Hydraulic Engineering Eng. Osama Dawoud

Lecture 14 Open Channel Flow

Open Channel Open channel hydraulics, a subject of great importance to civil engineers, deals with flows having a free surface in channels constructed for water supply, irrigation, drainage, and hydroelectric power generation; in sewers, culverts, and tunnels flowing partially full; and in natural streams and rivers.

Pipe system Open Channel

Classification Steady Flow Unsteady Flow Typical situations Not time dependent Unsteady Flow Is time dependent Typical situations Uniform flow Gradually Varied Flow Rapidly Varied Flow

Open channel section types

Uniform Flow

Chezy equation C is the Chezy C, a dimensional factor which characterizes the resistance to flow

Manning equation

Example 1 open channel of width = 3m as shown, bed slope = 1:5000, d=1.5m find the flow rate using Manning equation, n=0.025.

Example 2 open channel as shown, bed slope = 69:1584, find the flow rate using Chezy equation, C=35.

Most Efficient Sections During the design stages of an open channel, the channel cross-section, roughness and bottom slope are given. The objective is to determine the flow velocity, depth and flow rate, given any one of them. The design of channels involves selecting the channel shape and bed slope to convey a given flow rate with a given flow depth. For a given discharge, slope and roughness, the designer aims to minimize the cross-sectional area A in order to reduce construction costs

Most Efficient Sections The most ‘efficient’ cross-sectional shape is determined for uniform flow conditions. Considering a given discharge Q, the velocity V is maximum for the minimum cross-section A. According to the Manning equation the hydraulic diameter is then maximum. It can be shown that: the wetted perimeter is also minimum, the semi-circle section (semi-circle having its centre in the surface) is the best hydraulic section

Most Efficient Sections Because the hydraulic radius is equal to the water cross section area divided by the wetted parameter, Channel section with the least wetted parameter is the best hydraulic section Rectangular section

Trapezoidal section or k k

Other criteria for economic Trapezoidal section k The best side slope for Trapezoidal section

Circular section Maximum Velocity using Manning or Chezy Maximum Flow using Manning Maximum Velocity using Manning or Chezy Maximum Flow using Chezy

Example 3 Circular open channel as shown d=1.68m, bed slope = 1:5000, find the Max. flow rate & the Max. velocity using Chezy equation, C=70. Max. flow rate

Max. Velocity

Variation of flow and velocity with depth in circular pipes

Example 4 Circular open channel as shown Q=10m3/s, velocity =1.5m/s, for most economic section. find wetted parameter, and the bed slope n=0.014.

To calculate bed Slope