Question

If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?

a) 5.0 mm Hg
b) 12.5 mm Hg
c) 22.5 mm Hg
d) 30.0 mm Hg

Answer 1

The pressure reading by the pitot tube at 700 km/h cannot be directly inferred from the given information and the simple square relationship, as the actual pressure will depend on factors not specified in the question. Thus, without additional context or assumptions, we cannot determine which of the provided options (a-d) is correct.

Step-by-step explanation:

The pitot tube measures fluid speed based on the dynamic pressure difference it experiences. According to Bernoulli's principle and the continuity equation, the speed of fluid flow and pressure are related, and this relationship, under certain assumptions, can be simplified to a proportional relationship between the square of the speed and the pressure difference recorded by the pitot tube.

Given the pressure reading of the pitot tube at one speed, you can find out the pressure at another speed using the following relation derived from Bernoulli's equations:

P ≈ speed2

In this case, since the pressure at 200 km/h was 15.0 mm Hg, we can determine the pressure at 700 km/h using a ratio:

1. Calculate the square of both speeds: (200 km/h)2 and (700 km/h)2.
2. Establish the ratio between the square of the new speed and the original speed.
3. Calculate the new pressure by multiplying the old pressure (15.0 mm Hg) by the ratio from step 2.

To calculate the ratio of the pressures:

Pressure Ratio = (New Speed / Original Speed)2 = (700 / 200)2 = 3.52 = 12.25

To calculate the new pressure:

ϴNew Pressure = Original Pressure x Pressure Ratio = 15.0 mm Hg x 12.25

ϴNew Pressure = 183.75 mm Hg

However, since the answer must match one of the provided options, we need to consider that this result is not a direct proportion but rather a relationship between the squares of the velocities. Due to the square relationship, this theoretical value of 183.75 mm Hg is not the actual answer. The problem does not specify the exact nature of the relationship between speed and pressure, and the expected answer likely involves a more specific context or assumption, so we should provide a note regarding the limitations of our calculation.