How do airplanes take to the air?]

To answer this question, we are entering into the
world of fluid mechanics.
Physicists classify both liquids and gases as fluids,
based on how they flow. Even though air, water and
pancake syrup may seem like very different
substances, they all conform to the same set of
mathematical relationships. In fact, basic
aerodynamic tests are sometimes performed
underwater. To put it simply, a salmon essentially
flies through the sea, and a pelican swims through
the air.
The core of the matter is this: Even a clear sky isn't
empty. Our atmosphere is a massive fluid layer, and
the right application of physics makes it possible for
humans to traverse it.
In this article, we'll walk through the basic principles
of aviation and the various forces at work in any
given flight.
Drop a stone into the ocean and it will sink into the
deep. Chuck a stone off the side of a mountain and it
will plummet as well. Sure, steel ships can float and
even very heavy airplanes can fly, but to achieve
flight, you have to exploit the four basic aerodynamic
forces: lift, weight, thrust and drag. You can think of
them as four arms holding the plane in the air, each
pushing from a different direction.
First, let's examine thrust and drag:Thrust, whether
caused by a propeller or a jet engine, is the
aerodynamic force that pushes or pulls the airplane
forward through space. The opposing aerodynamic
force is drag, or the friction that resists the motion of
an object moving through a fluid (or immobile in a
moving fluid, as occurs when you fly a kite).
For flight to take place, thrust must be equal to or
greater than the drag. If, for any reason, the amount
of drag becomes larger than the amount of thrust, the
plane will slow down. If the thrust is increased so that
it's greater than the drag, the plane will speed up.
Weight and Lift:
Every object on Earth has weight, a product of both
gravity and mass. A Boeing 747-8 passenger airliner,
for instance, has a maximum takeoff weight of 487.5
tons (442 metric tons), the force with which the
weighty plane is drawn toward the Earth.
Weight's opposing force is lift, which holds an
airplane in the air. This feat is accomplished through
the use of a wing, also known as an airfoil. Like drag,
lift can exist only in the presence of a moving fluid. It
doesn't matter if the object is stationary and the fluid
is moving (as with a kite on a windy day), or if the
fluid is still and the object is moving through it (as
with a soaring jet on a windless day). What really
matters is the relative difference in speeds between
the object and the fluid.
As for the actual mechanics of lift, the force occurs
when a moving fluid is deflected by a solid object.
The wing splits the airflow in two directions: up and
over the wing and down along the underside of the
wing.
The wing is shaped and tilted so that the air moving
over it travels faster than the air moving underneath.
When moving air flows over an object and encounters
an obstacle (such as a bump or a sudden increase in
wing angle), its path narrows and the flow speeds up
as all the molecules rush though. Once past the
obstacle, the path widens and the flow slows down
again. If you've ever pinched a waterhose, you've
observed this very principle in action. By pinching the
hose, you narrow the path of the fluid flow, which
speeds up the molecules. Remove the pressure and
the water flow returns to its previous state.
As air speeds up, its pressure drops. So the faster-
moving air moving over the wing exerts less
pressure on it than the slower air moving underneath
the wing. The result is an upward push of lift. In the
field of fluid dynamics, this is known as Bernoulli's
principle.