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Considering subsonic incompressible airflow through a Venturi, which statement is correct?

I. The dynamic pressure in the throat is the same as in the undisturbed airflow.
II. The total pressure in the throat is lower than in the undisturbed airflow.

  • A
    I is incorrect, II is correct.
  • B
    I is correct, II is incorrect.
  • C
    I is incorrect, II is incorrect.
  • D
    I is correct, II is correct.

Refer to figure.

To understand the venturi effect, we must first introduce two conditions: The conservation of mass (Continuity Equation) and the Conservation of Energy (Bernoulli’s Theorem).

Conservation of Mass (Continuity Equation)

The mass of air entering the pipe, in each unit of time, equals the mass of air leaving the pipe, in the same unit of time. The mass flow through the pipe must remain constant.

The mass air flow 'm' is the product of the density, the area and the velocity:

m = ρ * A * V

Continuity equation:

m1 = m2 = m3 = ρ1 * A1 * V1 = ρ2 * A2 * V2 = ρ3 * A3 * V3 = constant

The continuity equation explains the relationship between velocity and cross-sectional area: The speed is inversely proportional to the cross-sectional area.

Conservation of Energy (Bernoulli’s Theorem)

The total energy of an airstream comes in two forms: potential energy (static pressure) and kinetic energy (dynamic pressure).
The total pressure of the airstream is the sum of the static pressure and the dynamic pressure and must remain constant, according to the law of conservation of energy.
Thus, an increase in one form of pressure, must result in a decrease in the other.

Dynamic pressure (q) is expressed by:

q = 1 / 2 * ρ * V2

Assuming the total pressure to be constant, the static pressure and the dynamic pressure vary inversely: If one increases the other decreases and vice-versa.

In Conclusion:

With a decrease in section area (from station 1 to station 2), flow speed increases, increasing dynamic pressure. Statement 1 is therefore incorrect.
The total pressure of the airstream is the sum of the static pressure and the dynamic pressure and must remain constant, according to the law of conservation of energy. Statement 2 is therefore incorrect.

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