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The head loss was be determined by performing an energy balance around the rotameter.

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From the energy equation head loss can be expressed as a function of the difference in the pressure, velocity, and height difference.

Since flow is controlled by the peristalic pump, the flow is constant, and since the tube diameter is also constant, there would be no difference in the velocity.

If the pressure difference is measured when there is no flow, then the head loss and the velocity terms from the energy equation would be zero. This allows the height difference to be expressed as the pressure reading from the standing water.

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The pressure reading from the standing water is subtracted from the measured pressure difference values to cancel out the height term. The resulting pressure difference corresponds directly to head loss of the rotameter.

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As seen in Figures 2 and 3, the experimental data fit best to a 0.09 in orifice with a 2 cm offset in pressure. This 2 cm of extra head needed to fit the 0.09 in orifice model has been hypothesized to be caused by the energy needed to lift the ball float.

In Figures 2 and 3 there is also a seemingly linear response in the data at low flow rates. Another experiment was performed at 8 to 40 mL/min flow rates to determine if this was indeed linear.

From the data, it seems that there is a linear response at low flow rates until about 25-30 mL/min. (All data and results can be found on the attached file.

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