Rotameter Head Loss Experiment
Overview
A rotameter can be included between the constant head tank and the flow control orifice in the dose controller to verify the flow rate of chemical. The motivation for this experiment was to determine whether the use of a rotameter would be feasible in the chemical dose controlling system. The head loss through the rotameter would need to follow the relationship of head loss proportional to the square of the flow rate. The head loss through the rotameter was measured to determine if it is suitable for use in the dose controller.
Experimental Setup
Figure 1: Experimental Setup
The head loss through the rotameter was be determined using the setup that is diagrammed in Figure 1. A peristalic pump was used to circulate the fluid at a certain flow rate. Two attenuators were used to minimize the effect of the pulsing from the peristalic pump, and one pressure sensor was used to measure the pressure difference before and after the rotameter.
A ramp function in process controller was used to control the flow rate of the circulating fluid. The flow rate was gradually increased from 8 ml/min to 380 ml/min.
The head loss was be determined by performing an energy balance around the rotameter.
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Figure 2: Measurement Diagram
From the energy equation head loss can be expressed as a function of the difference in the pressure, velocity, and height difference.
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\begin{eqnarray}
y&=&ax^{2}+bx+c \nonumber\\
E&=&mc^2 \nonumber\\
{\delta y \over \delta x}
&=& {{a\over b}\over c}
\end{eqnarray}
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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.
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\begin{eqnarray}
y&=&ax^{2}+bx+c \nonumber\\
E&=&mc^2 \nonumber\\
{\delta y \over \delta x}
&=& {{a\over b}\over c}
\end{eqnarray}
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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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No preview is available, please have your Latex markup text selected when inserting the Latex macro or click edit on an existing Latex macro when text is present to preview the rendered result.
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\begin{eqnarray}
y&=&ax^{2}+bx+c \nonumber\\
E&=&mc^2 \nonumber\\
{\delta y \over \delta x}
&=& {{a\over b}\over c}
\end{eqnarray}
Example Render
For more information about Latex, you can find in the following documentation LaTeX Plugin
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.
Results
The experiment looked at the response of the rotameter to flow rates of 8 to 380 mL/min. This range is in the alum flow range of 5 to 100 mL/min, at which the current nonlinear doser operates. For larger plants which would have higher plant flow rates and thus would require higher dosing, the maximum alum flow rate would be larger. Thus, the range investigate in this experiment appropriately depicted reasonable flow rates through the doser.
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.
Figure 2: Full Flow Experiment #1 (3/09/10): 8 - 380 mL/min
Figure 3: Full Flow Experiment #2 (3/11/10): 8 - 380 mL/min
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.
Figure 4: Low Flow Experiment #1 (3/11/10): 8 - 40 mL/min
Figure 5: Low Flow Experiment #2 (3/12/10): 8 - 40 mL/min
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.
Conclusions/Future Work
It was concluded that the relationship between head loss and flow rate in the rotameter has an inconsistent relationship. At the lower flow rates, there seems to be a linear relationship until about 25-30 mL. At higher flow rates it behaves like an orifice with head loss varying with the square of the flow rate. When we modeled the rotameter as a 0.09 in orifice, the data fit if we added a 2 cm offset to the head loss. Thus, there seems to be an additional amount of energy needed by the rotameter. We believe this energy is required to lift the ball float. This extra energy needed will always be present and causes errors at lower flow rates. This also results in a non-zero intercept for the flow vs. head loss relationship in the rotameters, making them inappropriate to use with the doser which was designed using a flow varying with the square root of h relationship. Thus, we recommend using other flow measurement devices, such as calibration columns, with the doser.