Question

How to find the critical depth of triangular channel if discharge and side slope is known?

Answer 1

s Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
12.1 Critical flow depth computations
One of the important aspects in Hydraulic Engineering is to compute the critical depth if
discharge is given.
Following methods are used for determining the critical depth.
(i) Algebraic method.
(ii) Graphical method.
(iii) Design chart.
(iv) Numerical method. Bi section method/ Newton Raphson method.
(v) Semi empirical approach - a method has introduced by Strarb.
12.1.1 Algebraic method
In this method the algebraic equation is formulated and then solved by trial and error.
The following example illustrates the method.
1. Consider a trapezoidal channel:
2.
( )
( )
( )
( ) ( )
( )
( )( )
c c
c c
c
c 1
1/2
c c 1 cc
c
2 3 3
1 c cc
6 5 43
c c ccc
A b my y
b my y D
b 2my
Q Z constant C known
g
b my y C b my y (1) b 2my
C b 2my b my y
leads to
y py qy ry sy t 0
in which the cons tan ts p,q,r,s and t are known.


= +
+ = +
= = ==
⎧ ⎫ ⎪ ⎪ +
= + ⎨ ⎬ ⎪ ⎪ + ⎩ ⎭
+ =+
+ + + + +=
Solve this by polynomial or by trial and error method.
It would be easier to solve the equation (1) by trial and error procedure.
After obtaining the answer check for the Froude number which should be eq


ual to 1.

Answer 2

Normal and critical depths are important parameters in the design of open channels and analysis of gradually varied flow. In trapezoidal and parabolic channels, the governing equations are highly nonlinear in the normal and critical flow depths and thus solution of the implicit equations involves numerical methods (except for critical depth in parabolic channels). In current research explicit solutions have been obtained using the non-dimensional forms of the governing equations. For the trapezoidal cross section, the maximum error of critical flow depth is less than 6 × 10−6% (near exact solution) and the maximum error of normal depth is less than 0.25% (very accurate solution). The maximum error of normal flow depth for parabolic cross section is also less than 8 × 10−3% (near exact solution). Proposed explicit equations have definite physical concept, high accuracy, easy calculation, and wide application range compared with the existing direct equations.