expansion losses as K2.3 m – 0.345, where m is the ratio of the
obstructed and channel areas for 0.324 m0.65.
(b) Discharge computations at bridge piers
- Nagler (1918) proposed a discharge formula for subcritical and near-
critical flows as follows:
QKNb(2g)1/2(y 3 V^23 /2g)(h 3 V^21 /2g)1/2 (10.16)
the notation used in equation (10.16) being shown in Fig. 10.12(a). KN
is a coefficient depending on the degree of channel contraction and on
the characteristics of the obstruction (Table 10.4); is a correction
factor intended to reduce the depth y 3 toy 2 andis the correction for
the velocity of approach, depending on the conveyance ratio
(Fig. 10.12(b)).
- d’Aubuisson (1940) suggested the formula
QKAb 2 y 3 (2gh 3 V^21 )1/2 (10.17)
whereKAis a function of the degree of channel contraction and of
the shape and orientation of the obstruction (Table 10.4).
d’Aubuisson made no distinction between y 3 andy 2 , and, although
in many cases there is a small difference between them, equation
(10.17) is recognized as an approximate formula.
- Chow (1983) presents a comprehensive discussion of the discharge
relationship between the flow through contracted openings and their
shape, and other characteristics, together with a series of design
charts produced by Kindsvater, Carter and Tracy (1953).
438 CROSS-DRAINAGE AND DROP STRUCTURES
Fig. 10.12 Discharge computations through obstructions (definition sketch)
