Gradually Varied Flow (GVF, Steady) Occurs in many situations likeupstream of a barrier, downstream of a sluice gate, due to changeof slopes of a channel etc. Therefore, study on this type of flow isimportant from particle point of view. To study this flow and itsprofiles knowledge of normal depth and critical depth is essential.

The Gradually Varied Flow (GVF) is the steady flow whose depthvaries gradually along the length of the channel. The definitionsignifies two conditions. The flow steady means hydrauliccharacteristics of flow does not change for the time interval underconsideration and streamlines remain practically parallel; that is,hydrostatic pressure distribution prevails over the channel section.

Learning Objectives Dynamic Equation Profiles of Gradually Varied Flow Computations of Profiles Computation Methods

Introduction

Assumption

Dynamic Equation of Gradually Varied Flow

Classification of Flow Profile

The Channel bed slopes are classified five categories:Critical Slope Sc:For given discharge and channel shape critical depth yc of flow exists.From this known critical dept yc, corresponding slope may be computedand this computed slope is called Critical Slope and is denoted as sc.Hence in this situation sb = sc and normal depth yn=yc, i.e., NDL and CDLcoincide.Mild Slope:When the channel bottom slope sb is less than the critical slope sc, i.e., <sc, slope is called Mild. Application of Manning’s or Chezy’s equationindicates that in mild slope, yn>yc.Steep Slope:The channel slope is called steep slope if sb>sc and yn<yc in this slope.Horizontal Slope:When channel bottom Slope is zero, i.e., sb=0. Application of Manning’sformula of Chezy’s formula shows that for sb=0, yn= (infinity).Adverse Slope:When slope of the Channel instead of falling, rises in flow direction, it iscalled adverse slope. Here sb<0, i.e., negative. Obviously in adverse ofnegative bed, yn is imaginary i.e., non-existent.

Classification of Channel Bed Slopes

Table 4.2 Types of GVF Profiles

Fig. 4.3. Various GVF profiles

Method of Computation

1- Direct Step Method

Steps of Computation

EXAMPLE

A rectangular channel 8 m wide carries discharge of

11m3/sec (Manning’s n = 0.0025, bed slope of 0.0016).

Compute the length of back water profile created by a

dam which backs up a depth 2 m immediately behind

the dam by direct step method. Take at least 3 steps

to compute the profile.

SOLUTION