Final answer:
The pressure reading of a pitot tube that is 15.0 mm Hg at 200 km/h will increase proportionally with the square of the increase in velocity, resulting in a new reading of 183.75 mm Hg at 700 km/h.
Step-by-step explanation:
The pitot tube measures dynamic pressure which can be related to the velocity of an aircraft or wind speed. According to Bernoulli's principle, the dynamic pressure is proportional to the square of the velocity. If the pressure reading of a pitot tube is 15.0 mm Hg at a velocity of 200 km/h, we need to determine what the reading will be at 700 km/h at the same altitude.
To find the new pressure reading, we can use the relationship that pressure is proportional to the square of the velocity. If we double the velocity, the dynamic pressure will increase by a factor of four. Increasing the speed from 200 km/h to 700 km/h is an increase by a factor of 3.5 (700 / 200 = 3.5).
Therefore, the new dynamic pressure will be 15.0 mm Hg multiplied by 3.52 (which is 12.25).
The pressure reading at 700 km/h will therefore be 15.0 mm Hg * 12.25, which equals 183.75 mm Hg.