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Variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length). Variables
accordingtodifferentknownconditions,weusetheundeterminedcoefficientmethodtocalculatethestandardequationofthecircleSelectthepropercoordinatesystemtosolvethepracticalproblemsrelatedtothecircle3,teachingprocess(1)creatingsituations(enlighteningthinking);Problem1:itisknownthatthecrosssectionofthetunnelisasemicirclewitharadiusof4m...
Preferably, the circle must be drawn on a coordinate system to facilitate finding positions and lengths. Preferably, at first, the center of the circle should coincide with the origin (0, 0) of the coordinate system. A segment r (for radius) must be drawn from the center of the circle ...
The Reynolds equation is for this case a linear one with partial derivatives of elliptical type. The frequently used numerical procedure is the finite difference method. This technique, already old, rather simple to implement, allows to solve most hydrodynamic and hydrostatic problems. It is largely...
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Afterward, we solve for y. The method is called the integrating factor method where the function r(x) is called the integrating factor (Lebl, 2022). The function r(x) is yet to be determined, such that if differentiated, we get the same function back multiplied by P(x). So, this ...
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which is used to calculate the water surface profile in an open channel where an obstacle impedes the flow. Standard techniques could be employed to solve this ordinary differential equation. For subcritical flows, where the control is downstream backwater analysis, which involves the solution of Eq...
Considering the implicit scheme to solve the convection equation in Eq. (11.73), the numerical equation is defined by (11.84a)uIn+1−uInΔt=−a2Δx(uI+1n+1−uI−1n+1), in which, for the time step n+1, the backward difference in time is adopted. The error equation of this ...