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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