7.6.2 A large, hot plate hangs vertically in a room. Heat transfer from the plate to the air near it causes the air density to decrease. This lighter air rises upward with a velocity proportional to the group [argL|Tp - Tr|] 1/2 where a+ is the coefficient of thermal expansion [units = (R)- or K-), g is the acceleration of gravity, Lis the plate length, and Tp and T, are the temperatures of the plate and fluid, respectively, in R or K. The resulting heat transfer process depends on the Grashof number, defined by G prg|T-Tr|L where p is density and is dynamic viscosity. Show that G is dimensionless. How is G related to the common dimensionless parameters of fluid mechanics? Is it equivalent to a combination, power, or product of one or more of the common dimensionless parameters listed in Table 7.1?