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In a wind tunnel, a flow is sped up. in the reservoir, the velocity is approximately zero; in the test section, the air is at standard conditions with a flow speed of 30 m/s. what is the total pressure in the test section (in pa)?

a. 101,000 Pa
b. 108,000 Pa
c. 120,000 Pa
d. 135,000 Pa

1 Answer

5 votes

Final answer:

The total pressure in the test section of the wind tunnel is approximately 101,513 Pa.

Step-by-step explanation:

In order to determine the total pressure in the test section of the wind tunnel, we need to consider Bernoulli's equation. Bernoulli's equation states that the total pressure is the sum of the static pressure, dynamic pressure, and gravitational potential energy per unit volume. Since the flow speed in the test section is 30 m/s, the dynamic pressure is given by:

Dynamic pressure = 0.5 * density * velocity^2

Substituting the values, we have:

Dynamic pressure = 0.5 * (density of air) * (velocity of air)^2

Static pressure represents the pressure exerted by the air at rest. In the reservoir, the air is at standard conditions with approximately zero velocity, so the static pressure is equivalent to the atmospheric pressure, which is 101,000 Pa. Therefore, the total pressure in the test section is:

Total pressure = Static pressure + Dynamic pressure = 101,000 Pa + 0.5 * (density of air) * (velocity of air)^2

Plugging in the values, we get:

Total pressure = 101,000 Pa + 0.5 * (1.14 kg/m^3) * (30 m/s)^2

Simplifying the equation gives us:

Total pressure = 101,000 Pa + 0.5 * 1.14 * 900

Total pressure = 101,000 Pa + 513

Total pressure = 101,513 Pa

Therefore, the total pressure in the test section of the wind tunnel is approximately 101,513 Pa.

User GavinR
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