Using Variable Area Flow Meters - L-Università ta' Malta
Using Variable Area Flow Meters
Variable area flow meters (or rotameters) operate principally on the fluid drag over the float or “bob”. A force balance on the bob gives
[pic]
Using subscripts “b” for the bob and “f” for the fluid, [pic] , where Ab is the frontal area of the bob, and Cd is a drag coefficient, and [pic] is the mean velocity in the annular area around the bob. Substituting drag, gravity and buoyancy forces into the above force balance,
[pic]
Solving for the mean velocity in the annular space,
[pic]
And so the volumetric flow rate becomes,
[pic] , where A is the annular area around the bob.
Recognizing that the first term in the square brackets is approximately constant for a given bob,
[pic]
Rotameters are typically calibrated for reference fluids (subscript “r”), like air or water at standard conditions, so that
[pic]
Writing the volumetric flow rate for any fluid, in terms of that for a reference fluid,
[pic]
or [pic]
For the case of gases, like air, and stainless steel floats, [pic] , so that
Volumetric flow rate at the measured conditions is [pic]
Hence the mass flow rate is [pic], and we can convert this to flow rate at the reference conditions also.
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[pic]
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