How high does the water need to be to hydroplane in a car?

not at all high. 1/2 inch or even less can hydroplane a car. all it means is that the vehicles tires are not spreading the water out or shedding it away from under the tire and is instead riding on top of it due to speed and condition of the tire. Once the car is riding on top of the film of water control is compromised and braking ability diminished.