A Power-Law Formulation of Laminar Flow in Short Pipes

In the quantification of air flow through penetrations in buildings, it is necessary to be able to characterize the flow without detailed knowledge of the geometry of the paths. At the conditions typical of buildings, the flow regime is partially developed laminar flow. This report develops a theoretical description of the hydrodynamic relationship based on a power-law representation between the air flow and applied pressure for laminar flow in short pipes. It is found that short pipes can be described with a simple power law dependence on pressure, but that the exponent of the power law is itself a function of pressure. The entry length of the flow is derived based on a formulation for short, sharp-edged pipes. The theoretical formulation is compared to measured data. A dimensionless quantity, S, is defined to account for the power law behavior and maps simply to the flow exponent. The exponent or S number can be used to infer many of the characteristics of the flow and may prove useful in the inverse problem of determining flow geometry from fluid properties and the measured pressure and flow.