Exercise 3

The torque produced by an engine has dimensional formula $L^{2}M^{1}T^{-2}$. We may first guess that it depends on the engine’s rotation rate (with dimensional formula $L^{0}M^{0}T^{-1}$), and the volume of air displaced (with dimensional formula $L^{3}M^{0}T^{0}$).

• Try to find a complete set of dimensionless products. What goes wrong?

• Adjust the guess by adding the density of the air (with dimensional formula $L^{-3}M^{1}T^{0}$). Now find a complete set of dimensionless products.