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

From the continuity equation, we know that the velocity of the flow through the constricted section is twice the velocity through the wider section. Therefore, the pressure drop in the constricted section is given by:

ΔP = (1/2)ρv² = (1/2)×1.2 kg/m³ × (3.0 m/s)² = 5.4 Pa

However, we must convert the units of diameter from cm to m:

d1 = 2.0 cm = 0.02 m
d2 = 1.0 cm = 0.01 m

Using the formula for the area of a circle, we find that the ratio of areas is:

A2/A1 = (d2/2)² / (d1/2)² = (0.01/0.02)² = 0.25

Therefore, the pressure drop in the constricted section is:

ΔP = ρv² (1 - A2/A1) = (1.2 kg/m³) × (3.0 m/s)² (1 - 0.25) = 81 Pa

The answer is E.

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