Manning’s Roughness Coefficient(n)

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

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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

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 derivedthe 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.

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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 .

Observations and Calculations

Formulas

Manning’s formula

v

=

× R

× S

v

=

× R

× S

Chaezy’s formula

v

=𝑐

√𝑅𝑆

v

=𝑐

√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 ;

v

=

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) (m}2_{) (m/s) (m) (m) (s/m}1/3_{) (s/m}1/3_{) (m}1/2_{/s) (m}1/2_/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 (m 1/ 2/s) Q (m3/s)

Relation bettwen Q & c

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)

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 n

& c

2, 0.0700 4, 0.0720 6, 0.0726 2, 0.055 4, 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 H e 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 H e 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 H e 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 H e 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 H e ad (m ) Axis Title

Hyraulic Grade Line & Energy Line # 4

EL HGL

2, 0.1135 4, 0.1145 6, 0.1138 2, 0.092 4, 0.092 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 H e ad (m ) Horizontal Distance (m)

Hyraulic Grade Line & Energy Line # 6

EL HGL