Calibration of a Flowmeter

It is frequently required to calibrate the hydraulic flowmeters on site and this is going to walk you through step by step how to do so and the significance of this task.

The two hydraulic flowmeters being calibrated include a Venturi flowmeter and an orifice-plate type, both of which are followed by a paddlewheel flowmeter, which is digital. Take note that throughout this process, the Paddlewheel voltage is being read automatically and the found hydraulic values will be compared to this one.

This general set up can be seen in the image pictured on the left, with the whole lab set up on the right.

Above is the key that explains every symbol included on the laboratory 'Plan view' map.

A Venturi Flowmeter and Orifice-Plate Flowmeter differ solely in their geometries.

A Venturi flowmeter, pictured left, constricts the flow and gradually pans back out to free flow. Due to this gradual widening, there is no energy loss from flow suppression and energy of the system is conserved. For this case the discharge coefficient is equal to 1, which means there are no losses.

However for a Orifice-Plate Flowmeter, pictured right, there is an abrupt disruption of flow that supports energy loss and introduces a discharge coefficient that is not equal to 1.

1 Preliminary Experiment Checks

• Check that the discharge valve is closed
• Check the levels of mercury in the mercury-water manometer for each hydraulic flowmeter
  • If the levels are not equal slowly open and close the manometer drain valves to allow entrapped air to escape
• Ensure the central scale gives a zero reading for no flow

4 Main Lab Procedures

1. Calibrate the Pressure Transducers
2. Set a Flow Rate
3. Measure Flow Rate & Pressures
4. Repeat 2-3 times for 9 other flow rates

This process is completed with no flow in the large pipe.

Use the valve (indicated with the red arrow) to create a pressure difference that leads to a height difference in the manometer. This data is completely collected as voltage readings that are controlled by the LabVIEW software where it is then stored as an output voltage proportional to the pressure difference.

This process is repeated 5-8 times for different pressure differences, producing a linear relationship between the pressure the transducer senses and its digital output.

Next up a maximum flow rate must be established that the following rates can be based on.

To do so, completely open the supply valve to allow maximum flow.

Record the flowrate using the weight-time method, the LabVIEW system can be used to average the output of both the paddlewheel and the pressure inducer. These averages will also be recorded, along with the manometer height difference readings.

Repeat step 2.2 for descending flow rates.

Recommended method: Rates reducing at 5% intervals of the maximum flow rate for a total of 10 flow rates.

The flow rate equation, seen above, can be applied to both hydraulic flowmeters. The only thing varying is the discharge coefficient, Cd. For the Venturi it is 1 and the pipes gradual geometry change supports a system with no energy loss. However for the orifice-plate system, the energy is not conserved due to the abrupt disruption in geometry.

LR1) Flow rate can be plotted against the manometer deflection for either hydraulic flowmeter. Then the plot can be fitted with a curve, which becomes the calibration curve for the respective flowmeter. Shown above is the

LR2) If instead plotted using logarithmic scales, the new curve, flow rate vs. manometer deflection can be used as an alternate calibration curve. When analyzing the obtained graph, one can see the data fits the applied line of best fit well, implying a power law relationship like the type shown center, might apply.

Upon plotting the voltage output of the paddlewheel against the actual discharge rate, Q, yet another calibration curve is obtained. Cutoff fluid velocities and maximum fluid velocity values can be calculated.

The image shown left is the discharge coefficient Cd plotted against the Reynolds number, Re. It was plotted using a linear-log scale, with the y-axis logarithmic, and displays how as the Cd increases, meaning more energy maintained in the system, the Reynolds number increases.

On the right, another calibration curve is shown, with paddlewheel flowmeter output plotted against the actual discharge rate, Q. The linear trend is constant with no rising or falling cutoff flow rates.

Some good questions to ask after the test to ensure everything went well include:

1) "Is the discharge coefficient Cd essentially constant over the range of Reynolds numbers tested? Are the experimentally measured values for Cd close to the ideal value of unity derived theoretically? What corrections might need to be made to the theory to obtain more realistic values for Cd?"

In this case, the discharge coefficient increases linearly on a log-linear scale with the Reynolds numbers until a Re of roughly 0.54. After that the trend is not constant. To obtain more realistic values for Cd one could test more trials and average their values. The flowmeter can be slightly affected by varying viscosity in layered flows, or from friction developed at a lower flow rate so to obtain realistic values it may be wise to test at higher flow rates.

2) "How reliable is the paddlewheel flowmeter? Was the reading more accurate at high or low flow rates?"

The paddlewheel flowmeter is reliable as it is a digitalized measurement system and removes any uncertainty from human error. It may be affected by varying viscosity in layered flows, or from friction developed at a lower flow rates passing through it, so the reading will be more accurate at higher flow rates, up until a certain maximum.