How to determine Manning's and Chezy's Coefficients for Laboratory Flume.

Applications of Chezy’s and Manning’s Formulas.

OBJECTIVES:

-        To study the variation of Chezy’s “C” and Manning’s “ȵ” as a function of velocity in the flume.
-           To study the applications of Manning’s and Chezy’s formulas.
-           To investigate the relationship between the Manning’s and Chezy’s coefficients for the flume.

Apparatus Used:

-          S-6 glass sided tilting flume.
-          Point gauge with railing.
-          Manometer
-          Pump
-          Intake tank
-          Outlet

Flume:

    It is an open channel which is supported on or above ground and is used for conveying water. It is in the form of an open declined gravity chute whose walls are raised above the surrounding terrain.

Types of Fluid Flows

-   Open Channel flow
-   Steady Uniform flow
-   Steady non-Uniform flow.
-   Non-Uniform flow.

-   Laminar flow
-   Turbulent flow
-   Transient flow
                             Details

Chezy’s formula:

              Chezy’s formula was presented in 1775. It states that:
                        Velocity is an open channel is a function of hydraulics radius and slope of the channel bed.
                          Mathematically it is equal to:
                             V = C * sqrt(RS)
Where,
V = Velocity of the flow
R = Hydraulic Radius
C = Slope of Channel Bed
C = Chezy’s Coefficient

According to Kutler’s Formula.

C= sqrt(8g)/f


Manning’s Formula:
              V = 1/ ȵ *(R)^2/3 * (S)^1/2

Where,

V = Velocity of the flow
R = Hydraulic Radius
C = Slope of Channel Bed
ȵ = Manning’s Coefficient

Hydraulic Radius:
            The hydraulic radius is defined as the measure of channel flow efficiency.

                               R = A/P
Where,
      R = Hydraulics Radius.
      A = Cross-sectional Area of flow.
      P = Wetted Perimeter.
  The efficiency of channel depends on hydraulic radius. More will be the hydraulic radius more will be the efficiency of channel.

Relationship between Manning’s and Chezy’s Coefficient:

           Chezy Coefficient ‘C’ and Manning’s Coefficient ‘ȵ’ are inversely proportional to each other.
                    
                                               Chezy’s:
                                                         V = C * sqrt(RS)-------------Eq. (1)
                                               Manning’s:
                                                         V = 1/ ȵ *(R)^2/3 * (S)^1/2-------------Eq. (2)

                                               Comparing both equations:
                                                    C * sqrt(RS) = 1/ ȵ *(R)^2/3 * (S)^1/2

                                                      C = (Rh)^1/6 / ȵ     OR    ȵ = (Rh)^1/6 / C

                                                            C inversely proportional to ȵ.

PROCEDURE:

-      Turn on the Apparatus.
-      Allow the water in the flume to stabilize so that the flow becomes uniform that is the depth and velocity of flow becomes constant.
-      Set the slope of the flow in the glass tilted flume.
-      Note the reading from the manometer. The manometric head difference will give total discharge ‘V’
-      Measure depth at 3 different locations for each discharge value.
-      Measure the hydraulic radius of the area.
-      Determine the roughness coefficients of Manning’s and Chezy’s using their respective equations.

Results:          After the performance of experiment we can now easily answer the question  that Do manning and chezy coefficients vary with discharge (at the same water depths)?
          Chezy's coefficient is directly proportional to discharge while manning's coefficient is inversely proportional to discharge.

        The graphs between:

-        Chezy coefficient and velocity.
-        Manning coefficient and velocity.
-        Chezy coefficient 'C' and Manning coefficient 'ȵ'
                                   is shown below.

           This graph shows that manning's coefficient is inversely proportional to velocity 'V'

 This graph shows that Chezy's coefficient "C' is directly proportional to velocity 'V'.

This graph shows that manning's coefficient is inversely proportional to Chezy's Coefficient 'C'