Flow rate - Burn O'Vat

Burn O'Vat is an amazing hole in a stream near Braemar. It was created when rocks blocked the flow of water and it backed up, forming a whirlpool which carved out a huge space. The bottom picture shows the area of the downstream hole in the rocks. Area might be 2 square metres. Water is incompressible so even if more pressure builds up, the water will back up. I need to find out a bit more about Bernoulli's theorem to come up with a better analysis. I have tried calculating the speed of the water for a Reynold's number of 50000 which would make the flow turbulent. I get 45 cm per second. This would give a flow rate of about 90 kg per second through the hole. It suggests that the flow rate off the hill must be bigger than that to carve out the hole.