[jffry]

For a sense of how crazy 30 detections per day is: Super-K is a cylinder 41.4m tall and 39.3m in diameter [1] and neutrino flux on Earth is 65 billion per square centimeter per second [2]

The tank's cross sectional area relative to the sun depends on its relative orientation to the sun. We'll ballpark it at somewhere between its circular endcaps (Pi x ((39.3/2)^2) = 1213 square meters) and its curved cylindrical face (which, pointed right at the sun, has a rectangular cross section of 41.4 x 39.3 = 1627 square meters).

So, conservatively, the neutrino flux through Super-K's tank is 1400 m^2 x (100cm/m)^2 x 6.5e10 neutrino/second/(cm^2) x 86400 seconds/day = 7.86e22 neutrinos/day passing through the tank. Of which 30 are detected.

[1] https://en.wikipedia.org/wiki/Super-Kamiokande

[2] https://en.wikipedia.org/wiki/Neutrino (end of intro section, just before History). Wikipedia says only that the "majority" of the 65 billion flux is from the sun, so we might be off by a factor of two-ish in the worst case.