Department of Civil Environmental and Geomatic Engineering CEGE105P: Applied Fluid Mechanics



Department of Civil Environmental and Geomatic Engineering CEGE105P: Applied Fluid Mechanics

Application of Bernoulli Equation in a Flume Experiment

Ob jectives

  1. To perform an experimental study of flow through a contracted open channel and various methods of flow measurement and control.

  2. Through analysis of experimental results gain better understanding of Bernoulli equation and its application to various hydraulic structures.

  3. To communicate experimental results and your understanding of properties of fluid flow trough a laboratory report.

Note: All lab materials are available on

Experimental setup

The experimental study of flow in a contracted current flume is taking place in the low-turbulence flume in the Pat Kemp Fluids Laboratory. The 6m long flume has width b = 495mm. A submersible pump delivers water from a sump under the lab floor to a constant head tank through a 100 mm hose. In the middle of the main supply hose a back-flow hose is connected and both hoses are fitted with butterfly valves controlling the flow rate of water flowing to the constant head tank. The total flow to the constant head tank is measured by an electronic water meter [1] fitted to the tank inlet pipe. The water from the constant head tank is delivered to the inlet tank of the flume via an orifice in the tank bottom of diameter d = 94.4 mm and the excess of water flows over a weir and is redirected back to the sump. A water level tube with a ruler allows measuring water level in the tank above the orifice. A static pressure tapping is installed right after the orifice and the corresponding static head can be measured by another tube and a ruler.

The inlet tank of the flume is carefully designed to provide a low-turbulence uniform flow at the flume inlet. An Acoustic Doppler Velocimeter (ADV) [2] is installed at the flume inlet. The software installed on the PC attached to the device gives the real-time measurement of the inlet flow velocity. In the middle of the flume the flow is contracted from one side by a curved vertical wall. The width of the channel at the throat of the flume is bt = 335 mm. An ultrasonic distance sensor [3] is installed on a carriage which can be moved along the top of the flume. The sensor allows measuring the vertical distance to the flume bed and the vertical distance to the flow surface at various positions along the contraction including positions before the contraction (position 1), at the contraction throat (position 2) and after the contraction (position 3). The readings of the sensor can be taken from the software installed on the computer connected to the device.

An impeller velocity meter [4] is installed after the flow contraction and allows measuring flow at various vertical positions through the flow depth. The meter gives the reading of the impeller rotation frequency, which can be converted to flow velocity using the provided calibration chart1. The velocity is measured at 5 position: 1 cm, 3 cm, 5 cm, 7 cm and 9 cm from the bed. A probe of an ultrasonic Open Channel Flow Meter [5] is installed at the channel bed in front of the flume outlet. The water discharges from the flume over a sharp-crested weir which is set to the

1Available from uceseug/Fluids1/Labs/Flume/Chart.jpg 1

height 56 mm over the flume bed. The water discharges into a rectangular outlet tank and then to the sump.

Experimental procedure

  1. Read the Fluids Laboratory safety rules. Read and sign the Risk Assessment Form. Make sure that you understand possible risks and risk control measures. Copies of Risk As- sessment Form and Fluids Laboratory local safety rules are available on the course web page2 .

  2. The experimental setup includes six measuring stations:

    1. 1:  ADV measurement of flow velocity at the flume inlet.

    2. 2:  Measurement of the total flow to the constant head tank by the water meter.

    3. 3:  Measurement of water level above the orifice of the constant head tank and the static head after the orifice.

    4. 4:  Measurement of water level at the positions 1, 2 and 3 along the contraction.

    5. 5:  Measurement of the outlet flow by an ultreasonic open channel flow meter.

    6. 6:  Measurement of velocity profile by the impeller velocity meter.

    Each station is provided with printed data sheets used to enter readings with short in- structions on measurement procedures. Follow these instructions and instructions of lab demonstrators.

  3. Organise yourselves to 6 small groups of 1-2 people. Each group starts measurement at one of the measuring stations. Measurements are repeated for 6 different values of flow rate. Flow rates must be set by a lab demonstrator or a technician!

  4. After each measurement groups move to the following measuring station and the lab demonstrator changes flow for the next measurement.

  5. After the flow is changed you should wait until the water level in the constant head tank stabilises on a new level. It can take several minutes.

  6. While taking readings study the experimental setup, equipment and instrumentation. Un- derstand how the setup and it components operate.
    Warning: Do not disturb the setup or any software settings. Treat all instruments with care.

  7. Observe flow behaviour in the flume along the contraction and over the outlet weir.

  8. After finishing measurements for the last case ask the lab demonstrator to move the outlet weir down and observe how this changes the flow.

  9. When you leave, do not take the completed experimental data sheets with you. They will be collected by the lab demonstrator and will be available for download on the course web page3 .

  10. After downloading data sheets transfer the data to a provided Excel spread sheet, which can be downloaded from the same web page. Send the filled Excel data sheet to Dr Buldakov, who will make them available for download and further analysis from the results web page. Data analysis and preparation of the laboratory report can be done in pairs.

2 3


Results, discussion and final report

Present your report in the form of a short journal or conference paper including the following parts:

Abstract: Give a short summary of your paper. It should excite the interest of potential readers and make them to read the paper.

Introduction: Put the paper into a scientific or engineering context. Set aims and objectives of your paper. Justify the need for your work and describe its applications. Possible aims of your experiment are: (1) To cross-verify various experimental methods of measuring flow rate; (2) To verify theoretical formulas for calculating flow rate through an orifice and over a sharp-crested weir; (3) To derive and validate a formula for estimating increase of mean flow velocity due to contraction of an open channel.

Experimental Setup and Methodology: Describe briefly experimental equipment, instru- mentation and principles of its operation and methodology of your measurements. Use images or diagrams if necessary.

Results and Discussion: Present your results and discuss their reliability and significance. Address the following points:

  1. Use ADV measurements of velocity at the inlet and measurements of depth at the Position 1 to calculate the flume flow rate for each experimental case (QADV ). Use standard deviation to estimate error of your measurements.

  2. Calculate standard deviation and estimate the error for measurements of the total flow to the head tank (Qht) by the water meter.

  3. Calculate standard deviation and estimate the error for measurements of the outlet flow (Qout) by the ultrasomic open channel flow meter.

  4. Plot the graphs of QADV and Qht vs Qout and compare values of the flow rate obtained by different methods. Use error bars to show experimental errors. To save space it is recommended to plot both lines at the same graph. Explain any anomalies you can see in the graphs. Plot the linear trend lines. Do they go inside error bars? How well tremd lines approximate the real data? How well values of the flow rate obtained by different methods compare between each other? Explain reasons for possible discrepancies. Select the most reliable measurements of the flow rate (or the corresponding trend line) and use it as the reference flow rate for the rest of your paper.

  5. Derive a formula to calculate the flow rate through a submerged orifice Qor using its diameter d, water level above the orifice Hor, static head after the orifice hor and the orifice discharge coefficient Cor. You may find helpful to refer to [6]. To validate your equation by experimental results plot the reference flow rate against the ideal orifice flow rate. Plot a linear trend line and discuss how well it approximates your data. Find the value of the discharge coefficient from the slope of the trend line. Compare its value with typical values available in the literature.

6. The flow rate over a sharp-crested weir can be calculate by the formula:
Q=C 2 2gbh3/2, (1)

where Qw is the flow rate over the weir, b is weir width, hw– upstream water level

above the weir edge and Cw is the weir discharge coefficient [6]. Calculate values of hw 3

for the experimental cases using channel depth measurements at the Position 3. To

validate equation (1) by your experimental results plot the reference flow rate against

the ideal weir flow rate Qid = (2/3) 2g b h3/2. Plot a linear trend line and discuss ww

how well it approximates your data. Find the value of the discharge coefficient from the slope of the trend line. Compare its value with typical values available in the literature.

  1. Apply Bernoulli equation with suitable assumptions to derive a formula for calculat- ing flow rate in a contracted channel from measurements of water depth before the contraction (Position 1) and and the contraction throat (Position 2). Clearly state all assumptions. Do you need any assumptions in addition to the assumptions of Bernoulli equation? Discuss the validity of your formula and introduce a suitable discharge coefficient to correct errors caused by the assumptions. Use the approach described in the previous two paragraphs to validate your formula and to calculate the value of the discharge coefficient. Can your formula be applied for calculating increase of velocity in a contracted channel flows? Suggest possible practical applications of your formula.

  2. Use the calibration chart to calculate velocities measured by the impeller velocity meter. Plot vertical velocity profiles for all cases. To save space you can plot all profiles at the same graph. Use reasonable extrapolation to guess the value of velocity at the water surface. What is the velocity at the channel bed? Explain the shape of profiles. Compare them to the mean flow velocity. Why some of the values are smaller and some are larger than the mean flow velocity? Use the measured velocity profile to calculate flume flow rate. Compare with other measurements and discuss possible differences.

Conclusions: Give a conclusions to your work. It is a good practice to make Introduction and Conclusions read as a single document. Many readers interested by the abstract read Introduction and Conclusions and only then the rest of the paper if they find it relevant and important to them.

References: List references used in the paper using an appropriate referencing format.

Follow good examples of paper structure and format in engineering and scientific journals such as Coastal Engineering, Experiments in Fluid, Journal of Waterway Port Coastal and Ocean Engineering and many others. Examples of papers can be found on the lab web page4. You are suggested to use the provided paper template. It is recommended that you prepare the text and figures and then use the template to provide the final formatted paper. Make efficient use of illustrative material such as graphs, pictures and diagrams. Give detailed explanations in figure captions. Ideally a reader should understand figures without referring to the main text of the paper. The report will be marked for both scientific content and efficiency of conveying scientific information. Lab reports may be prepared in pairs. The recommended length of the paper is 5 pages or less. Be brief but precise.

[1] GPI (2013) TM Series Electronic Water Meters: User Manual. Wichita, KS USA: Great

Plains Industries Inc.
[2] Nortek (2009) Vectrino Velocimeter: User Guide. Rud, Norway: Nortek AS

4 5References [1-4] are available on


  1. [3]  Pepperl+Fuchs (2014) Ultrasonic sensor UC500-30GM-IUR2-V15. Mannheim, Germany: Pepperl+Fuchs GmbH

  2. [4]  Nixon Flowmeters (n.d.) Streamflo Velocity Meter V1.3: Installation and Operation. Chel- tenham, UK: Nixon Flowmeters Ltd.

  3. [5]  Greyline Instriments (n.d.) Portable Open Channel Flow Meter for Partially-filled Pipes and Open Channels. Long Sault, Ontario, Canada: Greyline Instriments Ltd.

[6] Massey, B. (2006) Mechanics of Fluids. 8thed., London, New York: Taylor & Francis .

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