To compute the Gradually varied flow profiles

Gradually Varied FlowThe flow in which the changes in depth and velocity take place slowly over large distances, resistance to flow dominate and acceleration forces are neglected is called gradually varied flow.

In gradually varied flow, the actual flow depth y is either larger or smaller than the normal depth yoand either larger or smaller than the critical depth yc. The water surface profiles, which are oftencalled backwater curves, depend on the magnitude of the actual depth of flow y in relation to thenormal depth yo and the critical depth yc. Normal depth yo is the depth of flow that would exist forsteady-uniform flow as determined using the Manning or Chezy velocity equations, and thecritical depth is the depth of flow when the Froude number equals 1.0. Reasons for the depthbeing different than the normal depth are changes in slope of the bed, changes in cross-section,obstruction to flow and imbalances between gravitational forces accelerating the flow and shearforces retarding the flow

Classification of Gradually Varied flow profiles

It is important to systematically classify the water surface profiles in a channel before computation of flow profiles is carried out. Such classification helps to get an overall understanding of how the flow depth varies in a channel. It also helps to detect any mistakes made in the flow computation.

We know that

dydx

=

1−( KnK )2

¿

1−( ZcZ )2

¿¿

¿ x So

Where:So = Channel bed slopeKn = Conveyance factor for normal flow conditions where y will be equal to yn and

Kn = Q√ So

K = Conveyance factor for the gradually varied flow condition and

K = A R0.667

nZc = Section factor for the critical slope

Zc = Q

√g /∝Z = Section factor for gradually varied flow condition

Z = √ A3TA gradually varied flow profile is classified based on the channel slope, and themagnitude of flow depth, y in relation to yn and yc. The channel slope is classifiedbased on the relative magnitudes of the normal depth, yn and the critical depth, yc .

y > y : Mild slope (M) y < y : Steep slope (S) y = y : Critical slope (C) S =0 : Horizontal slope (H) S <0 : Adverse slope (A)

Flow profiles associated with mild, steep, critical, horizontal, and adverseslopes are designated as M, S, C, H and A profiles, respectively. The space above the channel bed can be divided into three zones. Figure shows these zones fora mild and a steep channel.

The space above both the CDL and the NDL is designated as zone-1. The spacebetween the CDL and the NDL is designated as zone-2. The space between thechannel bed and CDL/NDL (whichever is lower) is designated as zone-3. Flow profilesare finally classified based on (i) the channel slope and (ii) the zone in which they occur.For example, if the water surface lies in zone-1 in a channel with mild slope (Figure 2), it is designated as M1 profile. Here, M stands for a mild channel and 1 stands for zone-

1.It may be noted that an M1 profile indicates a subcritical flow since flow depth, y is greater than the critical depth, yc .

Similarly, an S2 profile (Figure 3) indicates the water surface lies in zone-2 in a steepchannel. It may be noted that a S2 profile indicates a supercritical flow since flow depth,y is lower than yc.

Table 1 presents types of flow profiles in prismatic channels. In this table, a channelslope is described as critical slope when critical conditions occur for uniform flow i.e.when yn = yc.