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Experiment #9: Flow Over Weirs

1. introduction.

A weir is a barrier across the width of a river or stream that alters the characteristics of the flow and usually results in a change in the height of the water level. Several types of weirs are designed for application in natural channels and laboratory flumes. Weirs can be broad-crested, short-crested, or sharp-crested. Sharp-crested weirs, commonly referred to as notches , are manufactured from sharp-edged thin plates. The relationship between the flow rate and water depth above the weir can be derived by applying the Bernoulli’s equation and by making some assumptions with regard to head loss and pressure distribution of the flow passing over the weir. A coefficient of discharge needs to be determined experimentally for each weir to account for errors in estimating the flow rate that is due to these assumptions.

2. Practical Application

Weirs are commonly used to measure or regulate flow in rivers, streams, irrigation canals, etc. Installing a weir in an open channel system causes critical depth to form over the weir. Since there is a unique relationship between the critical depth and discharge, a weir can be designed as a flow-measuring device. Weirs are also built to raise the water level in a channel to divert the flow to irrigation systems that are located at higher elevations.

3. Objective

The objectives of this experiment are to:

a) determine the characteristics of flow over a rectangular and a triangular weir, and

b) determine the value of the discharge coefficient for both notches.

The coefficients of discharge are determined by measuring the height of the water surface above the notch base and the corresponding flow rate. The general features of the flow can be determined by direct observation.

5. Equipment

The following equipment is required to perform the flow over weirs experiment:

• F1-10 hydraulics bench;
• F1-13 rectangular and triangular weirs;
• Vernier height gauge; and

6. Equipment Description

The flow over the weir apparatus includes the following elements that are used in conjunction with the flow channel in the molded bench top of the hydraulics bench (Figure 9.1).

• A combination of a stilling baffle and the inlet nozzle to promote smooth flow conditions in the channel.
• A vernier hook and point gauge, mounted on an instrument carrier, to allow measurement of the depth of flow above the base of the notch.
• The weir notches that are mounted in a carrier at the outlet end of the flow channel [9].

The depth of water above the base of a weir is related to the flow rate through it; therefore, the weir can be used as a flow measuring device. The relationships of flow over weirs can be obtained by applying the energy equation from a point well upstream of the weir to a point just above the weir crest. This approach requires a number of assumptions, and it yields the following results:

• for a triangular weir (Figure 9.2a):

• for a rectangular weir (Figure 9.2b):

Q : flow rate;

H : height above the weir base;

b : width of rectangular weir (R-notch);

C d : discharge coefficient to account for the effects of simplifying assumptions in the theory, which has to be determined by experiment [9].

• for a V-notch

• for a R-notch:

8.  Experimental Procedure

This experiment will be performed by taking the following steps:

• Ensure that the hydraulics bench is positioned so that its surface is horizontal. This is necessary because the flow over the notch is driven by gravity.
• Mount the rectangular notch plate onto the flow channel, and position the stilling baffle as shown in Figure 9.3.
• Turn on the pump, and slightly adjust the flow control to fill the channel upstream of the weir with water.
• Turn off the pump when the water starts to flow over the weir.
• Wait a few minutes to allow the water to settle.
• Level the point gauge with the water level in the channel. Record the reading as ho .

Note: To measure the datum height of the base of the notch ( ho ), position the instrument carrier as shown in Figure 9.3. Then carefully lower the gauge until the point is just above the notch base, and lock the coarse adjustment screw. Then, using the fine adjustment, adjust the gauge until the point just touches the water surface and take a reading, being careful not to damage the notch.

• Adjust the point gauge to read 10 mm greater than the datum.
• Record the reading as h .
• Turn on the pump, and slightly adjust the flow until the water level coincides with the point gauge. Check that the level has stabilized before taking readings.
• Measure the flow rate using the volumetric tank.
• Observe the shape of the nappe and take pictures of it.

Note : The surface of the water will fall as it approaches the weir. This is particularly noticeable at high flow rates by high heads. To obtain an accurate measurement of the undisturbed water level above the crest of the weir, it is necessary to place the measuring gauge at a distance of at least three times the head above the weir.

• Increase the flow by opening the bench regulating valve to set the heads above the datum level in 10 mm increments until the regulating valve is fully open. Take care not to allow spillage to occur over the plate top that is adjacent to the notch. At each condition, measure the flow rate and observe the shape of the nappe.

Note : To obtain a sufficiently accurate result, collect around 25 liters of water each time, or collect the water for at least 120 seconds.

• Close the regulating valve, stop the pump, and then replace the weir with the V-notch.
• Repeat the experiment with the V-notch weir plate, but with 5 mm increments in water surface elevation.
• Collect seven head and discharge readings for each weir.

9. Results and Calculations

Please visit this link for accessing excel workbook for this experiment.

9.1.  Result

Use the following tables to record your measurements. Record any observations of the shape and the type of nappe, paying particular attention to whether the nappe was clinging or sprung clear, and of the end contraction and general change in shape. (See Figure 9.4 to classify the nappe).

Raw Data Table: R-notch

Raw Data Table: V-notch

9.2. Calculations

The following dimensions from the equipment can be used in the appropriate calculations:

– width of rectangular notch ( b ) = 0.03 m

• Calculate discharge ( Q ) and head ( h ) for each experiment, and record them in the Result Tables. For calculation purposes, the depth of the water above the weir is the difference between each water level reading and the datum reading, i.e., H = h-h o
• Calculate H 5/2 and H 3/2 for the triangular and rectangular notches, respectively.
• For each measurement, calculate the experimental values of for the triangular and rectangular notches, using Equations 3 and 4, respectively.
• Record your calculations in the Results Tables.

Result Table: R-notch

Result Table: V-notch

Use the template provided to prepare your lab report for this experiment. Your report should include the following:

• Table(s) of raw data
• Table(s) of results
• Schematic drawings or photos of the nappes observed during each experiment, with an indication of their type.

• for a rectangular notch:

• for a triangular notch:

• Compare the experimental results to the theory by calculating the percentage of error.
• What are the limitations of the theory?
• Why would you expect wider variation of  C d values at lower flow rates?
• Compare the results for C d    of the weirs utilized in this experiment with those you may find in a reliable source (e.g., textbooks). Include in your report a copy of the tables or graphs you have used for textbook values of C d .
• Discuss your observations and any source of errors in calculation of C d .

Applied Fluid Mechanics Lab Manual Copyright © 2019 by Habib Ahmari and Shah Md Imran Kabir is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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EXPERIMENT # 5 FLOW OVER A 90˚V-NOTCH WEIR

Related Papers

LARHYSS Journal

bachir achour

Mohammad Ibraheem

Jaafar Maatooq

A preliminary experimental work were conducted to evaluate the hydraulics performance of half circle notch sharp-crested weir. The evaluation of results shows that , the variation of flow width crossing the circular notch not only affects the value of discharge coefficient but also have an influence on the exponent of the flow rate formula , the regression of the experimental results refers that the exponent of head would approaching to,2, compared to,1.5, and 2.5 those featured the fully contracted rectangular and V-notch weirs predictive formulas respectively. According to this finding the new formulas related the weir coefficient, C w and the discharge coefficient ,C d , were correlated corresponding with regressed curves to be helpful for designers related to this kind of weir. The study , also shows that , in spite of the simplicity of a present equation , its usefulness were at an acceptable error compared with previously presented by another researchers that have more complicated in configuration and related factors , wherefore , it may be impractical. Thereby the simplicity and an acceptable precise of a present formula refers to be a useful tool for practical purposes .

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Sami Shokrana

HighlightsAn empirical flow equation was developed for a metal-edge sharp-crest V-notch weir.A top-down approach was used to determine the height of the V-notch apex.A combination of the weighing method and a flow meter was used to develop the stage-discharge equation.A standard procedure was presented to accurately estimate the flow rate.. A reliable empirical flow equation for V-notch weirs will provide flow estimates that can be used to calculate nutrient loads leaving fields with subsurface drainage. The objective of this study was to develop such an equation for an AgriDrain metal-edge sharp-crest 45° V-notch weir. In this undertaking, we measured flow rate with a combination of the weighing method for low flow and a turbine flow meter for high flow. The head of water (H) was measured inside a 25-cm AgriDrain control structure with a three-step method. First, we measured the water level (a) and height of the control structure (b). Second, we measured the height of the V-notch a...

Anees K A D H U M Idrees

The weir applications in the measurement of discharge large and small channels are open in the field or the laboratory, and in general can be defined weir as a handicap regularly happen flow from it. More weirs widespread and commonly used is the weirs sharp with a notch of rectangular and triangular, which is often where the coefficient of discharge cd starts from 0.55 for the rectangular notch and 0.59 for the triangular notch, but these transactions are affected by viscosity and surface tension, roughness of the plate and weir. In this research was the work of models with semi-circular notch, meaning it took half a circular notch in three different models diameters (6cm, 8cm, 10cm) and operated with hydraulic bench in the laboratory, all models in the same conditions in terms of temperature and for several times and is intended here all models are models of the notch-sections (semi-circular, v-notch and rectangular). The values of discharge coefficient (cd) of the rectangular notch between (0.73-0.71) while the discharge coefficient (cd) of the Vnotch between (0.85-0.78), while the discharge coefficient (cd) for the half-circular notch between are such that no (0.93-0.88). To find out the best form of notch weir took the coefficient of discharge (cd) function on it. From above can be inferred that the weirs with a half-circular notch is the best in terms of hydraulic discharge measurement in rectangular notch weirs with and v-notch.

Kerengga Puteh

Siamak Gharahjeh

MD S H A H E E R ALI

Triangular weir is a simple form of weir best matched for low discharge and is free from aeration difficulties. It is mostly used in various branches of engineering like hydraulics, environmental, chemical and irrigation for the purpose of discharge measurement. Earlier studies conducted on triangular weir indicate that the discharge coefficient related to head or head to weir height ratio covering a limited range of head and vertex angles. Further, no generalized equation proposed to compute either discharge coefficient or discharge for any head and vertex angle. In this study, a total of 160 experimental runs were taken for five weir vertex angles (from 30◦ to 90◦) at apex elevations of16,18,and 20cm. Using the general formula for triangular weir dimensionless discharge and dimensionless head has been defined that helps in merging all the data points of five angles to one single curve. A generalized equation between dimensionless discharge and dimensionless head has been obtained. The maximum error obtained in the discharge computed from this equation is ±7%. This equation also validates the data of previous study (Wahaj, 1999).

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Practical 2 - Flow Measurement

Description

Table of contents, introduction, experimental method, data for analysis, calculations.

The measurement of flow in hydraulic systems may be divided into two broad categories:

• flows in pipes or conduits, and
• flows in open channel device.

In this experiment five commonly used devices (four conduit and one open channel) will be calibrated for water flow. Use the 360 panorama to view the pipe flow rig for this experiment in the laboratory at Mawson Lakes.

In this practical, water flows through a pipe (Nominal pipe diameter = 80 mm) containing a series of different devices.

The first is a magnetic meter, which is simply used to provide an accurate measurement of flow rate against which we will be calibrating the other devices. The next four devices in the pipe all rely on the measurement of a differential pressure which we use to infer the velocity from the energy equation.

For all of these meters, two “tapping points” have been attached to allow pressure to be measured. These are all connected by small pipes to a central manifold and differential manometer (see photos) where the readings are taken.

At the end of the pipe, water empties into a short open channel containing a V-notch weir (in this experiment, θ = 30 degrees). This provides a further opportunity to measure flow by recording the height of water above the crest. A clear plastic tube is attached to the side of the channel alongside a ruler, to provide an accurate reading of water level.

The individual devices are:

1. Bend meter – this simple device relies on the water moving at different velocities on the inside and outside of a bend. From the energy equation we know that this difference in velocity will correspond to a measurable pressure difference.

2. Venturi meter – this is a classic flow measurement device, where water is passed through a narrow throat (throat diameter = 38 mm) in order to induce a higher velocity. Pressure is measured upstream and in the throat, to give the two values corresponding to high and low velocity.

3. Pitot tube – this device is useful for measuring high flows as it results in minimal disruption to the flow. A tube is inserted into the flow such that the water at the entrance of the tube stagnates. The pressure measured in this tube (the “stagnation pressure”) is equal to the pressure head plus velocity head. By comparing against a measurement of pressure head (“static pressure”) taken in the main flow field nearby, the difference between these measurements will be the velocity head.

4. Orifice meter – this is like a crude version of a Venturi meter and follows exactly the same principles by forcing water through a smaller section. The only physical difference between the two devices is that the orifice is simply a flat plate (perpendicular to the direction of the flow) with a hole in it (orifice diameter 26 mm), whereas a Venturi contains a gradual contraction and expansion. The result of this is that the orifice meter induces a far great pressure difference (and head loss) for a given velocity.

These images are of the rig for the pipe flow experiment showing the conduit (left) and the manometer (right).

Slides and notes as PDF

In this experiment, flow rate, Q, is measured using a magnetic flow meter, located at the upstream end of the experimental rig and head, h, is measured using a differential manometer.

Observe that with NO FLOW, there is zero pressure head difference indicated by the manometers connected to station pairs, A and B.

Note: Ensure bypass valve in the open position.

With a small flow passing through the bend meter, pitot tube meter and the venturi meter, observe the small pressure head difference:

(h A - h B ) = h

Record flow rate Q from magnetic flow meter and height of water in the V-notch weir tank (see note below.

Repeat STEPS 2 and 3 for several different flows (up to ~4L/s), recording Q and h in each case.

Repeat STEPS 1 - 4 inclusive for flow passing through the orifice plate. The pressure differences are more sensitive, so the test flow rates will need to be less (up to ~1 L/s).

Note: turn bypass valve in the closed position to force flow through the orifice!

Please download this spreadsheet to obtain data for this experiment.

Supporting Information

(C d ~ 0.60 for comparison with experimental value)

Nominal pipe diameter = 80 mm

Q = C d x a x √(2g) x h 0.5

Venturi meter

(C d ~ 0.97 for comparison with experimental value)

Approach pipe diameter = 80 mm and throat diameter = 38 mm

Q = C d x a 1 x √(2g/(k 2 – 1)) x h 0.5

Where k = a 1 /a 2 (a 1 and a 2 is the upstream pipe and throat diameter, respectively)

Pitot tube meter

(C d ~ 0.99 for comparison with experimental value)

Orifice meter

(C d ~ 0.66 for comparison with experimental value)

Approach pipe diameter = 80 mm and throat diameter = 26 mm

(Discharge equation identical to Venturi)

• Plot the discharge relationship for each device in Excel and determine the equation using a “power” type trendline.
• Determine k and n values for each device from the trendline.
• Re-calculate k using least-squares, by setting n = 0.5 (use Solver to minimise total error by changing the value of k)
• Using the two values of k (from trendline and Solver), derive the value of C d from the discharge equation for each device as shown below. Approximate expected values of C d are also provided below for comparison with your results.
• Comment on the results, and in particular how the results compared to expected values for C d .

For each device, you will need to look at the discharge equation (see equations for each device, listed below) in the form Q = kh n and then, using the “k” values obtained from the procedure on the left, rearrange the discharge equation to solve for C d .

Bend meter , (C d ~ 0.60 for comparison with experimental value)

where A is the cross-sectional area of the pipe (use nominal diameter given in the Apparatus section) and H is the difference in pressure head measured on the inside and outside of the bend.

Venturi meter , (Cd ~ 0.97 for comparison with experimental value)

where A 1 is the upstream cross-sectional area of the pipe (use nominal diameter given in the Apparatus section), H is the difference in pressure head measured on the inside and outside of the bend, D 1 is the upstream pipe diameter and D2 is the diameter in the throat (see Apparatus section).

Pitot tube meter (Cd ~ 0.99 for comparison with experimental value)

where A is the cross-sectional area of the pipe (use nominal diameter given in the Apparatus section) and H is the difference between the stagnation pressure and the static pressure.

Orifice meter (Cd ~ 0.66 for comparison with experimental value). Discharge equation identical to Venturi

Triangular weir (Cd ~ 0.6 for comparison with experimental value)

where θ is the weir angle and H is the height of water above the crest.

VIRTUAL  FLUID  LABORATORY

The objective of our project is to help students understand the experiments better without being physically requiring the experiment setup. In this Virtual Fluid Laboratory, we have added 7 experiments that we usually perform physically in any Fluid Lab.

Below is the list of experiments available to perform virtually. On opening any experiment there is a list with headings like introduction, about setup, procedure, etc. related to an experiment having explanation about the particular experiment, which can be accessed by clicking on it. We have also added 2D simulation of the experiments for generating readings and getting observations, doing calculations and producing results from that.

Reynolds Experiment

The Reynolds experiment is among the most significant laboratory experiment in fluid mechanics that helps in distinguishing between different flow regimes. In this experiment we will identify and differentiate between Laminar, transition and turbulent flow regimes.

Bernoulli's Experiment

As the name suggest this is experiment to verify Bernoulli’s Theorem. In this Experiment we will calculate total energy at different points in a venturi and will plot the graph between Total Energy, Pressure Energy, Velocity Energy with respect to distance.

Pitot Tube Apparatus

The Pitot tube is a simple and convenient instrument to measure the velocity of any point in a pipe. In this experiment we determine the velocity profile across cross section. Also, we find the coefficient of pitot tube and point velocity at centre of a tube for different flow rate.

Wind Tunnel Apparatus

In this experiment we will visualize the flow around different body shapes. We will also draw comparision of drag for shapes of equal equatorial diameter.

Center of Pressure

As the name suggests in this experiment, we will determine Center of Pressure and hydrostatic force on a plane surface under partial submerge and full submerge condition.

V-Notch Experiment

A sharp crested notch is a vertical flat plate with a sharp edge which is positioned across the channel such that the fluid must flow past the sharp edge and subsequently into the pool downstream of the weir or notch plate. We will use V-Notch to estimate the discharge coefficient of a triangular notch and plot several curves in this experiment.

Stability of Floating Bodies

When a body is tilted at a slight angle, the point around which it is tilted tends to oscillate, and this point is known as the meta-centre. Here we are supposed to determine the meta-centric height with change in angle of heel of the given ship model.

Losses in Pipes

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CHE241 Lab Report Solteq Flow Over Weirs

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