Here's a nice one. What is the energy flux = power per unit area F (W m^-2 = kg s^-3) carried by a gravitational wave of strain h? Strain is dimensionless, and the only physical constants available are speed of light c (m s^-1) and Newton's G (kg^-1 m^3 s^-2), since this is not a quantum phenomenon. Since the power flux should vary as h^2, we can write F = c^x G^y h^2. Expanding out, kg: 1 = -ym: 0 = x + 3ys: -3 = -x - 2y But these are inconsistent. So something is missing. Let's put in the frequency f (s^-1), and write F = c^x G^y f^z h^2. kg: 1 = -ym: 0 = x + 3ys: -3 = -x - 2y - z Then y = -1, x = 3, z=2, and F = (c^3 / G) (f h)^2. This makes sense. Strain is the deviation of the metric from flat space, but the gravitational energy should vary as the square of the connection coefficients, which are first derivatives of the metric. There is some proportionality constant which cannot be found from dimensional analysis. Is all this correct? Indeed it is. According to https://arxiv.org/pdf/1209.0667.pdf eq. (25) for a linearly polarized wave, the constant is π/8. -- Gene