School of Vocational Engineering

CIVE 5688

Simple and Complex Fluid Systems

Introduction to the Topic

In hydraulic engineering, weirs (notches) are commonly used to regulate the water level and the flow in rivers and other open channels as well as for measuring the rates of discharge in such water courses.

It is the purpose of this experiment to use the relationship between the head on a weir and the discharge to establish the Coefficient of Discharge for a rectangular weir.

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The equipment

Flow over weir (notch) equipment

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Safety issues

Students must not operate the equipment until they have received an orientation in its use by their instructor.

The first, and foremost, precaution is:

NEVER UNDERTAKE AN EXPERIMENT UNLESS A STAFF MEMBER IS PRESENT.

Water-borne diseases

Most equipment in a fluids laboratory contains water. Although every precaution has been taken by RMIT to ensure that the water is safe, the student must constantly be aware of the fact that water may contain pathogens (disease-causing bacteria). Contact with water must be avoided; this is especially important if there are any exposed cuts or abrasions through which the bacteria may enter the body.

Footwear

Wear sensible footwear. You will not be allowed to enter the lab with bare feet, sandals or thong-type footwear.

Trip hazards

Be aware of such things as electrical cables, wet floors, patches of oil, etc.

Behaviour in the laboratory Many incidents of injury have been caused by a disregard of safety precautions and/or unruly or ‘larrikin’ type behaviour. Should your instructor be aware that this is occurring, a warning (one and only) will be issued. A second occurrence will result in the offender being barred from entering the laboratory for the remainder of the semester and a FAIL being recorded for the course.

Be Aware Safety is the responsibility of everybody present in the laboratory. If you are aware of any fault with a piece of equipment, any action by a student which may lead to injury, or any safety hazard in general, it is your responsibility to report it to your instructor.

Objective

To determine the value of the Coefficient of Discharge for a rectangular notch.

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Theory

The equation for flow over a rectangular notch, derived using calculus is :

3/ 22 2 3

Q g bH

where b = width of the notch, H = depth of water above the notch

However, when flow occurs in practice, there is a contraction of the area of flow as it passes through the notch. The top surface drops, the bottom springs upwards and the sides curve inwards as shown.

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Plan View

Side Contractions

Flow

Side View

Top Bottom Contractions

Flow

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To compensate for this contraction, the above formula is therefore written:

322 2

3 dQ C g bH

where Cd is a coefficient which accounts for this loss.

To determine the value of Cd, we can write this equation in the form :

Q = kHn

where 2 2g 3 dk C b

and n = the exponent of H (which should prove later to be 3/2)

By taking logs of this equation,

log Q = log k + nlogH

By plotting the experimental results on a graph having axes of log H and log Q, then, providing that k and n are constant over the range of the results, they will lie on a straight line of slope n

and intercept log k on the axis of log Q. The intercept log k will be derived by extrapolation.

This is indicated in the Appendix.

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Operation / Data collection

Initial set-up: Zero the depth gauge

Using the flow control valve on the hydraulic bench, fill the apparatus until the water level is approximately level with the crest of the weir. Now lower the rule until it just touches the water surface and record the reading at the very top. This reading represents zero water depth and hence is subtracted from all future readings to give the actual water depth H at the weir. (Because the gauge reads in reverse, you will actually subtract all readings from this sill measurement).

Gauge

Flow measurement and data collection

A series of measurements of discharge and head on the weir are then taken, the flow being regulated at the bench supply valve. It is recommended that the first reading is taken at maximum discharge, and subsequent readings with approximately equal decrements in head. (You will establish the value of these decrements by first measuring the total range of flow levels and dividing by the total number of readings you anticipate taking).

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Readings should be discontinued when the level has fallen to a point at which the stream ceases to spring clear of the notch plate; this is likely to occur when the head has been reduced to about 10 mm for a rectangular notch. About eight different discharges for each notch should be sufficient.

To measure the head at each decrement, simply lower the rule until it just touches the water surface. Note the scale reading and enter it into the table below.

To measure the flow rate through the hydraulic bench for each decrement, lift the plunger in the flow measurement tank to release all water back into the lower reservoir. When the tank is empty, replace the plunger. As it fills, observe the level indicator on the outside of the tank. When it reaches the zero mark, start the stopwatch. When it reaches the top of the scale, stop the stopwatch. Note the time elapsed and the number of litres that flowed in that time. (Ensure that you check for leakage around the bung before commencement).

Measuring tank

Recording of data

Results given in this section are typical of those which you should have obtained.

Data recorded

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Sill level mm

Surface level mm

Measuring tank L

Time to fill

seconds

115.5 56.5 35 38.25

115.5 61.5 35 45.29

115.5 66.5 25 34.81

115.5 71.5 25 44.61

115.5 76.5 15 30.84

115.5 81.5 15 39.73

115.5 86.5 15 45.82

115.5 91.5 5 21.31

115.5 96.5 5 25.47

115.5 101.5 5 52.71

Computation of results

H = Sill– Surf level m

Flow rate Q x 103 m3/s

Log H Log Q

0.059 0.915 -1.23 -3.04

0.054 0.73 -1.27 -3.11

0.049 0.718 --1.31 -3.14

0.044 0.560 -1.36 -3.25

0.039 0.486 -1.41 -3.31

0.034 0.378 -1.47 -3.42

0.029 0.327 -1.54 -3.49

0.024 0.235 -1.62 -3.63

0.019 0.196 -1.72 -3.71

0.014 0.095 -1.85 -4.02

Analysis of data

In accordance with the theory section, plot a graph of log Q against log H, extrapolate the straight line and read the intercept with the y-axis.

Presentation of findings

For this experiment, a typical calculation is as follows:

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From previous theory, k = 2/3 Cd √(2g) b,

where width of notch b = 30mm (0.03m)

By simplifying this, k = 0.0886 Cd

The intercept on the y axis = log k and, from the plot of the

data contained in the table, log k = -1.13 (by extrapolation)

Therefore, log (0.0886 Cd) = -1.13

Expressed another way, 0.0886 Cd = 10 -1.13 = 1/101.13

Therefore, Cd = 1/(101.13 x 0.0886)

= 0.84

From the graph, the slope (n) measures 1.55 which is very close to the 1.5 expected from the theory shown earlier.

Refer to the sample plot in the Appendix for guidance in plotting the results.

Sources of error

Identify the sources of any errors which may have occurred –

through operator error

in the initial set-up

inherent in the equipment

Estimate the effect which they had, or may have had, on the findings.

Format of the report – Follow these precisely

1. It is expected that all team members contribute equally in in carrying out the experiment and producing a group report. Each is to sign the declaration stating the percentage contribution. Include this with the report. Individual marks will be allotted according to each student’s contribution. If no form is included, no mark will be awarded.

2. The report is to be typed on A4 paper. Calculations may be hand-written and the results plotted on A4 graph paper. Staple the report in the top left corner only and do not insert in any folder or plastic sleeve.

3. Page 1: a) Title of the experiment

b) Names of the team members

c) The date and time the experiment took place

d) The date of the report

(Include RMIT logo and ‘School of Engineering’)

Page 2: Team declaration

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Page 3 (onwards): In generating a report, you may reproduce any of the headings, text, diagrams and procedures as they appear in these notes, inserting results and findings where appropriate. However, you must ensure that you change the tense of the text. For example,

‘To measure the head at each decrement, simply lower the rule until it just touches the water surface. Note the scale reading and enter it into the table below’.

Must be changed to,

‘To measure the head at each decrement, the rule was lowered until it just touched the water surface. The scale reading was noted and entered into the table below’.

Finally, include your team’s answer to the question, ‘How can the results be used to determine the flow Q for any specific value of H ?’

Conclusion: Summarise your findings of Cd and n

Appendix: Plot of Log H v Log Q

Marking schedule

Feature Marks (20)

Results

a)Tabular calculations 2

b) Interpretation of theory 2

c) Plotting of results 2

Observation of errors, problems 2

Answer to the ‘Question’ above 2

Following instructions above 5

Standard of presentation 5

Appendix

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