Calibration of a Flowmeter

Calibration of bulk-flow measuring devices is vital to the accuracy of measurements and ultimately the products we iterate as engineers. Quantitative metrics for flow can be determined through analysis of physical properties of a flow through a system as that flow changes. This outline will serve to address the calibration of Venturi and orifice-plate flowmeters, which utilize constriction to introduce a pressure change in the system, and a Paddlewheel flowmeter which correlates flow velocity to a voltage readout. By analyzing the pressure differential in an orifice-plate meter, we're able to determine flow coefficients and tailor functions for flow rate to the system in question. The figure here depicts an experimental set-up with both flowmeters in a plumbed system, to give an idea of what the general structure of the materials for this calibration look like as you proceed with the analysis.

This calibration also relies on varying flow through the system and the employment of the weight-time method of mass, & with fluid properties, volumetric, flow rate determinations

This specific analysis requires an orifice plate flowmeter with both a pressure transducer and manometer with taps placed before and in a constriction of the pipe. I trust in your experience as an engineer to know how to read a manometer, but if not, or if you'd like a refresher, please refer to the following tutorial [https://sciencing.com/read-manometer-5250401.html]. While the reliability of the transducer in our system set-up is fallible, it can be utilized for calibration but it'd likely be helpful to simultaneously check the manometer to verify the transducer's output. The paddlewheel flowmeter is found further down the pipe than the orifice-plate flowmeter, however in a section with the expected diameter of the pipe.

Determination of flow rates is also dependent on a base knowledge of the weigh-time method of volumetric flow rates, and I trust your experience, but am including a refresher just in case [https://www.smdsensors.com/blog-calculate-flow-rate-using-weight/].

Lastly, operation of globe/gate valve knowledge is expected but if you're interested in further reading or want to verify your understanding of them, please utilize the following [https://www.theprocesspiping.com/introduction-to-globe-valve/]. This valve type allows for variable flow through the pipe so the calibration curves can be determined for the system based on different flow rates.

https://www.processindustryforum.com/article/tutorial-paddle-flow-meters-flow-measurement-control

Open the ball valve that operates the weigh basin drain by rotating it 90 degrees until it is in alignment with the pipe, or as indicated for the system being analyzed. Allow water to drain from the basin while there is no flow through the pipe feeding the basin.

Open the globe valve by rotating it counterclockwise. This step will be repeated numerous times to varying degrees to allow different amounts of flow through the system to make determinations about the specific set-up. My advice would be to start off with a fully open valve and lessen the amount it's open per measurement iteration.

Rotate weigh basin ball valve to the closed position by turning it 90*, or perpendicular to the pipe it's attached to. The following step is done in parallel to keeping an eye on the scale beam to accurately asses the volumetric flow rate with the weight time method.

WEIGHT-TIME:

Monitor the scale beam and start a timer once the weight on the scale is in balance with the weight in the tank. Add a weight to the scale and stop the timer once the scale becomes level again. These measurements determine the mass flow rate and can be used to determine the volumetric flow rate with physical properties of the fluid.

MANOMETER

Take a measurement of the difference in height between the left and right sides of the manometer in centimeters.

PADDLEWHEEL

Take a reading of the paddlewheel output voltage.

RECORD

Weight, Time, Height Difference, and Voltage

Repeat steps 1, 2, 3, and 4, for at least 10 different flows through the system. Record measurements noted in Step 4 in a table.

The goal of the manometer measurements and the weight-time flow rate determinations is to create a calibration curve depicting flow rate as a function of a pressure differential for the system. Manometer height differences and the fluid properties can be used to determine the proportional pressure changes in the system as the flow rate changes. The specific weight of water and mercury and the change in height can be used to determine the pressure difference and compared to the calculated flow rate from the weight time method.

Graph flow rate as a function of pressure difference for an orifice plate calibration curve.

Flow rate and the voltage output from a paddlewheel flowmeter should have a fairly linear relationship. In order to determine this, graph flow rate (as determined by the weight-time method) as a function of voltage for the calibration curve.

For this analysis, reference the dimensions and description of pipe F-4

Q (flow rate in m^3/s) vs manometer deflection (cm) on a linear scale

Lab Report 1

Q (flow rate in m^3/s) vs manometer deflection (cm) on a logarithmic scale

Lab Report 2

Cd vs Re plotted on linear and logarithmic scales

Lab Report 5

Calibration curve of paddlewheel flowmeter, flow rate as a function of output voltage. Rising and falling cutoff flow rates are 0.02 m^3/s and 0.005 m^3/s respectively. There is undeniably a reliable range for the paddlewheel flowmeter however above and below the cutoff rates, there would be inaccurate readings, and even the potential to act as a barrier to flow rather than a mostly inconsequential measurement device.

Lab Report 6, Q 4

The discharge coefficient as shown in Step 11 is not constant over the range of Reynolds numbers tested. The ideal Cd is equal to 1, however it was experimentally shown to be lower than that. We assumed a uniform velocity profile and don't have a full understanding of how the fluid is interacting at the pressure taps along the system so the variation seen in relation to the Reynolds number (essentially a metric of the turbidity of flow) would need to account for those assumptions to approach the theoretical value of 1. Corrections to be made to determine a more realistic Cd could utilize a multitude of pressure taps throughout the cross section and around the circumference of the pipe could start mediating the discrepancies seen here.

Q2