Gas flow via flow rotameters

Constant Pressure Flowmeter [Variable Orifice]

• The bobbin, with fluted edges to encourage rotation is supported by the gas flow through a glass tube whose bore is wider at the top than at the bottom
• The greater the flow, the higher the bobbin is forced up the tube, though the pressure difference across the bobbin remains the same
• Gas flow through a rotameter may be laminar or turbulent:
• When at low flows, the bobbin is at the lower end of the tapered tube. The gap between the annulus and the bobbin is small and the restriction is approximately tubular; he flow is predominantly laminar and therefore dependent on the viscosity of the gas
• When at high flows, the bobbin is at the upper end of the tapered tube, the annulus has a greater area compared with its length, approximating to flow through an orifice, and is therefore density dependent
• Therefore, a flow meter calibrated under specified conditions of temperature and pressure for one gas may not be used with any degree of accuracy for a different gas or under different conditions due to differences in viscosity & density
• The rate of gas flow through the tube is dependent on:

1) size of the annular opening

2) pressure drop across the constriction

3) physical properties of the gas

1) Size of annular opening

• The larger the annular opening around the float, the greater will be the flow of gas

2) Pressure drop across the constriction

• As gas flows around the indicator, it encounters frictional resistance between the float and the wall of the tube
• Also the flow becomes less laminar and more turbulent
• There is a resultant loss of energy reflected as a pressure drop
• This pressure loss is constant for all positions in the tube and is equal to the weight of the float

3) Physical characteristics of the gas

• The physical properties that relates gas flow to the pressure difference on the two sides of the constriction varies with the form of the constriction
• Low Flows: annular opening between float and the wall of the tube is narrow resulting in a longer and narrower constriction; flow rate is a function of the viscosity of the gas (Poiseuille’s law)
• Higher flows: annular opening becomes wider resulting in a shorter and wider constriction; flow rate depends on the density of the gas (Grahams law)

• In a variable orifice flow meter, the pressure drop across the indicator remains constant and the annular cross-sectional area is varied. Increasing the flow rate does not increase the pressure drop across the float but causes the flow to rise to a higher position in the tube, thereby providing a greater flow area for the gas. The elevation of the float is a measure of the annular area flow and therefore the flow itself.