GROUP NAME: Charlie and the Charlie’s Angels DATE: July 19, 2010

NAME: Mujette G. Godmalin Instructor’s Signature:_______

ACTIVITY NO. 2

FLOW OF WATERS OVER WEIRS

OBJECTIVE:

To determine the flow of water and the coefficient of discharge in a triangular

weir.

To determine the relationship between the head H of the weir and the discharge

of water over the weir.

APPARATUS:

Water Source ● Stopwatch ● Container

Water Tank ● Meter Stick ● Hook Gage

THEORETICAL BACKGROUND:

A weir is a notch of regular form through which water may flow. It serves as a barrier for the flow of water in an open channel. The edge or surface over which the water flows is called the crest. In open channel hydraulics, weirs are commonly used to either regulate or to measure the volumetric flow rate. They are of particular use in large scale situations such as irrigation schemes, canals and rivers. Weirs can be made with plywood or with l-inch boards and 2 x 4’s. The reliability of weir measurements is affected by construction and installation, but when properly constructed and installed, weirs are one of the simplest and most accurate methods of measuring water flow. In fact, hydrologists and engineers treat this as a simple method of measuring the rate of fluid flow in small to medium-sized streams, or in industrial discharge locations.

There are different types of weir. It may be a simple metal plate with a V-notch

cut into it, or it may be a concrete and steel structure across the bed of a river. Common

weir constructions are the rectangular weir, the triangular or v-notch weir, and the

broad-crested weir. Weirs are called sharp-crested if their crests are constructed of thin

metal plates, and broad-crested if they are made of wide timber or concrete. A weir

which causes a large change of water level behind it, compared to the error inherent in

the depth measurement method, will give an accurate indication of the flow rate.

The triangular notch has advantages over the rectangular notch since the shape

of the nappe does not change with head so that the coefficient of discharge does not

vary so much. A triangular notch can also accommodate a wide range of flow rates.

The V-notch functions to control the flow of the water out of the basin. Stream

water passes between the concrete "wings", through the flume and ponds in the

concrete basin. Water flows out through a steel V-shaped notch situated in the basin's

downstream wall. The V-notch controls the flow of water out of the ponding basin and

the more water there is coming down the stream, the higher it will rise in the basin and

V-notch as it spills over. Therefore, the amount of water flowing out of the watershed

can be measured by recording the height of the water in the basin, and translating this

height to a flow rate in cubic feet per second or liters per second. Mathematical

functions are available which relate the height of the water in the basin to the flow rate.

Source: http://www.hubbardbrook.org/w6_tour/weir-stop/weirwork.htm

EQUIPMENT SET-UP:

12.5 cm Note: tan (θ/2) = 6.25/11.7 Θ H 11.7 cm Therefore, θ = 56.221° PROCEDURE:

1. Take note of the initial reading on the wall of the water tank.

2. Set the stopwatch to zero.

3. Open the main valve.

4. Run the pump until the level of the water is just above the level of the weir crest.

5. Determine the head on the weir using the hook gage by measuring the distance

between the crest of the weir and the liquid surface. To set point of the hook in

the liquid surface, it is first placed below the surface and then released until a

small pimple just appears; its point is accurately at the same elevation as the

liquid surface. From the graduated scale and the vernier on the hook gage shaft,

the surface elevation of liquid is read.

6. Let the water flow out into the container. The time it takes the water to reach a

certain level in the container is determined with the aid of the stopwatch.

7. Measure the actual discharge collected in the container.

8. After five observations, close the main valve.

DATA AND RESULTS: Temperature: 30 °C, 29°C Density: 9.95774 x 10-4 kg/cm3 @ 31 °C

9.96091 x 10-4 kg/cm3 @ 29 °C

No. of Runs 1 2 3

Duration of Run, sec. 5.31 6.03 9.53

Hook Gage ave. reading, cm. 26 25.1 22.6

Hook Gage, zero reading, cm. 16 16 16

Head on weir, cm. 10 9.1 6.6

Temperature of water, °C 30 29 30

Water over weir, Volume of water collected in container, cm3 13,600 11,200 8,375

Net water, Kg 13.542 11,200 8.337

Actual volumetric flow rate, cm3/sec 2561.2 1857.4 878.8

Theoretical volumetric flow rate, cm3/sec 2740.0 2199.1 667.5

Average coefficient of discharge 0.69746

COMPUTATIONS:

The discharge over the triangular weir is given by the following formula: Q = C 4/15 √ (2g) L H3/4 OR Q = C 8/15 √ (2g) tan (Θ/2) H5/2

Where: Q = discharge over the triangular weir C = coefficient of discharge Θ = angle of opening of the triangular weir H = Head of the weir g = pull of gravity L = horizontal length of liquid surface over the weir

a.) Finding kg. net water: Density of water @ 30 °C is 9.95774 x 10-4 kg/cm3

Net water = volume collected x density

For Run 1, Net water = 13,600 cm3

x (9.95774 x 10−4kg/cm3)

Net water=13.542 kg.

b.) Finding actual volumetric flow: Actual volumetric flow= water collected in container,cm3

average time, s For Run 1,

Actual volumetric flow= 13,600 cm3 5.31 sec

Actual volumetric flow = 2561.2 cm3/sec

c.) Finding coefficient of discharge and theoretical volumetric flow:

From the plot of the graph of the log of the flowrate, Q, on the y-axis versus the

log of the water height, H, on the x-axis, the slope and the y – intercept can be obtained. The best fit equation in the form,

y = nx + b

is, y=2.511 x+0.880

Where = slope.

Plug in value of slope in the empirical equation,

Q=k x Hn

Q=k x H2.511

Where b is the y – intercept from the plot equal to 0.880, hence,

Q=k x Hn Q=k x H2.511

Theoretically:

Equating the empirical and theoretical equations,

Since 2.511 ≈ 5/2

Solving for C, we get:

C = 0.69746 Substitute calculated value for Cd. For , use 980.665 cm/s2,

For g, use 980.665 cm/s2.

For Run 1:

Q = 2782.804

Calculations for other runs. PROBLEM: Plot H vs Qa. Discuss.

Run No. Weir Head , H Vol. Flow Rate, Q logH logQ

1 10 2561.2 1.00000 3.408

2 9.1 1857.4 0.95904 3.269

3 6.6 878.8 0.81954 2.944

GRAPHS AND FIGURES

Figure I. Plot of Qa vs. H

DISCUSSION:

The flow of water and the coefficient of discharge in an approx. 60° (as measured and calculated) triangular notch weir were determined during the experiment. The calculated coefficient of discharge is 0.69746.

During the experiment, a smooth flow of the fluid was favored before measuring the head on weir. It was due to the assumption that the distribution of velocities in approach flow has a definite influence on the discharge over the weir. As the valve loosened, the head increased. This increase resulted in the change of the fluid flow. From 6.6 to 10 cm head, the water discharged also changed from 8.337 to 13.542 kg. Thus, an increase in the head causes an increase in the discharge.

Volumetric flowrate averaging to 2561.2 cm3/sec was calculated reflecting the manner of fluid flow. Temperature reading ranging from 29° to 30°C was also obtained. Variation of the temperature was too small that there were no observed effects of it in the fluid flow.

CONCLUSION:

The smooth flow to and over the weir is essential to the determination of accurate rates of flow since the distribution of velocities in the approach flow has a definite influence on the discharge over the weir. Kinetic energy correction factor can account

for the variation in the approach velocity. The value of the coefficient of discharge depends on the degree of non uniformity of the approach velocity distribution.

It was also noted that the head affects the flow of water. The relationship between the head of the weir and the discharge of the water over the weir is directly proportional.

Aside from the velocity and the head, temperature variations influence the fluid properties like viscosity and surface tension. The variations in these fluid properties in turn will influence the discharge over the weir. However, the effect of small temperature variations on the water flow over weirs is negligible.

Moreover, geometry of the weir will also affect the flow of water as discussed in literatures but comparison is not covered since triangular notch is the only one used in the experiment.

APPENDIX A

Raw Data

Hook Gage (ave.)

Trial 1 Trial 2 Trial 3 Trial 4

26

Volume of water (ml)

3450 3300 3450 3400

Duration 1.47 1.37 1.16 1.31

25.1

Volume of water (ml)

2700 2750 2850 2900

Duration 1.47 1.59 1.50 1.47

22.6

Volume of water (ml)

1400 2600 2250 2125

Duration 1.43 2.94 2.66 2.50

REFERENCES:

Lange’s Handbook of Chemistry

Perry’s Chemical Engineering Handbook

Physical Chemistry by Atkins and Paula

Unit Operations, 5th Edition, McCabe and Smith