Balance-of-Pressure Flow Meters (Bourdon Tube, Thorpe Tube)

If flow in a tube passes through a sudden restriction such as an orifice, the volume flow () is proportional to the area of the orifice and the square root of the pressure drop through the orifice. (The Bernoulli Equation 5 does not apply to this flow geometry.) This is the principle of all orifice flow meters, including the floating bobbin rotameter of an anesthesia machine (see Appendix 5 ).

The most common flow meter seen by anesthesiologists is the rotameter on the anesthesia machine ( Fig. 30-20 ). This variable-orifice flow meter uses a balance of forces to determine pressure change. When the flow meter valve is opened, the flow of gases through the annular orifice between the bobbin and the tapered glass tube provides a force to raise the bobbin. As the bobbin rises, the area of the annular gap between the bobbin and the tube increases as a result of the taper of the tube. As the area of this gap (orifice) increases, the pressure change across the bobbin decreases because the pressure change across an orifice is inversely proportional to the square of the orifice area. The bobbin ceases its upward motion at an equilibrium point when the downward force of gravity is balanced by the upward pressure forces. Thus, the height of the bobbin in the tube is proportional to the gas flow. Although this flow meter is simple in principle, its application becomes more complex when the flow in the tube changes from laminar to turbulent as velocity and diameter increase. For mathematical derivations, see Appendix 5 .

Figure 30-20 Thorpe tube flow meter. At low flows, the viscosity of gas predominates (acts like a tube), and the flows balance when the gravitational attraction equals the pressure gradient across the equivalent orifice. At higher flows, density takes over, and the balance is the same, except for the formula determining pressure (acts like an orifice) (see Appendix 5 ).

1205

Another flow meter (Bourdon tube, Fig. 30-21 ) keeps the orifice constant and allows the pressure to vary. As flow () increases, the gradient of P₁ to P₂ increases and causes the flattened metal tube to uncoil and move the pointer.