DIRECT SOLUTION TO PROBLEMS OF OPEN CHANNEL FLOW FOR VERTICAL TRANSITIONS

The vertical transition occurred in open channel when the bed goes up or down
suddenly or gradually. Such problem could be solved using the specific energy equation.
Since the specific energy is measured with respect to channel bed as the datum, a rise or
a fall in the bed of the channel causes a decrease or an increase in specific energy.
The authors presents in this paper new equations for the solution of ihe vertical
transition problems for rectangular open channels.
The specific energy in this paper takes a dimensionless form to make the solution of
the problem easier. By using the new dimensionless equation, the solution of the two
types of vertical transition problems (rise or fall) would be available if the flow through
channel subcritical or supercritical. Thus, the new dimensionless equation became very
simple in use. Also the new derived cqualions were used to solve the problem if the rise
in bed was bigger than the critical rise (maximum rise in bed).
From the above it was evident that, if the height of rise in channel bed (hump) was
increased further the maximum value and the specific energy held constant with the
hump and the discharge would be decreased until the given specific energy was equal to
the minimum specific energy corresponding to the new discharge, as the energy could be
increased without outside affect. Also, the upstream water depth would be changed to a
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new value called