A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.0 cm diameter narrows to 1.0 cm diameter,what is the pressure drop in the constricted section for airflow of 2.5 m/s in the 2-cm section? (Assume air density is 1.25 kg/m³. ) A) 16 Pa B) 59 Pa C) 61 Pa D) 23 Pa E) 117 Pa

Question

Quizplus · Accepted Answer

First, we can use the continuity equation to find the airflow speed in the 1-cm section: A1V1=A2V2, where A is cross-sectional area and V is speed. Since A1=π(0.01 m)²/4=7.85×10⁻⁵ m² and A2=π(0.005 m)²/4=1.96×10⁻⁵ m², V2=4V1. Thus, V1=2.5 m/s, and V2=10 m/s.

Next, we can use Bernoulli's equation, which states that pressure plus (1/2)ρv² plus ρgh is constant along a streamline. Since the height and speed are constant, we have pressure1+(1/2)ρv1²=pressure2+(1/2)ρv2². Rearranging, pressure2=pressure1+(1/2)ρ(v1²-v2²). Plugging in the given numbers, we get pressure2-pressure1=59 Pa.

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