To Establish the Steady Uniform Flow Condition in a Laboratory Flume and to Determine the Manning’s Roughness Coefficient “n” and Chezy’s Coefficient “c”.

Objective:

1.    To physically measure the Manning’s Coefficient and Chezy’s Coefficient.
2. .      To study the variation of ‘n’ and ‘c’ as a function of velocity.
3. .      To study the relationship between ‘n’ and ‘c’.

Apparatus:

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

(As shown in figure 1.1)

Figure 1.1:   View of S6 glass sided tilting lab flume

RELATED THEORY

Flume

Open channel generally supported on or above the ground.

Uniform Flow:

A uniform flow is one in which flow parameters and channel parameters remain same with respect to distance between two sections.

 Non-Uniform Flow:

A non-uniform flow is one in which flow parameters and channel parameters not remain same with respect to distance between 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.

Unsteady Flow:

If at any point in the fluid, the conditions change with time, the flow is described as unsteady.

Steady Uniform Flow:

Conditions do not change with position in the stream or with time. An example is the flow of water in a pipe of constant diameter at constant velocity.

Steady Non-Uniform 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.

Unsteady Uniform Flow:

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

Unsteady Non-Uniform Flow:

Every condition of the flow may change from point to point and with time at every point. For example waves in a channel.

Manning’s Roughness Equation (1889):

Where,

V    is the average velocity of flow (ft/s, m/s)

n    is the Manning coefficient

R    is the hydraulic radius (ft, m)

S     is the slope of the water surface (m/m,ft/ft)

The Manning’s Equation is an empirical equation which applies on open channel flow and is a function of velocity, flow area and channel slope. Manning’s Coefficient represents the roughness or friction applied to the flow by channel.

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.

Hydraulics Radius:

The hydraulic radius is a measure of channel flow efficiency.

Where:

R is the hydraulic radius.

A is the cross sectional area of flow,

P is wetted perimeter.

It is a function of the shape of the pipe, channel, or river in which the water is flowing. In wide rectangular channels, the hydraulic radius is approximated by the flow depth. The measure of a channel's efficiency (its ability to move water and sediment) is used by water engineers to assess the channel's capacity.

Chezy’s  Formula:

Chezy’s formula can be used to calculate mean flow velocity in conduits and is expressed as

Where

V = mean velocity (m/s, ft/s)

C = the Chezy’s roughness and conduit coefficient

    R = hydraulic radius (ft, m)

    S = slope (m/m, ft/ft)

Derive relationship between ‘C’ and ‘n’: 

Procedure:

·         Measure Channel (Flume) width.

·         Switch on the machine.

·         Wait to stabilize the water in the flume.

·         Set the slope of the flume to 1/400.

·         Fill the S-6 tilting flume up to some depth.

·         Note down the readings of differential manometer and see the corresponding discharge from the discharge chart.

·         Note down the depth of flow at three different points.

·         Calculate the Co-efficient “C” and “n” accordingly by the given formulas.

Precautions:

·         Take manometric reading only when flow is steady.

·         The height should not be measured near the joints or at points where there is turbulence in flume.

·         The height measuring needle must be adjusted precisely.

·         The tip of the needle must be just touching the water surface while taking observations.

Observations and Calculations:

Width (b) =                 ______5.28 cm________

Length of Flume =      ______1.83 m______6 ft___

Slope =                        ______1 cm_________

0.00029 m3/s

Sr No.	Flow Rate (Q)	Avg Depth 'y'				Area of Flow (A)	R	n	c	v
		y1	y2	y3	yavg
	m3/s	mm	mm	mm	mm	m2				m/s
					12.5

Attach following graphs

1.      n vs C

2.      v vs n

3.      v vs C

  

Comments:-

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