Starting with reality

• Airplanes weigh thousands of kilograms. Thus they are pulled down by a large force of gravity. Despite this they are able to stay afloat while flying ! How is it possible ?
• It is often said that deep waters run slow. Is this just a proverbial saying or does the speed of water in rivers and streams really have anything to do with their depth ?

Mathematically modeling the systems will help us answer these questions.