Specifically talking about the p51, why do they have intakes? Don't propeller-driven planes not require any sort of intake because the propeller is what propels it by pushing air behind it?
Propellers are driven by engines, and engines burn fuel, and burning requires oxygen from the air. The intake supplies air to the engine. Burning creates heat, and air intakes also direct cooler air onto the engine to keep it from overheating.
In the case of the P-51, the duct you see is actually to feed the radiator. As the P-51's engine was water cooled, the radiator could be mounted in the belly of the airplane. The duct used the Meredith Effect to produce thrust through the expansion of air due to heating.
The design of the P-51 means the engine radiator (a component of the cooling system) is situated behind and below the pilot, as in this diagram (from here):
don't propeller-driven planes not require any sort of intake
No, propeller-driven planes (piston or turboprop) require air intakes for a variety of purposes:
- Combustion air
- Engine cooling (whether air-cooled or liquid cooled)
- Oil cooling
- Cabin ventilation and heating
- Fuel tank venting
And perhaps more.
The p51 has an inline engine which makes cooling with just air flow infeasible since the pistons are not all exposed to air flow equally. If you look at pictures of other WW2 era planes like the F4U Corsair or F6F Hellcat have radial engines where all the pistons are exposed to the airflow allowing air cooling. These pistons form circle at the front exposing them all to airflow. Because of the cooling problems the p51 was water cooled using an inlet scoop underneath the plane. Supermarine Spitfires also had inline engines and have a cooling intake underneath as well.
That’s the intake duct for the radiator for the liquid cooled engine. Similar to the radiator in your car, the radiator for the engine in the airplane is cooled by ram air from the intake passing through it and exiting a variable geometry ramp aft of it. Some of the air also bleeds off that ram air scoop and is fed through the oil cooler just below the radiator.
The smaller intake scoop just under the propeller spinner is the supercharger inlet that the engine aspires through.