which, modified after experimental studies (UPIRI, 1940), gives
xLBo3/2[1 (Bf/Bx)3/2]/(Bo3/2 B3/2f)whereLis length of the transition.
The following table shows the calculated geometries of the transition
provided:
Bx(m) 12.5 15.0 17.5 20.0 22.5 25.0
x(m) 00 04.64 07.69 09.73 11.31 12.5 (contraction)
x(m) 00 06.96 11.53 14.59 16.96 18.75 (expansion)
The transitions are streamlined and warped to avoid any abrupt
changes in the width.
Transitions with a cylindrical inlet with an average splay of 2:1 and a
linear outlet with a splay of 3:1 provided with flow deflectors (Fig. 10.3;
Ranga Raju, 1993) have been found to perform better than lengthy curved
expansions.
As the flow is accelerating in a contracting transition and the energy
loss is minimal any gradual contraction with a smooth and continuous
boundary should be satisfactory, e.g. an elliptical quadrant is an altern-
ative to a cylindrical quadrant for inlet transitions. The bedline profile for
an elliptical quadrant transition has the equation
2
2
1and the length of transition given by
Lc2(Bo Bf).At any location (x) from flume end of the transition yis computed and the
bed width Bxcalculated by
BxBo 2 y.The side slope (m) of the transition (m0 for flume section and m'2 for
canal side slope) and bed elevation may be varied linearly along the trans-
ition length.
The expansion experiences considerable energy loss and care must
be exercised in designing a hydraulically satisfactory transition.
On the basis of theoretical and experimental investigations Vittal
and Chiranjeevi (1983) proposed the following design equations for bed
width and the side slopes of an expanding transition. The bed widths Bx
are fixed by
y
0.5(Bo Bf)x
2(Bo Bf)