Type 2:
Gradually Varied Flow Apply
Conservation of Mass and of Energy.
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Consider varied flow
in channels with a rectangular cross
section of width, w: Conservation of
mass: w
y1 V1 = w y2 V2 = Q Conservation of
Energy: y1 + V12
/ 2g =
y2 + V22 / 2g + ( Sf
˗ So ) L where y1 and
y2 are the upstream
and downstream depths in ft or in m z1 and
z2 are the upstream
and downstream lengths in ft or in m to the channel bed V1 and V2 are the upstream and downstream fluid
speeds in ft/sec or in m/sec Q is the discharge in ft3/sec or
in m3/sec Sf is the head loss per unit length of channel
So is the channel slope, (z1 - z2 )/L L
is the length along the channel in ft or in m Sf ≈
[ (k/n) RH1/6 ] -2 V2 / RH Since
changes in y and V are gradual, the energy loss can be represented by the Manning
equation and can be used to evaluate the slope for gradually varied flow. In
addition, construct a specific energy plot to aid in evaluation. |
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here for discussion of strategies involving hydraulic jumps. |
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