A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 kg/m³.) A) 70 Pa B) 85 Pa C) 100 Pa D) 120 Pa E) 81 Pa

Question

Quizplus · Accepted Answer

We can use the Bernoulli's equation which states:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

where P1 and v1 are the pressure and velocity at the wider section and P2 and v2 are the pressure and velocity at the constricted section.

Since the venturi tube is horizontal, we can assume that the height difference between the two sections is negligible and can be ignored. Therefore, the Bernoulli's equation can be simplified as:

P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2

Rearranging the equation, we get:

P2 - P1 = (1/2)ρ(v1^2 - v2^2)

Substituting the given values, we have:

P2 - P1 = (1/2)(1.2 kg/m3)(3.0 m/s)^2((2.0 cm/2)^2 - (1.0 cm/2)^2)/100 cm/m = 0.81 kPa

Converting kPa to Pa, we get the answer:

P2 - P1 = 81 Pa

Therefore, the correct choice is E.

A Venturi Tube May Be Used as the Inlet to an Automobile