Determine Mannings Roughness Coefficient and Chezy Roughness Coefficient in a Labortary Flume

[FAISAL SARDAR] 2009-CIV-122

Experiment # 1 TO DETERMINE MANNINGS ROUGHNESS COEFFICIENT “n” AND CHEZY ROUGHNESS COEFFICIENT “C” IN A LABORTARY FLUME . OBJECTIVE :  To study the variation of “n “ & “c” as a function of velocity .  To investigate the relation between “n” & “c”

APPARATUS:  S6 glass sided Tilting lab flume with manometric flow arrangement and slope adjusting scale.  Point gauge (For measuring depth of channel)

RELATED THEORY: FLUME: Open channel generally supported on or above the ground.

S6 GLASS SIDED TILTING LAB FLUME

[FAISAL SARDAR] 2009-CIV-122

UNIFORM FLOW: A uniform flow is one in which flow parameters and channel parameters remain same with respect tondistance b/w two sections. this type of flow only possible in prismatic channel .

PRISMATIC CHSNNEL : channel with defined cross section and bed slope .

NON-UNIFORM FLOW: A non-uniform flow is one in which flow parameters and channel parameters not remain same with respect to distance b/w two sections.

STEADY FLOW: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time.

UN STEADY FLOW: If at any point in the fluid, the conditions change with time, the flow is described as unsteady (Inpractice there are always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady .

STEADY UNIFORMM FLOW: Conditions do not change with position in the stream or with time. An example is the flow of water in apipe of constant diameter at constant velocity.

STEADY NON-UNIFORMM FLOW: Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet - velocity will change as you move along the length of the pipe toward the exit.

STEADY UNIFORMM FLOW: At a given instant in time the conditions at every point are the same, but will change with time. Anexample is a pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off.

UNSTEADY NON-UNIFORMM FLOW: Every condition of the flow may change from point to point and with time at every point. For examplewaves in a channel.

[FAISAL SARDAR] 2009-CIV-122

CHEZY’S FORMULA : Chezy formula can be used to calculate mean flow velocity in conduits and is expressed as

V= C√ 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)

MANNING’S FORMULA : The Manning formula states

V= where v = mean velocity (m/s, ft/s) n = mannings roughness coefficient R =hydraulic radius of the conduit (m, ft) S = slope of the conduit (m/m, ft/ft)

HYDRAULICS RADIUS:

.

The hydraulic radius is a measure of channel flow efficiency

R= Where: R = hydraulic radius, A = cross sectional area of flow , P = wetted perimeter . The greater the hydraulic radius, the greater the efficiency of the channel and the less likely the river isto flood. For channels of a given width, the hydraulic radius is greater for the deeper channels.

ROUGHNESS: Roughness Is Actually Resistance To Floew

COMPOSITE OR EQUILENT ROUGHNESS : when the bed & side material and condition are different then we use equilent roughness.

[FAISAL SARDAR] 2009-CIV-122

PROCEDURE :      

switch on the apparatus Wait to stabilize the water in the flume Set the slope of the flume Note the discharge reading . Measure the depth at three different location for one discharge reading . Then change the discharge and measure the depth reading again .

OBSERVATION & CALCULATION Depth Of Flow (y) SR #

CHANNEL BED SLOPE

FLOW RATE

m3/sec

y1

y2

y3

yavj

mm

mm

mm

mm

AREA OF FLOW

WETTED PERIMETER

HYDROLIC RADIUS

FLOW VELACITY

m2

m

m

m/sec

MANNINGS ROUGHNESS COEFFICENT(n)

CHEZYS ROUGHNESS COEFFICENT(c)

1

0.0020

0.007998

30.3

47.5

51 42.93

0.01288

0.385867

0.033379

0.620963

0.007466

75.99959

2

0.0020

0.009795

39.3

53.7

57 50.00

0.015

0.4

0.0375

0.653

0.007673

75.40195

3

0.0020

0.011311

42.3

59.6

61 54.30

0.01629

0.4086

0.039868

0.694352

0.007517

77.75952

4

0.0020

0.012646

46.1

59.4

64.7 56.73

0.01702

0.413467

0.041164

0.743008

0.007176

81.88778

5

0.0020

0.013853

49.6

70

70.4 63.33

0.019

0.426667

0.044531

0.729105

0.007706

77.25788

6

0.0020

0.015996

54.3

66.6

72.8 64.57

0.01937

0.429133

0.045137

0.825813

0.006865

86.91567

[FAISAL SARDAR] 2009-CIV-122

GRAPHS n vs c

n vs v

0.0078

0.0078

0.0077 M A N N I N G S C O E F F I C E N T

M A N N I N G S

0.0076 0.0075

0.0074 0.0073 n vs c 0.0072 0.0071 0.007

C O E F F I C E N T

0.0077 0.0076 0.0075 0.0074 0.0073 n vs v 0.0072 0.0071 0.007

( (

n )

n )

0.0069

0.0069 0.0068

0.0068 70

75

80

85

CHEZYS COEFFICENT (C)

90

0

0.2

0.4

0.6

VELOCITY (m/sec) V

0.8

1

[FAISAL SARDAR] 2009-CIV-122

CHEZY'S COFF(C) VS VELOCITY (V) 88

C H E Z Y S

86

84

C 82 O t E l F e 80 F I C E 78 N T

c vs v

( C

76

) 74

0

0.1

0.2

0.3

0.4

0.5

VELOCITY (m/sec) V

0.6

0.7

0.8

0.9

[FAISAL SARDAR] 2009-CIV-122

COMMENTS :  value of chezy’s co-efficient increases with increase in discharge.  Manning’s co-efficient decreases with increase in discharge.  There is a inverse relation between mannings coefficent & velocity .  There is a direct relation between chezy;s coefficent & velocity  There is inverse relation b/w manning’s co-efficient and chezy’s co –efficient

taken manometric reading when flow is steady .  If the bed and sides material and conditions are different then we take equivaent roughness coefficent .  The manning formula is simple, accurate and values of for a very wide range of channels are available