What would be the effects of installing pitot tubes on the engine covers? What are the effects on airspeed measurements, if the pitot tubes were installed right on the engine covers of an aircraft instead of being on the nose.  Would the reading be false? If so, would the reading be underestimated or overestimated and why?
There is a very good reason to install pitot tubes in a place with relatively constant environmental circumstances: calibration.

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When installed at around the nose of the aircraft, the pitot always have a good view of the airflow, at all angles of attack and of sideslip. These parameters do distort the pressure reading, that is why during aircraft development the prototype tows a flying pitot tube and compares measurements. These measurement sets are used for calibration.

If it was installed on the engine covers, not only the aircraft state but also the engine state would have influence on the reading. A nightmare to calibrate, and prone to unforeseen errors for instance if a fan blade breaks off and the wobbling fan causes an airstream situation that was not accounted for.

Best to use the prime location: the nose.