Nce403 mod unit2
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Transcript of Nce403 mod unit2
Chezy’s and Manning’s equations for uniform flow in open channel,
Velocity distribution, Most efficient channel section, Compound channels.
05/03/23 1MODASSAR ANSARI
BY MODASSAR ANSARI 2nd Year Department of civil Engineering SUBJECT- HYDRAULICS & HYDRAULIC
MACHINES SUBJECT CODE-NCE 403
05/03/23 2MODASSAR ANSARI
Introduced by the French engineer Antoine Chezy in 1768 while designing a canal for the water-supply system of Paris
05/03/23
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
05/03/23
(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
05/03/23 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 +
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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
05/03/23 7MODASSAR ANSARI
Derive P = f(y) and A = f(y) for a trapezoidal channel How would you obtain y
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z1
b
y
zyybA 2
2/13/21oh SAR
nQ
8MODASSAR ANSARI
05/03/23
ryrarccos
cossin2 rA
sin2rT
y
T
A
rrP 2
radians
Maximum discharge when y = ______
0.938d
9MODASSAR ANSARI