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5.1 Introduction

One of the branches of the fluid mechanics discussed in Chapter [*]. Here we expand this issue further because it is give the basic understanding to the ``wave'' phenomenon. There are numerous books that dealing with open channel flow and the interested reader can broader his/her knowledge by reading book such as Open-Channel Hydraulics by Ven Te Chow (New York: McGraw-Hill Book Company, Inc. 1959). Here a basic concepts for the non-Fluid Mechanics Engineers are given.

= 0.7:w

Figure: Equilibrium of Forces in an open channel

The flow in open channel flow in steady state is balanced by between the gravity forces and mostly by the friction at the channel bed. As one might expect, the friction factor for open channel flow has similar behaver to to one of the pipe flow with transition from laminar flow to the turbulent at about . Nevertheless, the open channel flow has several respects the cross section are variable, the surface is at almost constant pressure and the gravity force are important.

to be continue

The flow of a liquid in a channel can be characterized by the specific energy that is associated with it. This specific energy is comprised of two components: the hydrostatic pressure and the liquid velocity1.

The energy at any point of height in a rectangular channel is

    (5.1)

why? explain

and, since for any point in the cross section (free surface),

    (5.2)

where:

 specific energy per unit  

height of the liquid in the channel
acceleration of gravity
average velocity of the liquid

= 100 true mm

Figure: Specific Energy and momentum Curves

If the velocity of the liquid is increased, the height, , has to change to keep the same flow rate . For a specific flow rate and cross section, there are many combinations of velocity and height. Plotting these points on a diagram, with the -coordinate as the height and the -coordinate as the specific energy, , creates a parabola on a graph. This line is known as the ``specific energy curve''. Several conclusions can be drawn from Figure [*]. First, there is a minimum energy at a specific height known as the ``critical height''. Second, the energy increases with a decrease in the height when the liquid height is below the critical height. In this case, the main contribution to the energy is due to the increase in the velocity. This flow is known as the ``supercritical flow''. Third, when the height is above the critical height, the energy increases again. This flow is known as the ``subcritical flow'', and the energy increase is due to the hydrostatic pressure component.

The minimum point of energy curve happens to be at

    (5.3)

where the critical height is defined by
    (5.4)

Thrust is defined as
    (5.5)

The minimum thrust also happens to be at the same point . Therefore, one can define the dimensionless number as:
    (5.6)

Dividing the velocity by provides one with the ability to check if the flow is above or below critical velocity. This quantity is very important, and its significance can be studied from many books on fluid mechanics. The gravity effects are ``measured'' by the Froude number which is defined by equation ([*]).


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