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An analysis has been completed for a comprehensive set of pressure drop data from the acceleration region of seven vertical, dilute-phase pneumatic conveyors. The data provided are for materials with terminal velocities from 2.05 to 22.4 m/s conveyed in risers with heights from 3 to 11.2 m and internal diameters from 0.028 to 0.083 m. Particle velocities derived from the pressure drop data were used to develop an equation of motion that includes terms for terminal velocity, and the distance traveled from the feed point. Despite covering a range of conditions, no effect of other variables was identified. Particle velocities were predicted by the equation of motion and used to calculate total pressure gradients that are within 97 Pa/m (95% confidence limits) of the measured values. The voidage correction of gas and terminal velocities recommended by other studies did not improve the pressure drop predictions. The spreadsheet model developed is simpler than the available complex numerical models and provides more accurate results. Acceleration lengths are longer than allowed for in many studies, and erstwhile established-flow data and correlations likely contain acceleration effects. [ABSTRACT FROM AUTHOR]

Cervical spondylosis is a degenerative disease of the cervical spine that affects over 50% of the population older than 50 years. Spondylosis is a progressive disease where the intervertebral disc degenerates and bony growths called osteophytes form. Osteophyte growth has been identified by numerous investigators as an example of Wolff's law of bone remodeling acting on the abnormal strain energy density (SED) caused by the degenerating spine. A series of finite element models of the progressively degenerating cervical spine was developed to determine the SED of normal spinal vertebral bodies and the SED of degenerating vertebral bodies. The values of SED of the degenerated vertebral bodies were used to find C and HSED, two constants used in the bone remodeling equation: ?X = C (SED-HSED). ?X is the amount of osteophyte growth normal to the vertebral body surface. A bone remodeling algorithm was developed using this equation and implemented on the FEM of the degenerated spine. C was determined to be 99 mm4/mJ and HSED was found to be 24.8 mJ/mm3. An osteophyte 3.9 mm long was grown on a FEM of a degenerated spine with a disc height loss of 37%.