A formula for calculating Grashof number: (gcdot beta cdot Delta tcdot l^2)/(v^3) (gcdot beta cdot Delta tcdot l^3)/(v^2) (gcdot beta cdot t_(c)cdot l^3)/(v^2) (gcdot beta cdot Delta tcdot l^3)/(vcdot a)

Grashof number is a dimensionless number used in fluid mechanics to characterize the flow regime in natural convection. It is defined as the ratio of the buoyancy force to the viscous force. The correct formula for calculating Grashof number is:<br /><br />$\displaystyle Gr = \frac{g \cdot \beta \cdot \Delta T \cdot L^3}{\nu^2}$<br /><br />where:<br />- $g$ is the acceleration due to gravity,<br />- $\beta$ is the coefficient of thermal expansion,<br />- $\Delta T$ is the temperature difference between the fluid and the heated surface,<br />- $L$ is the characteristic length (e.g., the distance from the heated surface to the center of the fluid),<br />- $\nu$ is the kinematic viscosity of the fluid.<br /><br />The other formulas provided in the question are incorrect.