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Gradually Varied Flow

Gradually Varied Flow. Basin Assumptions. We consider the flow to be Gradually Varied Flows if the rate of variation of depth with respect to distance is small. The theory of Gradually Varied Flow is based upon:

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Gradually Varied Flow

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  1. Gradually Varied Flow

  2. Basin Assumptions • We consider the flow to be Gradually Varied Flows if the rate of variation of depth with respect to distance is small. • The theory of Gradually Varied Flow is based upon: • The head loess at a section is the same as for a uniform flow having the velocity and hydraulic radius of the section • The slope of the channel is small • The channel is prismatic; that is, the channel has constant alignment and shape • The velocity distribution in the channel section is fixed. • The conveyance factor and section factor are exponential functions of the depth of flow • The roughness coefficient is independent of the depth of flow and constant throughout the channel under construction.

  3. Governing Equations • Consider a distance, , as positive in the down streamflow direction. • + • (Eq. 5-7; important in water surface) • The negative sign since both and decrease as increases (Choudhry, 2008)

  4. Classification of Water-Surface Profiles • Notation (CDL; NDL) critical depth line; normal depth line • Channel bottom slopes are classified into the following five categories: mild (), steep (), critical (), horizontal () [zero slope] and adverse () [negative slope] • Bottom slope • Mild if ; • Steep if ; and • Critical if • Zone 1: region above both critical and normal lines. Zone 2 between upper and lower lines. Zone 3 between lower line and channel bottom = Steep channel bottom slope at Zone 1 (Choudhry, 2008)

  5. Water surface profiles (Choudhry, 2008)

  6. Remarks • By determining the sign of the numerator and the denominator of we can make qualitative observations about various types of water surface profiles. • Observations indicate whether the depth increases or decreases with distance, how the profiles end at the upstream and at the downstream limits.

  7. Remarks 2 • The flow depth increases with distance if is positive and it decreases if is negative. • By determining the sign of the numerator and the denominator of we can say whether the flow depth for a particular profile increases of decreases with distance.

  8. Remarks 3 • As discussed before for a uniform flow when . • From Manning and Chezy Equations for a specified discharge, , • if . • if • Using these inequalities and the Froude number will determine the sign of the numerator and the denominator

  9. Types of Flow Profiles (Chow, 1959)

  10. Profiles (Chow, 1959)

  11. Example • The normal and critical depths of the flow in a channel have been computed and are shown in Figure below. Sketch the possible flow profile.

  12. Sketch (Chow, 1959)

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