It can be seen from the differential geometry theorem that if there are an infinite number of meridian planes, their inclination with the x-axis is 0 to 2n, and they intersect with the circles and rectangles at both ends of the pipe, then an infinite number of ruled surface primes can be generated, thus forming As shown in the "meridian surface" straight grain gradient surface. If the pipeline is cut with 6 equally spaced cross-sections along the longitudinal direction of the meridian plane, 6 cross-sectional views can be obtained. Obviously, the section 1 is a circle, and the section 6 is a rectangle (not shown). The shapes of the sections 2 to 5 are as shown. The figure also shows the four values ​​of the gradient surface. Here, 24 meridian planes are used to produce straight plain lines on the gradient surface. Let the length of this section of the pipeline be L. For any given position z along the longitudinal direction of the pipeline, the area of ​​its cross section is then = z / L = A (z) / Acir plane for analysis.
No unit ratio; the area of ​​the end surface of the cir circle, Ac. = NR2. Obviously, A (z) is a function of the variable Z. This function is projected on the VH plane and cross section of the meridian surface pipe after this paper. The second straight grain gradient surface pipe is Generated by such a straight-grained bus: one end of the line is a certain bisector on the circumference, and the other end is a point corresponding to a certain bisector on the circumference, with a certain proportional spacing on the rectangle, as shown. It is assumed that the arc length between a certain bisector on the circumference and the intersection point of the circumference and the x-axis (positive direction) is a length corresponding to a certain length on the periphery of the rectangle. The following relationship: where K is the ratio of the circumference of the rectangle Crec to the circumference of the circle Cc.
The VH plane projection of this pipeline is shown in (a). The four parameters (b, h, R, L) have the same value as the first type of pipeline.
According to any prime line of the relationship, the equation through a certain point (x, yz) in space can be expressed as (X0, y0) and (XL, yL) refer to the prime line at the inlet end of the pipeline (= 0) and the outlet end (z = L) The x and y coordinates of the upper and lower points.
= 0fL (ciyi0 equation group (4) is enough to express a contour line with abrupt changes like a rectangle.
Among them, assuming that y0 and yi are functions of x0 and xi, respectively, that is now using this complementary relationship to connect the "movement path" of the ruled bus on both ends, according to a certain instant of the bus surface A certain position on one end (= 0) to determine the corresponding position on the other end (= L). Suppose there is the following functional form for such a supplementary relationship: Substituting equation (6) into the system of equations results in the following system of equations: This system of equations contains only one parameter x and x is eliminated, and an equation containing x, yz can be obtained. When z is a fixed value, the corresponding cross-sectional profile curve can be determined. By integrating this curve, the area of ​​the cross section can be obtained.
On the other hand, if x is not eliminated, and the system of equations (7) is integrated by parameters, the general expression of the area function can be obtained. Since z = 0 at the pipe entrance, the function (8) can be further simplified to be available now Equation (3) describes the contour curve of any cross-section between the two ends of the pipe. From equation (3), the following equations can be obtained: For the two straight-grained gradient curved pipes discussed above, from section 2 to section 5 will meet Type: For the "meridian surface" pipeline: this
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