Pressure Gradient Flow Transducers

Bernoulliās equation for the flow of incompressible fluids between two points can be written as:


(P1-P2)/r = (V22-V12)/2gc + (Z2 - Z1)g/gc


where P is pressure, r is the density, V is the linear velocity, gc is a dimensional constant, Z is the elevation and g is the acceleration due to gravity. The equation assumes there is no mechanical work and no heat transfer between points 1 and 2. If the effects of change in elevation are eliminated, it can be seen that a change in pressure is proportional to the velocity change. This provides the basis for many flow measuring devices which relate fluid pressure change in a vessel to velocity.


In Figure 24 an arrangement for measuring flowrate using the differential pressure at two points in a stream of a flow is shown. For the arrangement shown and at steady state flow conditions the relationship between pressure drop and fluid flowrate can be described by the following equation:


DP / DX = -(12.8m)/(gpa4) Q

where DP is the differential pressure (cm H2O), DX is the distance between the two sensing tubes in the stream of the flow (cm), m is the viscosity (poise), g = 980 cm/s2, a is the inner diameter of the sensing tube or lumen, and Q is the flowrate in cm3/s.

Figure 24 Differential Pressure Flowrate Measuring System [2]


The main drawback to the use of the differential pressure method in biological systems is that the values of DX and DP tend to be small and are prone to background noise and interference. In addition the introduction of sensing tubes in a flow may appreciably change characteristics being monitored.


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Support for the development of this module was provided by the National Science Foundation and The Cooper Union for the Advancement of Science and Art.

Please send questions or comments to Professor Ron Adrezin or Professor Daniel Raichel.