Continuum Physics by A.Cemal Eringen

By A.Cemal Eringen

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The spacecraft was slated to begin orbiting Mars on September 23, 1999. However, NASA officials lost communication with the spacecraft early that day, and it is believed that the spacecraft broke apart or overheated because it came too close to the surface of Mars. Errors t h e N e w s in the maneuvering commands sent from Earth caused the Orbiter to sweep within 37 miles of the surface rather than the intended 93 miles. The subsequent investigation revealed that the errors were due to a simple mix-up in units.

90 A1h and, therefore, the equation expressed as Eq. 90, has the dimensions of L1/ 2T Ϫ1. Whenever a number appearing in an equation or formula has dimensions, it means that the specific value of the number will depend on the system of units used. 90 has units of ft1/ 2/s. Equation 1 will only give the correct value for Q (in ft3/s) when A is expressed in square feet and h in feet. Thus, Eq. 1 is a restricted homogeneous equation, whereas the original equation is a general homogeneous equation that would be valid for any consistent system of units.

B) Free-body diagram for calculating column height. (c) Depression of column for a nonwetting liquid. 9 h Surface Tension 23 The angle of contact is a function of both the liquid and the surface. For water in contact with clean glass ␪ Ϸ 0°. It is clear from Eq. 16 (and shown by the figure in the margin) that the height is inversely proportional to the tube radius. Therefore, the rise of a liquid in a tube as a result of capillary action becomes increasingly pronounced as the tube radius is decreased.

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