The inflow flood flow is a time series, the inflow flood hydrograph can be defined as a linear interpolation function, and the inflow q corresponding to time t can be linearly interpolated: Qt (x): = l interp (t, q, x) x:: = 0.9.
(2) Establish the curve fitting function of the relationship between water level and storage capacity.
The reservoir water level-storage capacity curve can be fitted by the following cubic spline interpolation function:
VS:=lspline(zt，v) ①
V(z):=interp(VS，zt，v，z) ②
① The formula is to find the second derivative value VS of each point according to the water level (zz) and storage capacity (V) of each point.
② The formula is to calculate the storage capacity V(z) corresponding to any water level (z) according to the second derivative value VS, water level and storage capacity value of each point.
(3) Establish reservoir water level and flow function.
Reservoir discharge
(4) The differential equations of reservoir water area and storage capacity are established.
(5) establish water balance equation
The calculation period △t is 1 hour (3600 seconds), the total time is 108 hours, and the initial water level is 1 16m.
(6) Calculation results
After editing the above steps, MathCAD will automatically calculate and display the calculation results.
(7) drawing a plane rectangular coordinate system graph
Press the @ key and fill in the variable name or function expression at the coordinate between the horizontal axis and the vertical axis to generate the corresponding graph, which can change instantly with the change of the variable value. Right-click the graph and set the display format of the graph to get better display effect, such as adding title and axis title, setting grid, etc.
Draw the relationship curve between reservoir water level and storage capacity, as well as the inflow and outflow hydrographs as shown in the figure.