River flow

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A river runs through it - my garden. With increasing concern about floods, insurance companies are waking up ad asking questions. Council planning departments are asking a lot more about environmental impact too: bats, birds, bushes, rivers, run-off and trees.

The UK Environment Agency manages the waterways. It uses LIDAR a radar measurement system to generate flood maps and keeps a data-base of flows along rivers. But that doesn't help with individual properties. They can only tell me that the house is 33m above datum sea level and the worst case flow past it would be 41.2 cu.m/sec.

I'm on a hill at 1:18 slope. The river is straight and the banks are vertical sheer stone , straight and regular with no necking. The bed is rough with slabs or rock jutting at random. In Summer it's a slow run that just covers your boot. In a winter storm it's a torrent doing 2m/sec about thigh deep and could sweep you away like a leaf.

So how high will it rise? That's a complicated calculation using the Navier-Stokes formulae for conservation of mass of a viscous liquid flowing down an inclined plane, corrected by the Poiseuille equation for flow against a surface that drags. Laminar flows considered as ribbons moving past each other at different speeds, the fastest being at the top in the centre for an open channel like a river, the slowest at the bottom touching a bank. Then there's turbulence, seemingly unpredictable.

So I know that the river's length (300m), width (9,2m) and depth (Z) are not going to change from minute to minute and I know the volume passing and the slope. That should be enough to get a rough solution to these equations. I just need to find a mathemetician working in the civil engineering field.

(to be continued if I EVER find such a rare beast!)