ANALYSIS OF GRADUALLY VARIED FLOW BY USING DIFFERENT METHODS

[B]ANALYSIS OF GRADUALLY VARIED FLOW BY USING DIFFERENT METHODS[/B]

[B]ABSTRACT:[/B]

A steady non uniform flow in a prismatic channel with gradual changes in it’s water surface elevation is termed as gradually varied flow. Almost all major hydraulic engineering activities involves the computation GVF profile. Because of it’s practical importance the computation of GVF has been a topic of continue interest to hydraulic engineers for the last 150 years. Considerable computational effort is involved in the analysis of problem such as, determination of the effect of a hydraulic structure on the channel, induation of land due to a dam or weir construction and estimation of flood zone.

[B]INTRODUCTION:[/B]

The gradually varied flow is the steady flow whose depth varies gradually along the length of the channel. A steady non uniform flow in a prismatic channel with gradual changes in its water surface elevation is termed as gradually varied flow (GVF)

The backwater produced by a dam or weir across a river and the drawdown produced at a sudden drop in a channel are few typical example of GVF.

In a GVF, the velocity varies along the channel and consequently the bed slope, water surface slope and energy slope will all differ from each others. Regions of high curvature are excluded in the analysis of this slope.

This definition signifies two conditions

a) The flow is steady: that is, the various characteristics of flow such as velocity, pressure, density, temperature etc. do not change with respect to time.

b) The flow is non-uniform: the depth of flow is not constant throughout the channel section.

The two basic assumptions involved in the analysis of GVF are:

1. The pressure distribution at any section is assumed to be hydrostatic. This follows from the definition of the flow to have a gradually varied water surface. As gradual changes in the surface curvature giverise to negligible normal accelerations, the departure from the hydrostatic pressure distribution is negligible. The exclusion of the region of high curvature from the analysis of GVF, as indicated earlier, is only to meet this requirement.

2. The resistance to flow at any depth is assumed to be given by the corresponding uniform-flow equation, such as the Manning’s formula, with the condition that the slope term to be used in the equation is the energy slope and not the bed slope. Thus, if in a GVF the depth of flow at any section is y, the energy slope Sf is given by,

Sf = n2y2/R4/3

Where,

R- hydraulic radius of the section at depth y

Almost all major hydraulic engineering activities involves the computation of GVF profiles. Because of it’s practical importance the computation of GVF has been a topic of continue interest to hydraulic engineers for the last 150 years.

A GVF computation methods for use in artificial channel may or may not be of applicable to natural channels of irregular cross-sections, Since in a natural channel, the cross-sectional properties are known only at specified locations while in a prismatic artificial channels the cross section are constant all along the channels. Because this some methods have been developed particularly for use in natural channels.

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