Work/Lost Work, Fan/System Characteristic Curves

It has been known for a long time that summing pressure drops and rises due to friction, shock, fans and natural ventilation is incorrect. In fact, lost works and works should be summed. In spite of this, the traditional method of finding a fan/system operating position has been the H/Q Curve. This paper presents (lost) work/m curves, progressing from a single fan moved around the system to include natural ventilation work, and fans in a series, parallel and series/parallel. The solutions obtained graphically are substantiated by dry air thermodynamic solutions, and the traditional solutions are shown to be in error. This method of solving problems is particularly useful when moving fans around the system, and essential in series/parallel and series situations with substantially different fan densities. The dry air analysis is employed because of its simplicity. Real air, with evaporation and condensation, will react somewhat differently, and one should use real densities (i.e.[l + w +w]/va ) when using this method. One source of error when applying this method to real air, although probably not major, will be investigated in a subsequent paper. Friction and shock losses are proportional to the square of the mass rate of flow, leading to the typical parabolic system curve. However, the unbalanced water stuff potential energy term, on a unit mass basis, is substantially independent of the mass rate of flow. It is possible that this could be handled as a negative natural ventilation work.