Resolve normal depth from Manning's equation

Hello,

I aim to obtain the normal depth of a channel using Mannig's equation. Somehow I don't manage to resolve its value. Here it's the pieco of code that I'm using:

riverSlope=0.0114;  % [m/m] - inletSlope, outletSlope or riverSlope
bottom_width=33.5937;   % [m] - inlet or outlet bottom width
slope_Rbank=1.1336;     % [m/m] - slope_Rbank_in or slope_Rbank_out
slope_Lbank=0.3334;     % [m/m] - slope_Lbank_in or slope_Lbank_out
q=10;      % [m3/s] - Flow discharge
n=0.04;     % [-] - Manning's roughness coefficient

syms y
area=(bottom_width+(y/(2*slope_Rbank))+(y/(2*slope_Lbank)))*y;
wetted_perimeter=bottom_width+y*(sqrt(1+(1/slope_Rbank)^2)+sqrt(1+(1/slope_Lbank)^2));
manning_eqn=@(y)(1/n)*((area/wetted_perimeter)^(2/3))*(riverSlope^(1/2))*area==q;
soly=solve(manning_eqn,y)

I would really appreciate if someone can help to fix it in order to obtain the desired values and avoid the coding of an iteration loop for the manual calculation. Thanks in advance!!

Álvaro

Answer 1

[Alan Stevens]

This shoud do it:

depth0 = 1; % Initial guess 

depth = fzero(@manningfn, depth0);

function manning = manningfn(y)

riverSlope=0.0114;  % [m/m] - inletSlope, outletSlope or riverSlope
bottom_width=33.5937;   % [m] - inlet or outlet bottom width
slope_Rbank=1.1336;     % [m/m] - slope_Rbank_in or slope_Rbank_out
slope_Lbank=0.3334;     % [m/m] - slope_Lbank_in or slope_Lbank_out
q=10;      % [m3/s] - Flow discharge
n=0.04;     % [-] - Manning's roughness coefficient

area=(bottom_width+(y/(2*slope_Rbank))+(y/(2*slope_Lbank)))*y;
wetted_perimeter=bottom_width+y*(sqrt(1+(1/slope_Rbank)^2)+sqrt(1+(1/slope_Lbank)^2));
manning = (1/n)*((area/wetted_perimeter)^(2/3))*(riverSlope^(1/2))*area-q;

end

[Álvaro Pardo]

Is there any way I can define the parameters out of the function? That would be nice because I aim to use them for other applications. Many thanks!!

[Alan Stevens]

Yes, you could do this:

riverSlope=0.0114;  % [m/m] - inletSlope, outletSlope or riverSlope
bottom_width=33.5937;   % [m] - inlet or outlet bottom width
slope_Rbank=1.1336;     % [m/m] - slope_Rbank_in or slope_Rbank_out
slope_Lbank=0.3334;     % [m/m] - slope_Lbank_in or slope_Lbank_out
q=10;      % [m3/s] - Flow discharge
n=0.04;     % [-] - Manning's roughness coefficient

data =[riverSlope; bottom_width; slope_Rbank; slope_Lbank; q; n];

depth0 = 1; % Initial guess 

depth = fzero(@manningfn, depth0,[],data);

function manning = manningfn(y, data)

riverSlope=data(1);
bottom_width=data(2);
slope_Rbank=data(3);
slope_Lbank=data(4);
q=data(5);
n=data(6);
area=(bottom_width+(y/(2*slope_Rbank))+(y/(2*slope_Lbank)))*y;
wetted_perimeter=bottom_width+y*(sqrt(1+(1/slope_Rbank)^2)+sqrt(1+(1/slope_Lbank)^2));
manning = (1/n)*((area/wetted_perimeter)^(2/3))*(riverSlope^(1/2))*area-q;

end

[Álvaro Pardo]

Many thanks Alan!