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Hydraulics Engineering

Hydraulics Engineering. Engr. Muhammad Hassan Hassan25.arif@gmail.com. Water Surface Profiles In Gradually Varied Flow. Characteristics of Gradually Varied Flow Water depth and velocity change gradually. Flow is uniform. Water surface changes smoothly and continuously.

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Hydraulics Engineering

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  1. Hydraulics Engineering Engr. Muhammad Hassan Hassan25.arif@gmail.com

  2. Water Surface Profiles In Gradually Varied Flow Characteristics of Gradually Varied Flow • Water depth and velocity change gradually. • Flow is uniform. • Water surface changes smoothly and continuously. • Friction loss along the channel is not negligible.

  3. TASKS Deduce the trend of water surface change (classification of surface profiles)

  4. Consider a channel having bottom slope So and Energy slope S.

  5. It should be noted that the friction loss dh is always a negative quantity in the direction of flow (unless outside energy is added to the course of the flow) and that the change in the bottom elevation dz is a negative quantity when the slope descends. • In the other words, they are negative because H and dz decrease in the flow direction

  6. Water Surface Profiles In Gradually Varied Flow

  7. Substituting this and the S and So terms in the differentiated equation.

  8. If dy/dx is positive, the depth of flow will be increasing along the channel and vice versa.

  9. The analysis of the numerator and denominator of eq. result in formation of a series of water surface profiles. • Also, S, the slope of energy line is given by

  10. Water Surface Profiles For a given channel with a known • Q = Discharge, • n = Manning coefficient • So = channel bed slope • yc = critical water depth yo = uniform flow depth can be computed. • There are three possible relations between yo and yc as • yo > yc , • yo < yc , • yo = yc .

  11. Water Surface Profiles Classification

  12. Thus, we have 13 different types of surface profiles: • three for the mild slope. • three for the steep slope. • two for the critical slope (zone 2 does not exist since yo = yc) and we do not consider the critical-depth line as a surface profile) • two for the horizontal slope (zone 1 does not exist since yo= ∞) • two for the adverse slope (there is no zone 1, since yo does not exist).

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