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Experiment # 1
To determine the Manning’s Roughness Coefficient(n) & Chézy Coefficient(c) in laboratory flume
Purpose:
To study changes in Manning’s Roughness coefficient (n) by varying discharge (Q) in
flume.
To study changes in Chezy Coefficient(c) by varying discharge (Q) in flume.
To investigate relation between Manning Roughness Coefficient(n) & Chezy Coefficient
(c)
To determine Manning Roughness Coefficient(n) and Chezy Coefficient (c)
Apparatus :
i. S6 glass sided tilting flume
Note: In this type of flume we can adjust
positive as well as negative slope. Positive
slope ranges between 0 to 1:40 and negative
upto 1:200.The bad of the flume is made up of
cold formed steel. Length of the channel is 7.5
m.
ii. Point Gauge
iii. Differential Manometer
Related Theory:
1) Uniform Flow:
That type of flow in which flow perimeters and channel perimeters remain constant as
a function of distance between two cross sections. In uniform flow, depth and velocity
remain constant along the flow direction for the given discharge in the given channel. We
can say that it is only possible in prismatic channels.
2) Non-Uniform Flow:
That type of flow in which flow perimeters and channel perimeters do not remain
constant as a function of distance between two cross sections.
3) Steady flow:
That type of flow in which flow perimeters and channel perimeters remains constant at a
particular cross-section with respect to time.
4) Unsteady flow:
That type of flow in which flow perimeters and channel perimeters remains do not remain
constant at a particular cross-section with respect to time.It can also be determined by noting
the depth of water.
There are four different flow combinations present.
i. Uniform-Steady
Generally flow in irrigation canals are maintained uniform and steady.
ii. Non-uniform-Steady
A typical example of such flow is back water flow on upstream of the dam.
iii. Unsteady-Uniform
An example is a pipe of constant diameter connected to a pump pumping at a
constant rate which is then switched off. This type of flow is practically not possible
in open channel.
iv. Unsteady-Non-uniform
Example of this type of flow is flood waves.
5) Manning’s Roughness Formula:
Assumptions
o Fluid is an ideal fluid just to simplify the calculations (ideal flow condition)
o Flow is steady flow
o Fluid is non-viscous
o Fluid is incompressible
The Manning formula, known also as the Gauckler–Manning formula, or Gauckler–
Manning–Strickler formula in Europe, is an empirical formula for open channel flow or free-
surface flow driven by gravity. It was first presented by the French engineer Philippe
Gauckler in 1867,and later re-developed by the Irish engineer Robert Manning in 1890.
The Gauckler–Manning formula states:
Where:
V = cross-sectional average velocity (ft/s, m/s)
k = 1.486 for U.S. customary units or 1.0 for SI units
n = Gauckler–Manning coefficient ( s/m1/3, s/ft1/3).
Rh = hydraulic radius (ft, m)
S = slope of the water surface or the linear hydraulic head loss (m/m.ft/ft)) (S = hf/L)
The Gauckler–Manning coefficient (n) depends upon roughness of the
channel,Vegitation,scavering and many other factors.
Hydraulic Radius (Rh) =A/P
P= wetted perimeter
A=area of flow of water
The discharge formula, Q = A V, can be used to manipulate Gauckler–Manning's equation
by substitution for V. Solving for Q then allows an estimate of the volumetric flow
rate (discharge) without knowing the limiting or actual flow velocity.
The Gauckler–Manning formula is used to estimate flow in open channel situations where it
is not practical to construct a weir or flume to measure flow with greater accuracy. The
friction coefficients across weirs and orifices are less subjective than “n” along a natural
(earthen, stone or vegetated) channel reach. Cross sectional area, as well as “n”, will likely
vary along a natural channel.
6) Effect of Gauckler–Manning coefficient(n) on channel:
The effect of Gauckler–Manning coefficient (n) on flow is very important because if value
of Gauckler–Manning coefficient (n) changes from the original value it will cause many
problems and efficiency of channel will decrease.
If Gauckler–Manning coefficient (n) increases velocity of water will decrease and due to
which sedimentation will increase,it will raise the bed channel and there are chances of over
flow of water. On the other hand if Gauckler–Manning coefficient (n) decreases than it will
increase the velocity and head depth of water will decreases. It will effect whole system of
irrigation as well as the hydro power projects.
7) Chezy Formula:
The Chézy formula describes the mean flow velocity of steady, turbulent open
channel flow:
v = c √(R S)
Where
v = mean velocity (m/s, ft/s)
c = the Chezy roughness and conduit coefficient
R = hydraulic radius of the conduit (m, ft)
S = slope of the conduit (m/m, ft/ft)
The formula is named after Antoine de Chézy, the French hydraulics engineer who
devised it in 177.
8) Relation between Mannning’s roughness coefficient and Chezy
Coefficient:
This formula can also be used with Manning's Roughness Coefficient, instead of
Chézy's coefficient. Manning derived the following relation to C based upon
experiments:
Where
“C” = the Chézy coefficient [m½/s],
“R” = the hydraulic radius [m],
“n” = Manning's roughness coefficient.
This relation is empirical.
Procedure:
i. Set the slope of the channel.
ii. Switched on the pump and left it to become fully operational.
iii. After some time uniform condition is achieved.
iv. Note down the manometric head attached to the flume and find the discharge
from the table provided by the Manufacturer.
v. Also we will note done the average depth of water in the flume by gauge by
measuring depth at 2,4,6 m .
vi. Repeat the same procedure for different values of discharge.
Observations and Calculations
Formulas
Manning’s formula
vavg=𝛼
𝑛1× Rh
2/3× S0
1/2
vavg=𝛼
𝑛2× Rh
2/3× S1/2
Chaezy’s formula
vavg =𝑐1√𝑅𝑆0
vavg =𝑐2√𝑅𝑆
Hydraulic radius =Rh = A/P ; Area of flow of water= A=b x yavg
Depth = yavg = (y1+y2+y3)/3 ; Wetted perimeter = P = b + 2yavg
S = Slope of Energy line ; Sw= Slope of Hydraulic Grade Line
S0=Slope of Channal Bed ; vavg= Average Velocity
For uniform flow conditions S = S0 = Sw
α =Conversion Constant = 1.00 in SI = 1.486 in FPS
n = Manning’s Roughness Coefficient; c = Chezy Coefficient
Sr No
So Q y A vavg S Pw Rh
Manning’s Roughness coefficient
Chezy’s Coefficient
y1 y2 y3 yavg n1 n2 c1 c2
(m3/s) (m) (m) (m) (m) (m2) (m/s) (m) (m) (s/m1/3) (s/m1/3) (m1/2/s) (m1/2/s)
1 0.002 0.008942 0.055 0.059 0.06 0.058 0.0174 0.513908 0.001 0.416 0.041827 0.010486 0.010486 56.18786 79.46163
2 0.002 0.011997 0.072 0.073 0.073 0.072667 0.0218 0.550321 0.00055 0.445333 0.048952 0.010875 0.010875 55.61802 106.0594
3 0.002 0.015996 0.079 0.081 0.079 0.079667 0.0239 0.669289 0.00045 0.459333 0.052032 0.009313 0.009313 65.60902 138.316
4 0.002 0.018326 0.084 0.083 0.081 0.082667 0.0248 0.738952 0.0003 0.465333 0.053295 0.008571 0.008571 71.57432 184.8041
5 0.002 0.0192 0.084 0.087 0.085 0.0853 0.0256 0.7610 0.0005 0.7521 0.749141 0.0005 0.470667 0.054391 0.00857
6 0.002 0.0204 0.092 0.092 0.085 0.0897 0.0269 0.7388 0.0011 0.7996 0.75803 0.0011 0.479333 0.05612 0.008648
0
20
40
60
80
100
120
140
160
180
200
0.0000 0.0050 0.0100 0.0150 0.0200 0.0250
c2
(m1
/2/s
)
Q(m3/s)
Relation bettwen Q & c2
0.0000
0.0050
0.0100
0.0150
0.0200
0.0250
0 0.002 0.004 0.006 0.008
Q(m
3/s
)
n2
(s/m)
Relation between Q & n2
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 50 100 150 200
n2
(s/m
1/3
)
c2
(m1/2/s)
Relation between n2 & c2
2, 0.0700 4, 0.0720 6, 0.0726
2, 0.0554, 0.059 6, 0.06
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0 1 2 3 4 5 6 7
He
ad(m
)
Horizontal Distance(m)
Hyraulic Grade Line & Energy Line # 1
EL 1
HGL 1
2, 0.1022 4, 0.1031 6, 0.1022
2, 0.079 4, 0.081 6, 0.079
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0 1 2 3 4 5 6 7
He
ad(m
)
Horizontal Distance(m)
Hyraulic Grade Line & Energy Line # 3
EL
HGL
2, 0.0877 4, 0.0883 6, 0.0883
2, 0.072 4, 0.073 6, 0.073
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.0900
0.1000
0 1 2 3 4 5 6 7
He
ad(m
)
Horizontal Distance(m)
Hyraulic Grade Line & Energy Line # 2
EL
HGL
2, 0.1198 4, 0.1198 6, 0.1176
2, 0.084 4, 0.087 6, 0.085
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0.1400
0 1 2 3 4 5 6 7
He
ad(m
)
Horizontal Distance(m)
Hyraulic Grade Line & Energy Line # 5
EL
HGL
2, 0.1110 4, 0.1106 6, 0.1100
2, 0.084 4, 0.083 6, 0.081
0.0000
0.0200
0.0400
0.0600
0.0800
0.1000
0.1200
0 1 2 3 4 5 6 7
He
ad(m
)
Axis Title
Hyraulic Grade Line & Energy Line # 4
EL
HGL