TAM335 Lab 6 Partial Report

The objective of this laboratory exercise is to calibrate bulk-flow measuring devices, specifically an orifice-plate meter and a Signet 3-8511-P0 paddlewheel flowmeter, by establishing a reliable, monotonic relation between the flow magnitude and the device output. The procedure involves determining the dimensionless discharge coefficient Cd for the hydraulic meter as a function of the flow rate, expressed in terms of the Reynolds number Red, and comparing these experimental results with ISO-published standards. For the paddlewheel meter, calibration is performed by plotting the electrical voltage output against the actual discharge rate Q determined via a weight-time measurement procedure using weighing tanks located in the basement. This analysis ensures the flowmeters can be used reliably for process monitoring and control by identifying their operational characteristics and cutoff fluid velocities.

Figure 1: Arrangement of flowmeters in a section of pipe.

Figure 2: Orifice-plate flowmeter schematic showing pressure taps and control volume.

To perform the calibration, you will need to identify and verify the following components within the laboratory setup:

1. Pipe section: This station utilizes an 8-inch nominal diameter pipe identified by gray and yellow color coding.
2. Orifice-plate flowmeter: A hydraulic bulk-flow measuring device installed within the pipe section.
3. Paddlewheel flowmeter: A Signet 3-8511-P0 sensor paired with a Signet 8511 transmitter.
4. Pressure measurement tools: A mercury-water differential manometer and a Validyne CD101 differential pressure transducer.
5. Electrical equipment: A computer with LabVIEW software and an 8-port BNC patch panel for data acquisition.
6. Standard for calibration: A weighing scale and a tank that provide a weight-to-time measurement standard.

Figure 3: Key to symbols for laboratory plan view, including pipe flow direction and valve locations.

The first step in the procedure is to calibrate the output voltage from the Validyne differential pressure transducer used to measure the pressure difference induced by the orifice-plate flowmeter. This process is performed statically, with no flow in the test section, to avoid measurement fluctuations. To begin, ensure the discharge valve is closed, then zero the transducer output on the interface box next to the computer. Check the mercury levels in the mercury-water manometer; if they are not equal, slowly open and close the manometer drain valves to bleed off any trapped air. With the discharge valve still closed, open the manometer bleed valve labeled CAL VALVE to artificially reduce the pressure in one of the lines, then take readings of the transducer output in volts and manometer levels in centimeters. Collect five data points ranging from zero pressure differential to the maximum differential possible with the bleed valve fully open, ensuring the maximum output voltage does not exceed 10 V to maintain accuracy with the data acquisition board. Close the CAL VALVE after the LabVIEW program performs a linear least-squares analysis on the collected data to determine the slope and intercept for the pressure relation defined by p₁ - p₂ = Δh(γ_Hg - γ_w) = Δh(S_Hg - 1)ρ_wg.

Once the pressure transducer is calibrated, you will proceed to dynamic data acquisition to determine the actual flow rate and the discharge coefficient for the flowmeters. Verify that the gain adjust control for the paddlewheel flowmeter is set to 6.25 turns and use the zero adjust control on the transmitter to ensure the paddlewheel output begins at zero volts. Open the discharge valve slowly until it is fully open or the allowable manometer deflection is reached, observing the paddlewheel voltage to record the exact point at which the voltage takes on a significant nonzero value.

Pro-Tip: Before taking dynamic readings, double-check the manometer lines for trapped air bubbles. Air in the lines will cause the mercury levels to oscillate or provide a significant offset that ruins your C_d calculation.

At the maximum flow rate, record the manometer readings and the paddlewheel voltage, then initiate a weight-time measurement using the weighing tank to calculate the actual flow rate Q using the relation:

Q = (Weight / Time) / γ_w

From this, you will calculate the experimental discharge coefficient C_d using the theoretical flowmeter relation where Q is proportional to the square root of the manometer deflection:

Q = (C_d / √(1 - β⁴)) * (πd² / 4) * √(2gΔh(S_Hg - 1))

Repeat the procedure at successively slower flow rates by adjusting the discharge valve until the manometer deflections reach approximately 90%, 80%, 70%, and so on, down to 10% of the maximum deflection. For each setting, wait until the mercury in the manometer has become reasonably steady before finalizing the data acquisition.

The final stage of the laboratory exercise involves evaluating the performance of the flowmeters by establishing a reliable, monotonic relationship between flow magnitude and device output. For the hydraulic orifice-plate meter, the experimental discharge coefficient C_d is analyzed as a function of the Reynolds number Re_D. This allow for a direct comparison with ISO-published standards to verify the meter's accuracy. Our analysis ensures that the measurements align with the theoretical square-root dependency between discharge and pressure drop.

For the paddlewheel flowmeter, the calibration curve highlights the device's high linearity within its operational range, though it is limited by its specific cutoff velocity. This cutoff represents the threshold at which fluid velocity can no longer overcome the sensor's mechanical friction. When comparing the two devices, consider the robust fundamentals of fluid mechanics in the hydraulic meter against the streamlined electronic output of the paddlewheel. Factors such as pressure loss across the orifice plate and the paddlewheel's mechanical threshold must be accounted for to ensure reliable process monitoring and control.

Parameter Measured / Calculated Value Notes on Device Performance

Orifice Plate Cd Range

0.50 – 0.63

Consistent with ISO standards for turbulent flow regimes.

Max Reynolds Number (ReD)

~2.81 x 10⁵

Represents the highest flow rate achieved during testing.

Paddlewheel Cutoff Velocity

~0.11 m/s

The threshold where mechanical friction overcomes fluid momentum.

Transducer Slope (m)

9.4457

Derived from linear least-squares analysis during static calibration.

Calibration Linearity (R²)

1.0

Indicates a near-perfect linear fit for the pressure transducer.