Method for measuring the volume and the horizontal cross-sectional area of a table-like irregular body at any height

Abstract

The application discloses a method for measuring the volume of a table-shaped irregular body at any height and the horizontal cross-sectional area, and the volume of the table-shaped irregular body is calculated, and then the volume of the table-shaped irregular body at any height and the horizontal cross-sectional area at any height are calculated, so that a curve of the volume of the part below the horizontal cross section at any height of the table-shaped irregular body with the change of the height, i.e. a water level-storage capacity curve, is drawn, and the curve of the volume of the part below the horizontal cross section at any height of the table-shaped irregular body with the change of the height, i.e. the water level-storage capacity curve, can be used for monitoring the water level and the water level area.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology, and relates to a method for measuring the volume of a platform-shaped irregular body at any height, as well as a method for measuring the horizontal cross-sectional area of ​​a platform-shaped irregular body at any height. Background Technology

[0002] In water conservancy and hydropower projects, it is essential to obtain timely and accurate water level-reservoir capacity curves and water level-water level area change curves to monitor water level changes and obtain accurate information such as regulating reservoir capacity, freezing capacity, and evaporation. This allows for timely adjustments to the water level, especially during the flood season, providing a basis for selecting flood control strategies based on water level changes. However, reservoirs and other structures are often irregular, platform-shaped bodies. Currently, water level information is obtained primarily through 3D modeling to measure the volume of such geometric shapes, the volume of the portion below the horizontal cross-section at any height, and the area of ​​the horizontal cross-section at any height. This method is time-consuming, results in delayed water level information, and requires highly skilled technicians. Summary of the Invention

[0003] The purpose of this invention is to provide a method for measuring the volume of an irregular, platform-shaped body at any height, which can quickly and accurately obtain the reservoir capacity curve so as to monitor water level changes in real time.

[0004] Another objective of this invention is a method for measuring the horizontal cross-sectional area of ​​an irregular, platform-shaped body at any height, which can quickly and accurately obtain the water level-water level area curve, so as to monitor changes in water level area in real time.

[0005] The first technical solution adopted in this invention is a method for measuring the volume of an irregular, platform-shaped body at any height, specifically implemented according to the following steps:

[0006] Step 1: Obtain the top and bottom areas of the frustum-shaped irregular geometry using software;

[0007] Step 2: Calculate the total volume of the frustum-shaped irregular body based on the top and bottom surface areas obtained in Step 1.

[0008] Step 3: Calculate the volume of the portion below the horizontal section at any height of the irregular frustum based on the total volume of the irregular frustum obtained in Step 2.

[0009] Step 4: Based on the relationship between the volume of the part below the horizontal section at any height of the platform-shaped irregular body obtained in Step 3 and the height, draw the water level-reservoir capacity change curve, and obtain water level information in real time based on the reservoir capacity curve.

[0010] The first technical solution of the present invention is further characterized in that,

[0011] In step 1, the definition of the frustum-shaped irregular geometry is: on the horizontal projection plane, the closed curve L2 is obtained by offsetting the closed curve L1 at equal distances, that is, the offset distance M is a constant value, and the bottom and top surfaces are both horizontal planes.

[0012] In step 1, the software is one of CAD, Catia, or Rhino.

[0013] In step 2, the expression for calculating the total volume of the frustum-shaped irregular body is:

[0014]

[0015] In equation (1), V is the total volume of the platform-shaped irregular body, S2 is the area of ​​the top surface, S1 is the area of ​​the bottom surface, M is the offset distance, H is the total height of the platform-shaped irregular body, and L1 is the length of the closed curve of the bottom surface.

[0016] If the offset distance M is unknown, then i represents the slope ratio.

[0017] In step 3, the expression for calculating the volume of the portion below the horizontal section at any height of the frustum-shaped irregular body is as follows:

[0018] V h =S1×h+(h×Δ2+L1)×A h (2)

[0019] In equation (2), V h Let h be the volume of the part below the horizontal section at any height of the irregular frustum, h be the arbitrary height of the irregular frustum, S1 be the area of ​​the bottom surface, and L1 be the length of the closed curve of the bottom surface.

[0020] in,

[0021]

[0022]

[0023]

[0024]

[0025] In equations (2)-(5), H is the total height of the platform-shaped irregular body, M is the offset distance, V is the total volume of the platform-shaped irregular body, and h is any height of the platform-shaped irregular body.

[0026] The second technical solution adopted in this invention is a method for measuring the horizontal cross-sectional area of ​​an irregular, frustum-shaped body at any height, specifically implemented according to the following steps:

[0027] Step 1: Obtain the top and bottom areas of the frustum-shaped irregular geometry using software;

[0028] Step 2: Calculate the total volume of the frustum-shaped irregular body based on the top and bottom surface areas obtained in Step 1.

[0029] Step 3: Calculate the horizontal cross-sectional area at any height of the irregular frustum body based on the total volume of the irregular frustum body obtained in Step 2.

[0030] Step 4: Based on the relationship between the horizontal cross-sectional area and the height at any height of the irregular platform obtained in Step 3, plot the water level-water level area change curve, and obtain water level area information in real time based on the water level-water level area change curve.

[0031] The second technical solution of the present invention is further characterized in that,

[0032] In step 1, the definition of the frustum-shaped irregular geometry is: on the horizontal projection plane, the closed curve L2 is obtained by offsetting the closed curve L1 at equal distances, that is, the offset distance M is a constant value, and the bottom and top surfaces are both horizontal planes.

[0033] In step 1, the software is one of CAD, Catia, or Rhino.

[0034] In step 2, the expression for calculating the total volume of the frustum-shaped irregular body is:

[0035]

[0036] In equation (7), V is the total volume of the platform-shaped irregular body, S2 is the area of ​​the top surface, S1 is the area of ​​the bottom surface, M is the offset distance, H is the total height of the platform-shaped irregular body, and L1 is the length of the closed curve of the bottom surface.

[0037] If the offset distance M is unknown, then i represents the slope ratio.

[0038] In step 3, the expression for calculating the horizontal cross-sectional area at any height of the frustum-shaped irregular body is:

[0039]

[0040] In equation (8), S h Let h be the horizontal cross-sectional area at any height of the irregular frustum, h be the height of the irregular frustum, S1 be the area of ​​the bottom surface, L1 be the length of the closed curve of the bottom surface, M be the offset distance, and H be the total height of the irregular frustum.

[0041] in,

[0042]

[0043]

[0044]

[0045]

[0046] In equations (9)-(12), V is the total volume of the platform-shaped irregular body; L1 is the length of the closed curve of the bottom surface; M is the offset distance; and H is the total height of the platform-shaped irregular body.

[0047] The beneficial effects of this invention are that the method for measuring the volume and horizontal cross-sectional area of ​​an irregular platform at any height involves few parameters and can quickly obtain the volume and horizontal cross-sectional area at any height. This allows for the rapid plotting of reservoir capacity curves and water level-water level area change curves in water conservancy and hydropower projects, facilitating real-time monitoring of water level and water level area. The method is simple, easy to operate, and requires less technical expertise. Furthermore, this invention is also applicable to geometric bodies composed of multiple irregular platform-shaped bodies stacked together. Attached Figure Description

[0048] Figure 1 This is a planar schematic diagram of the platform-shaped irregular body involved in this invention;

[0049] Figure 2 This is a cross-sectional view of the platform-shaped irregular body involved in the present invention;

[0050] Figure 3 This is a curve showing the change in volume with height obtained by the present invention;

[0051] Figure 4 This is a curve showing the change of cross-sectional area with height obtained by the present invention;

[0052] Figure 5 This is a schematic diagram of the multi-layered, platform-shaped, irregular body structure involved in this invention.

[0053] Figure 6 The figures represent water level-reservoir capacity and water level-water level area curves in an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0055] This invention provides a method for measuring the volume of an irregular, platform-shaped body at any height, specifically implemented according to the following steps:

[0056] Step 1: Draw the top and bottom surfaces of the frustum-shaped irregular geometry using software such as CAD, Catia, or Rhino to obtain the area of ​​the top and bottom surfaces of the frustum-shaped irregular geometry; for example... Figure 1 and Figure 2As shown, the platform-shaped irregular geometry is obtained by offsetting the closed curve L2 from the closed curve L1 at equal distances on the horizontal projection plane (that is, the closed curve L2 on the top surface is obtained by offsetting the closed curve L1 on the bottom surface at equal distances). The offset distance M is a constant value, and both the bottom and top surfaces are horizontal planes.

[0057] Step 2, calculate the total volume of the frustum-shaped irregular body, the specific expression is:

[0058]

[0059] In equation (1), V is the total volume of the platform-shaped irregular body, S2 is the area of ​​the top surface, S1 is the area of ​​the bottom surface, M is the offset distance, H is the total height of the platform-shaped irregular body, and L1 is the length of the closed curve of the bottom surface.

[0060] If the offset distance M is unknown, then i represents the slope ratio;

[0061] S1 and S2 were obtained using software such as CAD, Catia, and Rhino.

[0062] Step 3: Calculate the volume of the portion below the horizontal section at any height of the frustum-shaped irregular body. The specific expression is as follows:

[0063] V h =S1×h+(h×Δ2+L1)×A h (2)

[0064] In equation (2), V h Let h be the volume of the part below the horizontal section at any height of the irregular frustum, h be the arbitrary height of the irregular frustum, S1 be the area of ​​the bottom surface, and L1 be the length of the closed curve of the bottom surface.

[0065] in,

[0066]

[0067]

[0068]

[0069]

[0070] In equations (2)-(5), H is the total height of the truncated irregular body, M is the offset distance, and V is the total volume of the truncated irregular body;

[0071] Step 4: Plot the volume of the portion below the horizontal section at any height of the frustum-shaped irregular body as a function of height, i.e., h. i -V hi Relationship diagram, such as Figure 3As shown in the figure, this graph also represents the water level-reservoir capacity change curve in water conservancy and hydropower projects, thereby allowing for the rapid and accurate determination of reservoir capacity through water level.

[0072] This invention also provides a method for measuring the horizontal cross-sectional area of ​​an irregular, frustum-shaped body at any height, specifically implemented according to the following steps:

[0073] Step 1: Draw the top and bottom surfaces of the frustum-shaped irregular geometry using software such as CAD, Catia, or Rhino to obtain the area of ​​the top and bottom surfaces of the frustum-shaped irregular geometry; for example... Figure 1 and Figure 2 As shown, the platform-shaped irregular geometry is obtained by offsetting the closed curve L2 from the closed curve L1 at equal distances on the horizontal projection plane (that is, the closed curve L2 on the top surface is obtained by offsetting the closed curve L1 on the bottom surface at equal distances). The offset distance M is a constant value, and both the bottom and top surfaces are horizontal planes.

[0074] Step 2, calculate the total volume of the frustum-shaped irregular body, the specific expression is:

[0075]

[0076] In equation (7), V is the total volume of the platform-shaped irregular body, S2 is the area of ​​the top surface, S1 is the area of ​​the bottom surface, M is the offset distance, H is the total height of the platform-shaped irregular body, and L1 is the length of the closed curve of the bottom surface.

[0077] If the offset distance M is unknown, then i represents the slope ratio;

[0078] S1 and S2 were obtained using software such as CAD, Catia, and Rhino.

[0079] Step 3: Calculate the horizontal cross-sectional area at any height of the frustum-shaped irregular body. The specific expression is as follows:

[0080]

[0081] In equation (8), S h Let h be the horizontal cross-sectional area at any height of the irregular frustum, h be the height of the irregular frustum, S1 be the area of ​​the bottom surface, L1 be the length of the closed curve of the bottom surface, M be the offset distance, and H be the total height of the irregular frustum.

[0082] in,

[0083]

[0084]

[0085]

[0086]

[0087] In equations (9)-(12), V is the total volume of the truncated irregular body; L1 is the length of the closed curve of the bottom surface; M is the offset distance; and H is the total height of the truncated irregular body.

[0088] Step 4: Plot the curve of the horizontal cross-sectional area of ​​the irregular frustum at any height as a function of height, i.e., h. i -S hi Relationship diagram, such as Figure 4 As shown in the figure, this figure is also a water level-water level area change curve in water conservancy and hydropower projects, so that the water level area can be quickly obtained through the water level.

[0089] This invention is also applicable to geometric bodies composed of multiple stacked platform-shaped irregular bodies, such as... Figure 5 As shown, the expression for calculating the total volume of a geometric solid composed of multiple stacked platform-shaped irregular bodies is:

[0090]

[0091] Among them, V1~V n The calculation method uses formulas

[0092] Example

[0093] The application of the methods for calculating the volume of an irregularly shaped platform at any height and the method for calculating the horizontal cross-sectional area of ​​an irregularly shaped platform at any height in reservoirs with irregular platform shapes is as follows:

[0094] Table 1 Reservoir Parameters

[0095]

[0096] Wherein, total height = reservoir top elevation - reservoir bottom elevation, which is the total height H of the platform-shaped irregular body; the difference between the water level and the reservoir bottom elevation is the arbitrary height h of the platform-shaped irregular body; the perimeter of the reservoir bottom is the length L1 of the closed curve of the bottom surface;

[0097] Table 2 shows the water level area and reservoir capacity.

[0098] Water level (m) <![CDATA[Water level area (m 2 )]]> <![CDATA[Storage capacity (m 3 )]]> Remark 1159.0 315888 9305100 top of warehouse 1155.0 303977 8065434 Normal water level 1150.0 289365 6582206 - 1145.0 275061 5171269 - 1140.0 261065 3831082 - 1135.0 247376 2560107 - 1130.0 233996 1356804 - 1125.0 220923 219634 Dead water level 1124.0 218346 0 bottom of the warehouse

[0099] Based on the water level, water level area, and reservoir capacity information in Table 2, plot the water level-reservoir capacity and water level-water level area curves, as follows: Figure 6 As shown, the reservoir capacity curve is an important part of water conservancy and hydropower projects. The regulating capacity can be obtained by comparing the reservoir capacity corresponding to the normal water level and the dead water level. The total reservoir capacity can be obtained by comparing the reservoir capacity corresponding to the check water level. The water surface area corresponding to the characteristic water level can be used to calculate evaporation, freezing capacity, etc.

Claims

1. A method for measuring the volume of an irregular, platform-shaped body at any height, characterized in that, The specific steps are as follows: Step 1: Obtain the top and bottom areas of the frustum-shaped irregular geometry using software; In step 1, the definition of a frustum-shaped irregular geometry is: a closed curve on the horizontal projection plane. L 2. From closed curves L 1. Obtained by equidistant offset, i.e., offset distance M The value is constant, and both the bottom and top surfaces are horizontal. Step 2: Calculate the total volume of the frustum-shaped irregular body based on the top and bottom surface areas obtained in Step 1. In step 2, the expression for calculating the total volume of the frustum-shaped irregular body is: （1） In equation (1), V The total volume of the platform-shaped irregular body is... S 2 represents the area of ​​the top surface. S 1 represents the area of ​​the base. M This is the offset distance. H The total height of the platform-shaped irregular body. L 1 represents the length of the closed curve at the bottom. If the offset distance M Unknown, then , i Slope; Step 3: Calculate the volume of the portion below the horizontal section at any height of the irregular frustum based on the total volume of the irregular frustum obtained in Step 2. In step 3, the expression for calculating the volume of the portion below the horizontal section at any height of the frustum-shaped irregular body is as follows: （2） In equation (2), Let V be the volume of the portion below the horizontal cross-section at any height of the frustum-shaped irregular body. h For a platform-shaped irregular body of arbitrary height, S 1 represents the area of ​​the base. L 1 represents the length of the closed curve at the bottom. in, （3） （4） （5） （6） In equations (2)-(5), H The total height of the platform-shaped irregular body. M This is the offset distance. V The total volume of the irregular, platform-shaped body; Step 4: Based on the relationship between the volume of the part below the horizontal section at any height of the platform-shaped irregular body obtained in Step 3 and the height, draw the water level-reservoir capacity change curve and obtain water level information in real time.

2. The method for measuring the volume of an irregularly shaped, platform-like body at any height according to claim 1, characterized in that, In step 1, the software is one of CAD, Catia, or Rhino.

3. A method for measuring the horizontal cross-sectional area of ​​an irregular, frustum-shaped body at any height, characterized in that: The specific steps are as follows: Step 1: Obtain the top and bottom areas of the frustum-shaped irregular geometry using software; In step 1, the definition of a frustum-shaped irregular geometry is: a closed curve on a horizontal projection plane. L 2. From closed curves L 1. Obtained by equidistant offset, i.e., offset distance M The value is constant, and both the bottom and top surfaces are horizontal. Step 2: Calculate the total volume of the frustum-shaped irregular body based on the top and bottom surface areas obtained in Step 1. In step 2, the expression for calculating the total volume of the frustum-shaped irregular body is: （7） In equation (7), V The total volume of the platform-shaped irregular body is... S 2 represents the area of ​​the top surface. S 1 represents the area of ​​the base. M This is the offset distance. H The total height of the platform-shaped irregular body. L 1 represents the length of the closed curve at the bottom. If the offset distance M Unknown, then , i Slope; Step 3: Calculate the horizontal cross-sectional area at any height of the irregular frustum body based on the total volume of the irregular frustum body obtained in Step 2. In step 3, the expression for calculating the horizontal cross-sectional area at any height of the frustum-shaped irregular body is: （8） In equation (8), S h Let be the horizontal cross-sectional area at any height of the irregular, frustum-shaped body. h For a platform-shaped irregular body of arbitrary height, S 1 represents the area of ​​the base. L 1 represents the length of the closed curve at the bottom. M This is the offset distance. H The total height of the platform-shaped irregular body; in, （9） （10） （11） （12） In equations (9)-(12), V The total volume of the irregular, platform-shaped body; Step 4: Based on the relationship between the horizontal cross-sectional area and the height at any height of the irregular platform obtained in Step 3, plot the water level-water level area change curve to obtain water level area information in real time.

4. The method for measuring the horizontal cross-sectional area of ​​an irregularly shaped, frustum-shaped body at any height according to claim 3, characterized in that, In step 1, the software is one of CAD, Catia, or Rhino.

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