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Piston engines of propeller driven aircrafts need to be cooled. There are engine cowlings which accomodate the inflow of air to "wash" over the engines within them and which is then exhausted out into the freestream.

The model in question here would be a single block engine in the cowling of a tracktor configuration propeller aircraft. The airflow enters the cowling, washes over the engine, and then exits into the freestream.

The question is:

What would be a good estimate for the velocity of this air stream exhausted into the freestream?

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    $\begingroup$ I don’t understand your question. Can you please explain what you mean by “cooling exhaust velocity”. $\endgroup$
    – Mike Sowsun
    Dec 3 '18 at 16:55
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    $\begingroup$ Agree. It’s completely confusing. Are you asking “what is the velocity of the air that cools the external surfaces of the engine, as this air exits the engine nacelle?” That’s the only way I can make sense of this. $\endgroup$
    – Penguin
    Dec 3 '18 at 16:59
  • $\begingroup$ @Penguin: Not only confusing, as (if using your reformulated question) impossible to answer as it depends on the design and the airspeed. $\endgroup$
    – jamesqf
    Dec 5 '18 at 18:59
  • $\begingroup$ I would think that this would be heavily (totally) dependent on the aircraft and engine under consideration. They all use outside air in some manner to cool the engine(s), but how (fast) it exits the nacelle is specific to each particular installation - whether it flows through based solely on the aircraft's forward motion or if it's fan propelled; how many twists & turns it may take on its way out; how many other components it might cool before/after hitting the block & cylinders; etc. $\endgroup$
    – FreeMan
    Dec 5 '18 at 19:45
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    $\begingroup$ I am beginning to think that the estimation of such velocities is not widely known and is in the purview of a specialized investigation for each aircraft case. However, it also cannot be said that these velocities cannot be estimated, which would be necessary during conceptual design (apart of which I am at the moment). I have looked through the matter over the past few days and have found a conclusive method to estimate this velocity. For future reference of others, kindly reopen the question in order that I may provide my finding as an answer. Thank you. $\endgroup$
    – Guha.Gubin
    Dec 7 '18 at 11:24
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There are cases, as in the P-51 Mustang, where the cooling air adds to the THRUST of the aircraft as it is heated and expelled out the back of the air vent, much like a jet. This actually added a few knots its speed.

There is always an issue of cooling as one scales up a fuel burning engine. Towards the end of their time, piston engines for aircraft had grown exponentially in power in the race for performance. This lead to major issues in cooling of engines such as the "corn cob" R-4360 Wasp Major. Turbo or Super chargers also unavoidably raise the temperature of incoming air by compressing it.

So to estimate the velocity of the cooling airstream, one might begin a study of the principles of a jet engine. Since no mass is added to the cooling stream and there is no compressor (as in a turbo jet, although prop wash may give some effect) the only considerations are ram pressure and thermal expansion of the cooling air. Forward speed of the aircraft will be a major factor.

Study of the P-51 design may be a good place to start.

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