What happens if you drive your normal car through a flooding ford river?

The air intake is at the front of the car usually cars are lower, so when water goes into the air intake, it makes its way into the engine. water is incompressible so when the piston tries to compress it, everything basically breaks internally. so the whole engine is rekt. maybe not the whole engine, but the most important mechanical bits are ruined. this is why those offroader suv's have snorkels that go all the way to the top of their car to intake air. 

 It depends on how much water got through to the cylinders. as mentioned above water doesn't compress so it can do a varying amount of damage to the engine, depending on how the volume that entered the combustion chamber. Small amounts of water ingress can be solved by drying the engine and hoping for the best. Those cars with smaller fourbangers and drivers that forded this water on low RPMs could be lucky enough and only need a good drying of the engine. 

 The cars who went full throttle through the water, especially ones with larger displacement engines, probably had more water enter the engine, causing connecting rods to bend (metal rods that connect the piston to the crankshaft), which results in a hydrolocked engine. That type of damage is usually too expensive to fix, and a new (used) engine is recommended. Overall, don't drive through water higher than your bumper unless you know for a fact that your intake is up high. Even then, do it super slow and only if you absolutely have to. It's always better to take the long route than to spend thousands on fixing the mess that is a hydrolocked engine.