fluid to be measured continuously discharge by self gravity, and when the liquid level height h of the free zone is reduced1Height h from porous region2When equal, the valve is closed and the discharge time Δ t of the power-law fluid and the discharge volume V of the power-law fluid are recorded.
In the method for measuring and calculating the power-law fluid viscosity parameter, the specific process of processing the measurement data and establishing the first binary equation of the power-law fluid viscosity parameter in the third step comprises the following steps: height h of liquid level falling according to free zone1And the discharge time delta t, calculating the apparent velocity of the power law fluid in the porous zone
Figure GDA0003307110050000032
Calculating the flow rate Q and the speed u of the power-law fluid in the discharge pipe according to the discharge volume V and the discharge time delta t of the power-law fluid0(ii) a According to a viscous resistance formula of a uniform spherical particle stacking porous structure, a first binary equation of a power law fluid viscosity parameter is established as follows:
Figure GDA0003307110050000033
wherein rho is the density of the power law fluid to be measured, g is the gravity acceleration, xi is the local resistance coefficient, dpIs the diameter of the spherical particles filled in the porous area, K is the consistency coefficient, and n is the power law index.
In the method for measuring and calculating the power-law fluid viscosity parameter, the closed condition of the binary equation is supplemented in the fourth step, and the specific process of establishing the second binary equation of the power-law fluid viscosity parameter comprises the following steps: changing the diameter of spherical particles filled in a porous area in the measuring device, repeating the first step to the third step, and establishing a second binary equation of the power law fluid viscosity parameter.
In the method for measuring and calculating the power-law fluid viscosity parameter, in the fifth step, the viscosity parameter of the power-law fluid comprises a consistency coefficient K, a power-law index n and an apparent viscosity mu.
In the method for measuring and calculating the viscosity parameter of the power-law fluid, the specific process for calculating the viscosity parameter of the power-law fluid in the fifth step comprises the following steps: combining the first binary equation with the second binary equation to obtain a binary equation set related to the consistency coefficient K and the power law index n, and solving to obtain the consistency coefficient K and the power law index n of the power law fluid;the apparent viscosity mu is according to the formula
Figure GDA0003307110050000031
And (6) calculating.
Compared with the prior art, the invention has the following advantages:
1. the measuring device has the advantages of simple structure, reasonable design and convenient realization.
2. The measuring and calculating method provided by the invention is based on the seepage characteristics of the power law fluid in a regular and ordered porous structure, an equation of viscous flow resistance is established, the viscous parameters and the apparent viscosity of the power law fluid can be measured simultaneously, the established method has universality, the method is suitable for any power law fluid which can finish porous seepage by depending on gravity, no external power is required, and the detection cost and complexity are obviously reduced.
3. The method has the advantages of clear theory, few measurement parameters, high measurement accuracy, suitability for rapidly measuring the viscosity parameters of the power law fluid under limited conditions or crude experimental conditions, great portability and convenience, remarkable effect and convenience in popularization.
In conclusion, the measuring device disclosed by the invention is simple in structure, reasonable in design and convenient to implement, can be effectively applied to the rapid measurement of the viscosity parameters of the power law fluid under limited conditions or crude experimental conditions by combining with a measuring and calculating method, and is few in measurement parameters, high in measurement accuracy, remarkable in effect and convenient to popularize.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a schematic structural diagram of a measuring device according to the present invention;
FIG. 2 is a flowchart of the measurement and calculation method of the present invention.
Description of reference numerals:
1-a cylindrical container; 2-spherical particles; 3-a porous region;
4-free region; 5-a discharge pipe; 6, a valve.
Detailed Description
As shown in figure 1, the power law fluid viscosity parameter measuring device comprises an open cylindrical container 1, spherical particles 2 with equal diameters are filled in the cylindrical container 1 to form a porous region 3, a free region 4 for containing power law fluid is formed at the upper part of the porous region 3, a discharge pipe 5 is connected to the bottom of the cylindrical container 1, and a valve 6 for controlling the discharge of the power law fluid is arranged on the discharge pipe 5.
In practice, the upper part of the cylindrical container 1 and the lower part of the discharge pipe 5 are both open to the atmosphere.
In this embodiment, the ratio of the inner diameter of the cylindrical container 1 to the diameter of the spherical particles 2 is greater than or equal to 10, the ratio of the diameter of the discharge pipe 5 to the diameter of the spherical particles 2 ranges from 0.5 to 0.9, and the ratio of the length of the discharge pipe 5 to the inner diameter of the cylindrical container 1 ranges from 1 to 3.
In this embodiment, the ratio of the height of the porous region 3 to the inner diameter of the cylindrical container 1 is in the range of 1-2.
As shown in fig. 2, the method for measuring and calculating power law fluid viscosity parameters of the present invention includes the following steps:
step one, carrying out measurement preparation debugging on a measuring device;
step two, parameter measurement;
processing the measurement data, and establishing a first binary equation of the power law fluid viscosity parameter;
supplementing the closed condition of the binary equation, and establishing a second binary equation of the power law fluid viscosity parameter;
and step five, calculating the viscosity parameter of the power law fluid.
In this embodiment, the specific process of performing measurement preparation debugging on the measurement device in the first step includes: filling power-law fluid to be measured into the cylindrical container 1, and enabling the ratio of the height of the power-law fluid in the free region 4 to the height of the porous region 3 to be more than or equal to 2; the valve 6 is then opened to allow the power law fluid to settle out of the drain 5 by its own weight, and the valve 6 is closed when a continuous fluid column is formed.
In specific implementation, the power-law fluid to be measured comprises a pseudoplastic fluid and an expandable fluid, the power-law fluid is a non-Newtonian fluid subjected to shear stress tau and shear deformation rate u in a flowing process and obeying power-law exponential distribution, namely:
Figure GDA0003307110050000051
in the formula, K is the consistency coefficient of the power law fluid, n is the power law index, and y is the distance from the fluid to the wall surface. When n <1, the fluid is a pseudoplastic fluid; when n >1, the fluid is an intumescent fluid; in particular, when n is 1, the fluid is newtonian, and K is the viscosity of the fluid.
During specific implementation, the valve 6 is opened and the opening degree of the valve 6 is reasonably controlled, so that the discharged fluid is ensured to be in a laminar flow state, namely the discharged fluid is in a uniform and continuous fluid liquid column state.
In this embodiment, the specific process of measuring the parameters in step two includes: opening the valve 6 to continuously discharge the power law fluid to be measured by the gravity of the power law fluid, and when the free zone 4 is lowered, the liquid level h is lowered1Height h from porous region 32When equal, the valve 6 is closed and the discharge time Δ t of the power law fluid and the discharge volume V of the power law fluid are recorded.
In this embodiment, the specific process of processing the measurement data and establishing the first equation of the power-law fluid viscosity parameter in step three includes: the height h of the liquid level falling according to the free zone 41And the discharge time Deltat, calculating the apparent velocity of the power-law fluid in the porous zone 3
Figure GDA0003307110050000061
Calculating the flow rate Q and the speed u of the power-law fluid in the discharge pipe 5 according to the discharge volume V and the discharge time delta t of the power-law fluid0(ii) a According to a viscous resistance formula of a uniform spherical particle stacking porous structure, a first binary equation of a power law fluid viscosity parameter is established as follows:
Figure GDA0003307110050000062
wherein rho is the density of the power law fluid to be measured, g is the gravity acceleration, xi is the local resistance coefficient, dpThe diameter of the spherical particles 2 filled in the porous region 3, K is the consistency coefficient, and n is the power law index.
In particular, the apparent velocity of the power-law fluid in the porous region 3
Figure GDA0003307110050000065
The liquid level h which is the mean velocity of the power-law fluid in the porous zone 3 and which falls through the free zone 41Divided by the discharge time Δ t, i.e.
Figure GDA0003307110050000063
The flow rate Q of the power-law fluid in the discharge pipe 5 is obtained by dividing the discharge volume V of the power-law fluid by the discharge time Δ t, i.e. Q is V/Δ t; power law fluid velocity u in the exhaust pipe 50Obtained by dividing the flow rate Q of the power-law fluid in the discharge pipe 5 by the cross-sectional area of the discharge pipe 5, i.e.
Figure GDA0003307110050000064
Wherein d is0The diameter of the discharge pipe 5.
In this embodiment, the step four includes supplementing the closed condition of the binary equation and establishing a second binary equation of the power-law fluid viscosity parameter, where the second binary equation includes: changing the diameter of the spherical particles 2 filled in the porous zone 3 in the measuring device, repeating the first step to the third step, and establishing a second binary equation of the power law fluid viscosity parameter.
In this embodiment, the viscosity parameters of the power-law fluid in the fifth step include a consistency coefficient K, a power-law index n, and an apparent viscosity μ.
In this embodiment, the specific process of calculating the viscosity parameter of the power law fluid in the fifth step includes: combining the first binary equation with the second binary equation to obtain a binary equation set related to the consistency coefficient K and the power law index n, and solving to obtain the consistency coefficient K and the power law index n of the power law fluid; the apparent viscosity mu is determined by the parameters measured at the discharge tube 5, in combination with poiseDerived from leaf law calculations, i.e.
Figure GDA0003307110050000071
In specific implementation, the method can also measure and calculate the apparent viscosity of the power law fluid, the apparent viscosity can only qualitatively reflect the viscosity of the fluid when the fluid flows, and the method is not applicable to precise design or control of the flow of the power law fluid.
In order to verify the effect of the invention, the test is combined with a specific test process for verification.
Adopt transparent colourless organic glass cylinder to make 2 funnel-shaped containers that geometry is the same, the internal diameter of container is 10cm, 2 container bottoms fill respectively the steel ball granule of isodiametric, the diameter of steel ball is 8mm and 5mm respectively, two container distribution fill 10 layers and 16 layers of steel balls, obtain the porous region in two containers, highly be 70.35mm and 69.95mm respectively, consider the height 70mm in porous region, container bottom trompil, aperture 5mm, and connect the equal internal diameter plasticity hose, hose length 15cm, the valve adopts tweezers to replace.
A prepared xanthan gum solution (25 +/-5 ℃) with the concentration of 0.2g/L and the density of 0.99g/L is measured by a cylinder viscometer, and the viscosity parameter of the solution is 0.0054Ns0.887/m2The power law index n is 0.877, and the apparent viscosity mu is 0.00142Ns/m2. The xanthan gum solution was poured into a container with a steel ball diameter of 8mm and allowed to drain by gravity seepage down, indicating that the air in the porous region was emptied by the liquid, and the valve was closed. The xanthan gum solution is continuously poured into the container, and the pouring is stopped when the glue liquid level is 210mm, and the free zone height of the solution at the top of the porous zone is 140 mm.
Opening a valve, starting the test and timing, stopping the experiment when the liquid level of the free area is reduced by 70mm, measuring the time of the process to be 5.38s, measuring the volume of the solution discharged from the plastic hose to be 541.6mL in the whole process, and basically consistent with the calculated volume 0.5498L of the liquid level reduction height of the cylindrical container, thus obtaining the apparent velocity of the solution in the container with the diameter of a steel ball of 8mm to be 0.013m/s, substituting the obtained volume into a porous flow resistance formula to establish a first binary equation, and taking the local resistance coefficient to be 0.5.
The solution tested in the first vessel was poured into a second vessel with a steel ball diameter of 5mm, and the experiment was carried out again in the same procedure to establish a second equation of two elements, and the test time was recorded for 7.46s, so that the apparent velocity was 0.00938 m/s. By simultaneously solving the two equations, the consistency coefficient K is 0.0061, the power law index n is 0.821, and the relative errors with a precision instrument are respectively 12.94% and 6.4%.
In addition, through the Poiseue's formula, the apparent viscosities of the solutions in the two experiments can be further calculated to be 0.001458 and 0.002022 respectively, and the arithmetic mean value is 0.00174. In terms of apparent viscosity, the test results are compared with the results of a precise instrument, and although the relative error is 22.5%, the viscosity of the fluid can be accurately and qualitatively reflected.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (8)

1. The method for measuring and calculating the viscosity parameter of the power law fluid is characterized in that a measuring device is adopted, the measuring device comprises an open cylindrical container (1), spherical particles (2) with equal diameters are filled in the cylindrical container (1) to form a porous region (3), a free region (4) for containing the power law fluid is formed at the upper part of the porous region (3), a discharge pipe (5) is connected to the bottom of the cylindrical container (1), and a valve (6) for controlling the discharge of the power law fluid is arranged on the discharge pipe (5);
the measuring and calculating method comprises the following steps:
step one, carrying out measurement preparation debugging on the measuring device;
measuring parameters, and recording the discharge time delta t of the power-law fluid and the discharge volume V of the power-law fluid;
step three, processing the measured data, and descending according to the free area (4)Height h of liquid level1And the discharge time Deltat, calculating the apparent velocity of the power-law fluid in the porous zone (3)
Figure FDA0003500729560000011
Calculating the flow rate Q and the speed u of the power-law fluid in the discharge pipe (5) according to the discharge volume V and the discharge time delta t of the power-law fluid0Establishing a first binary equation of the power law fluid viscosity parameter;
step four, supplementing the closed condition of a binary equation, changing the diameter of spherical particles (2) filled in a porous region (3) in the measuring device, repeating the step one to the step three, and establishing a second binary equation of the power law fluid viscosity parameter;
and fifthly, combining the first binary equation and the second binary equation to obtain a binary equation set related to the consistency coefficient K and the power law index n, solving the binary equation set, and calculating to obtain the consistency coefficient K, the power law index n and the apparent viscosity mu of the power law fluid.
2. The method for estimating the viscosity parameter of a power law fluid according to claim 1, wherein the ratio of the inner diameter of the cylindrical container (1) to the diameter of the spherical particles (2) is 10 or more, the ratio of the diameter of the discharge pipe (5) to the diameter of the spherical particles (2) is in the range of 0.5 to 0.9, and the ratio of the length of the discharge pipe (5) to the inner diameter of the cylindrical container (1) is in the range of 1 to 3.
3. Method for estimating the viscosity parameters of a power law fluid according to claim 1, characterized in that the ratio of the height of the porous zone (3) to the internal diameter of the cylindrical container (1) ranges from 1 to 2.
4. The method for measuring and calculating the power law fluid viscosity parameter according to claim 1, wherein the step one of measuring the measuring device for preparing debugging comprises the following specific steps: filling power-law fluid to be detected into the cylindrical container (1) to enable the ratio of the height of the power-law fluid in the free region (4) to the height of the porous region (3) to be more than or equal to 2; then, the valve (6) is opened to allow the power law fluid to flow out of the discharge pipe (5) by its own weight, and the valve (6) is closed when a continuous fluid liquid column is formed.
5. The method for measuring and calculating the power law fluid viscosity parameter according to claim 1, wherein the specific process of measuring the parameter in the second step comprises the following steps: opening the valve (6) to continuously discharge the power law fluid to be measured by the gravity of the power law fluid, and when the free area (4) descends, the liquid level h1A height h from the porous region (3)2When the two phases are equal, the valve (6) is closed, and the discharge time delta t of the power law fluid and the discharge volume V of the power law fluid are recorded.
6. The method for measuring and calculating the power law fluid viscosity parameter as claimed in claim 5, wherein the first equation of two elements for establishing the power law fluid viscosity parameter in step three is established according to the viscous resistance formula of the uniform spherical particle packing porous structure, and the method comprises the following steps:
Figure FDA0003500729560000021
wherein rho is the density of the power law fluid to be measured, g is the gravity acceleration, xi is the local resistance coefficient, dpIs the diameter of spherical particles (2) filled in the porous zone (3), K is the consistency coefficient, and n is the power law index.
7. The method for measuring and calculating the viscosity parameter of the power-law fluid according to claim 6, wherein the viscosity parameter of the power-law fluid in the fifth step comprises a consistency coefficient K, a power-law index n and an apparent viscosity mu.
8. The method for estimating the power law fluid viscosity parameter of claim 7 wherein in step five the apparent viscosity μ is based on the equation
Figure FDA0003500729560000022
Calculating outAnd (6) obtaining.
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CA1258915A (en) * 1985-05-02 1989-08-29 Stephen C. Dodd Non-invasive, in-line consistency measurement of a non-newtonian fluid
US5646353A (en) * 1995-10-20 1997-07-08 Endress + Hauser Flowtec Ag Electromagnetic flowmeter for measuring non-newtonian fluids

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