TAM335 Lab 6 Partial Report
The purpose of this procedure is to calibrate two different flow measuring devices: a hydraulic orifice-plate flowmeter and an electric paddlewheel flowmeter. Calibration lets these flowmeter readings better relate to the actual volumetric flow rate of water.
The orifice-plate flowmeter measures the pressure difference across itself, which can be related to the flow rate. The paddlewheel flowmeter directly measured the fluid motion, producing a corresponding voltage output.
The standard for calibration in each experiment was using the weight-time method for finding the flow rate. The following procedure explains how to analyze the experimental data, construct calibration curves, and evaluate the reliability of each flowmeter.
Flow Rate Vs Manometer Deflection (Questions 1 and 2)
In the case of the hydraulic flowmeters, the relationship between Q and ∆h is
Q = C*B*sqrt(∆h),
where C is the dimensionless discharge coefficient, B is a derivable constant, and ∆h is the manometer deflection.
A power-law relationship can be expressed as
Q = K*(∆h)^m,
where K is the proportionality constant, ∆h is the manometer deflection, and m is the exponent describing the relationship between the flow rate and manometer deflection. Taking the logarithm of both sides, the equation resembles
y = m*x + b,
which is the straight line equation.
When analyzing the results, we see that a linear line doesn't fit the data when using linear scales, reassuring our assumption that the relationship isn't linear. When using logarithmic scales, the data falls in a straight line. This indicates a strong power-law relationship.
Plotting the Discharge Coefficient Against Reynolds Number (questions 5 and 9)
The results gathered vary drastically, with seemingly no visible relationship. The discharge coefficient is not constant over the range of Reynolds numbers tested. The coefficient ranges from 0.609 to 0.680. These values are significantly lower than the theoretical value of 1. This is because the ideal theoretical analysis assumes steady flow without energy losses. However, the actual flowmeter experiences energy losses and flow separation. The theory could be corrected by accounting for the contraction of the flow, velocity losses, and energy losses associated with turbulence and flow separation.
Paddlewheel Flowmeter Calibration Curve (Questions 6 & 11)
As shown in the graph, the output voltage displays a strong linear relationship with the flow rate, Q. The smallest flowrate observed was 0.00761 m^3/s, and the largest was 0.02019 m^3/s. Converting these to ft^3/s, we get 0.269 and 0.713 respectively. The electric flowmeter used was made to measure flowrates between 0.3 and 20 ft^3/s. This means that, although our graph looks nice, the measurements we received in some cases may not be completely accurate. Lower flow rates contain more inconsistencies which could affect the accuracy of the paddlewheel flowmeter.