Contraction, Enlargement, Step and Fall

The contraction, enlargement, step and fall are all treated in subroutine contraction.c. For these type of elements the width 'b' and the angle '$\theta$' may differ upstream and downstream, they are labeled bup, bdo, thetaup and thetado. The length of the element can be given explicitly by the user, or if it is zero it is calculated from the coordinates of nup and ndo. This length is used to calculate a contraction or expansion angle $\alpha$. Based on this angle a head loss coefficient is calculated and the earth acceleration $g$ is appropriately corrected. For the theory behind this the reader is referred to Section 6.6.5.

For a frontwater curve the specific energy is calculated in nup. Then, using subroutine henergy.f a supercritical depth is calculated corresponding to the same specific energy and discharge for the downstream geometry of the element (cf. Section 6.6.5) and defined as hdo. Two cases arise:

• If hdo is positive the solution is found.
• If hdo is negative it means that the specific energy downstream has to be increased such that it corresponds to the specific energy corresponding to hk for the given discharge. The values of nelem and ndo are stored to stack and a backwater curve is calculated starting at ndo.

For a backwater curve the specific energy is calculated in ndo. Then, using subroutine henergy.f a subcricital depth is calculated corresponding to the same specific energy and discharge for the upstream geometry of the element

• If hup is positive the solution is found.
• If hup is negative it means that the specific energy upstream has to be increased such that it corresponds to the specific energy corresponding to hk for the given discharge. The values of nelem and ndo are stored to stack and the backwater curve calculation is continued at nup.