Help regarding solving equations

I am trying to solve a iterative design problem using programming.

Design Problem

Determine Flow depth (d) for following conditions:

Diameter of sewer (D) = 200mm

Discharge through sewer (Q) = 122.3 LPM

Sewer Material = Concrete, Manning's coefficient = 0.013

Longitudinal slope = 1 in 1000.

The algorithm is:

i. Assume a value of a, which is in between 0 to 360.

ii. Calculate the other parameters ar, A, P, R, Qi. (Formulas are as mentioned in code).

iii. Compare that Qi to Qd (Pre defined as numeric value), if both are same then proceed for printing calculated variables, if not then repeat the process again until Qi = Qd.

I had tried this code, I used for loop but it is not working, and I tried while loop, it is struck in calculations.

D = 200; %Diameter of sewer in mm
D = D/1000; %dia in meter
n = 0.013; %Manning's coefficient
S0 = 1/1000; %Bed slope
Q = 122.3; %LPM
Qd = Q/(1000*60); % Discharge in LPM to Cumecs
n = 360;
for a = 1:1:n
    ar = a*0.0174; %theta in radians
    A = ((D^2)/8)*(ar-sin(a));
    P = (ar*D)/2;
    R = A/P;
    Qi = (A/n)*(R^(2/3))*sqrt(S0);
    while Qi == Qd
        fprintf('Area of flow is %d \n',A);
        fprintf('Discharge is %.5f \n', Qi);
    end
    while Qi~ Qd
        a= a+1 && a<360;
    end
end

Answer 1

[Torsten]

Change sin(a) to sind(a).

Further Qi will never be exactly Qd.

I suggest you print Qi-Qd over a and see if it intersects the a-axis.

For this, change the line

Qi = (A/n) ...

to Qi(a) = (A/n)...

and write

plot((1:360),Qi)

after the for loop.

[saiprasad bodapati]

I think Qi == Qd, is where it went wrong, can i some how define matlab to consider only upto 4 decimal digits in comparision. can i define it ...??