A venturi tube may be used as the inlet to an automobile carburettor. 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? ($\rho$ = 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 to solve for the pressure drop across the constricted section:

P1 + (1/2)rho*v1^2 = P2 + (1/2)rho*v2^2

Assuming P1 is atmospheric pressure (101325 Pa) and v1 = 3 m/s, we can solve for P2:

P2 = P1 + (1/2)rho*(v1^2 - v2^2)

P2 = 101325 Pa + (1/2)(1.2 kg/m3)(3 m/s)^2*(1 - (2/3)^2)

P2 = 101325 Pa + 81 Pa

P2 = 101406 Pa

Thus, the pressure drop across the constricted section is 101406 Pa - 101325 Pa = 81 Pa. Therefore, the correct answer is E.

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