2.8.3 Standard Step Method for the Computation of Water Surface Profiles
The standard step method is a simple computational procedure to determine the water surface
profile in gradually varied flows. Prior knowledge of the type of backwater curve as classified in
Section 2.8.2 is useful to determine whether the analysis should proceed upstream or
downstream.
The standard step method is derived from the energy equation
V12
V22
+ y1 + ∆z =
+ y 2 + HL
(2.173)
2g
2g
From Figure 2.30
V12
V22
+ y1 + S o ∆L =
+ y 2 + S f ∆L
(2.174)
2g
2g
H1 + S o ∆L = H2 + S f ∆L
(2.175)
and
H2 - H1
∆L =
(2.176)
So - S f
Figure 2.30. Definition sketch for the standard step method for computation of backwater
curves.
The procedure is to start from some known y, which can be obtained from a stage-discharge
relationship, assume another y either upstream or downstream depending on whether the flow is
tranquil or rapid, and compute the distance ∆L to the assumed depth using Equation 2.176. It is
recommended that the assumed depth be kept relatively close to the known value of y1 in order
to keep the interval ∆L as short as possible to obtain better accuracy in the calculation.
2.55
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