90 Computational Modelling in Hydraulic and Coastal Engineering
T(i)=b+2*m*yy(i);
Pw(i)=b+2*yy(i)*sqrt(1+m^2);
Rh(i)=A(i)/Pw(i);
u(i)=Q/A(i);
Sf(i)=n^2*u(i)^2/(Rh(i)^(4/3));
fnew(i)=(S-Sf(i))/(1-Q^2*T(i)/g/A(i)^3);
Y(i+1)=Y(i)+fnew(i)*Dx;
z(i+1)=-Dx*(i)*S;
h(i+1)=z(i+1)+Y(i+1);
x(i+1)=Dx*i;
end
plotyc=z+ycr(1);
plotyn=z+yn(1);
plot(x,z,'k','LineWidth',2); hold on;
plot (x,h,'b','LineWidth',2);
plot(x,plotyc,'r')
plot(x,plotyn,'g')
legend('Bed','Water Surface','Critical Depth','Normal
Depth',1);
xlabel('Distance [m]');
ylabel('Elevation [m]');
title('Water Surface Profile');
PROBLEM 5.1
By making the appropriate assumptions, modifying the computer code and
changing one or more of the following input data – flow rate, bed slope
and Manning’s coefficient of friction – as needed, create and plot the water
surface profiles under the following scenarios:
1. Subcritical flow with M2 surface profile
2. Supercritical flow with S2 surface profile
3. Supercritical flow with S3 surface profile
4. Supercritical flow with C3 surface profile
5. Subcritical flow with H2 surface profile
Justify and explain your assumptions made and comment on the simulation
results.
5.2.2 Unsteady-state open channel flow
5.2.2.1 Governing equations
The unsteady-state one-dimensional quasi-horizontal flows can be described
in terms of the average velocity, u(x,t), or the flow discharge, Q(x,t), and
the water depth, y(x,t), or the cross-section area, A(x,t). The two governing
equations of the phenomenon are based on the principles of mass conservation and momentum balance written along the channel axis, actually along