A Venturi tube may be used as the inlet to an automobile carburetor.If the inlet pipe of 2.00 cm diameter narrows to 1.00 cm diameter,what is the pressure drop in the constricted section for airflow of 2.16 m/s in the 2.00-cm section? (Assume air density is 1.25 kg/m³. ) A)11.7 Pa B)43.7 Pa C)45.7 Pa D)20.3 Pa E)87.5 Pa

Question

Quizplus · Accepted Answer

The pressure drop in the constricted section can be calculated using the Bernoulli's equation and the continuity equation. The continuity equation gives us the relationship between the velocities and cross-sectional areas at two points in a flow, $A_1V_1 = A_2V_2$, where $A$ is the area and $V$ is the velocity. Given the diameters, we can find the areas of the sections, $A_1 = \pi(0.02/2)^2$ m$^2$ and $A_2 = \pi(0.01/2)^2$ m$^2$. Using the given velocity in the 2.00-cm section, we can find the velocity in the 1.00-cm section using the continuity equation. Then, applying Bernoulli's equation, we find the pressure difference ($\Delta P$) between the two sections. The calculation involves using the air density ($1.25 kg/m^3$), and the velocities in both sections to find $\Delta P$, which results in a pressure drop of 43.7 Pa.

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