Chezy’s and Manning’s equations for uniform flow in open channel,

Velocity distribution, Most efficient channel section, Compound channels.

05/02/23 1MODASSAR ANSARI

BY MODASSAR ANSARI 2nd Year Department of civil Engineering SUBJECT- HYDRAULICS & HYDRAULIC

MACHINES SUBJECT CODE-NCE 403

05/02/23 2MODASSAR ANSARI

Introduced by the French engineer Antoine Chezy in 1768 while designing a canal for the water-supply system of Paris

05/02/23

h fV C R S=

150 < C < 60s

m

s

m

where C = Chezy coefficient

where 60 is for rough and 150 is for smooth also a function of R (like f in Darcy-Weisbach)

2f h

gV S Rl

=compare

0.0054 > > 0.00087l4 hd R

For a pipe0.022 > f > 0.0035

3MODASSAR ANSARI

Most popular in U.S. for open channels

05/02/23

(english system)

1/2o

2/3h SR

1

nV

1/2o

2/3h SR

49.1

nV

VAQ

2/13/21oh SAR

nQ very sensitive to n

Dimensions of Dimensions of nn??

is is nn only a function of roughness? only a function of roughness?

(MKS units!)

NO!

T /L1/3

Bottom slope

4MODASSAR ANSARI

A section of a channel is said to be most economical when the cost of construction of the channel is minimum. But the cost of construction of a channel depends on excavation and the lining.To keep the cost down or minimum, the wetted perimeter, for a given discharge, should be minimum. This condition is utilized for determining the dimensions of economical sections of different forms of channels. Most economical section is also called the best section or most efficient section as the discharge passing through a most economical section of channel for a given cross-sectional area A, slope of the bed So and a resistance coefficient, is maximum. But the discharge

05/02/23 5MODASSAR ANSARI

Consider a rectangular section of channel as shown. Let B = width of channel, D = depth of flow. B

∴ Area of flow, A = B x D, Wetted perimeter, P = 2D + B, Dwe have

we get P = 2D +

05/02/23

DAB

DA

6MODASSAR ANSARI

we get P =2D+ A/D For most economical cross section, P should be minimum for a given

area; dP/ dD = 0 So, dP/dD = 2-A/D2 =0 2=A/D2 =BD/D2

2=B/DHence D =B/2Hydraulic radius Rh=A/P = BxD/B+2D = 2D2 /4D = D/2

05/02/23 7MODASSAR ANSARI

Derive P = f(y) and A = f(y) for a trapezoidal channel How would you obtain y

05/02/23

z1

b

y

zyybA 2

2/13/21oh SAR

nQ

8MODASSAR ANSARI

05/02/23

ryrarccos

cossin2 rA

sin2rT

y

T

A

rrP 2

radians

Maximum discharge when y = ______

0.938d

9MODASSAR ANSARI