I have everything done for this, but I need help generating a plot for RK4 (parts #3 and #4).

I don`t need it solved exactly with the numbers or the criteria from the problem. An example of how to do it would be best.

I know the uniform depth, I was using the equation 3.1 as the diff. eq. for RK4.

1 INTRODUCTION You are part of an engineering team that is placing a small hydroelectric dam to power a remote village. Your role in the project is to find out how the dam will affect the upstream portions of the river. To do this, you will use the concepts of gradually-varied flow with numerical methods to create a program to calculate the backwater profile of the river after the dam has been installed. This project involves calculating the backwater profile caused by the dam using the fourth- order Runge-Kutta method (RK4) to within 1% of the uniform depth value of an ideal- ized trapezoidal channel. 2 TRAPEZOIDAL CHANNEL A river with trapezoidal cross section (Figure 2.1) reaches the dam your company is constructing, causing the water to back up. The channel characteristics are: z=1.5 b=8 [ft], where b is the width of the bottom of the channel and z is the transverse slope of the sides of the channe 2 Figure 2.1: Trapezoidal cross-section (source: Engineering Toolbox) 1 INTRODUCTION You are part of an engineering team that is placing a small hydroelectric dam to power a remote village. Your role in the project is to find out how the dam will affect the upstream portions of the river. To do this, you will use the concepts of gradually-varied flow with numerical methods to create a program to calculate the backwater profile of the river after the dam has been installed. This project involves calculating the backwater profile caused by the dam using the fourth- order Runge-Kutta method (RK4) to within 1% of the uniform depth value of an ideal- ized trapezoidal channel. 2 TRAPEZOIDAL CHANNEL A river with trapezoidal cross section (Figure 2.1) reaches the dam your company is constructing, causing the water to back up. The channel characteristics are: z=1.5 b=8 [ft], where b is the width of the bottom of the channel and z is the transverse slope of the sides of the channe 2 Figure 2.1: Trapezoidal cross-section (source: Engineering Toolbox)