Why use different airfoils on the same wing of an aircraft?

Question

Why different airfoils are used in different portions of the same wing of an aircraft, for example Boeing 737 wing?

Boeing Commercial Airplane Company model 737 airfoils' dat files from here: http://m-selig.ae.illinois.edu/ads/coord_database.html

BOEING 737 ROOT AIRFOIL (b737a-il), BOEING 737 MIDSPAN AIRFOIL (b737b-il), BOEING 737 MIDSPAN AIRFOIL (b737c-il) and BOEING 737 OUTBOARD AIRFOIL (b737d-il)

Answer 1

Because the wind tunnel has determined what the best airfoil is, at this particular span, over the whole operational range of flight:

• Stall speed: docile pre-stall behaviour with outboard wing stalling last to retain roll control.
• Landing speed with flaps & slats out: high stall angle, high $C_L$
• Climb speed: low drag in high lift conditions.
• Cruise speed in clean configuration: low drag, low pitching moment, high drag/lift divergence speeds.

The design goal is the performance of the total wing, wing profile is one of the parameters that can be used to optimise performance, minimise drag, provide good structural characteristics, and provide a large volume for the on-board fuel.

• For the wing root, the aerofoil must have a good cantilever ratio (thickness) for torsional and bending stiffness.
• For the wing inboard section with flaps extended, aerofoil drag must be low in high lift conditions.
• For the wing tip, the aerofoil must have a high maximum $C_L$ and gradual stall characteristics)
• For all wing sections, the aerofoil must have a sufficiently high critical Mach number.
• For all wing sections, pitching moment coefficient should be low to moderate, to avoid high trim drag, and high torsion at high dynamic pressure.
• For all wing sections, aerofoils must not be extremely sensitive to manufacturing tolerances, dirt/bug build-up etc.

So different bits of wing have different design characteristics. The whole wing is a gradually blending unit of different aerofoils.

Answer 2

For the same reason the wing root and wing tip don't always have the same incidence angles: you usually want the wing tip to be the last part of the wing that stalls in high angles of attack.

This is the reason that in some (most? all?) aircraft the wing tip has a lower incidence angle than the wing root.

I think this property is best visible on the F-18 (no, it's not an F-16 as the file name suggests):

http://duotechservices.com/wp-content/uploads/2015/04/f-16-The-AIM-9-Sidewinder.jpg

You can see the Sidewinder missile on the wing tip launch rail is actually pointing downward (=the F-18's wing tip has a negative angle of incidence).