A device called a venturi flowmeter can be used to determine the velocity of a flowing fluid by measuring the change in its pressure between two points (Figure P6.35, see on page 290). Water flows through a pipe, and, at the constriction, the cross-sectional area of the pipe reduces from A₁ to the smaller value A₂. Two pressure sensors are located just before and after the constriction, and the change p₁ - p₂ that they measure is enough information to determine the water’s velocity. By using Equations (6.13) and (6.17), show that the velocity downstream of the constriction is given by

This so-called venturi effect is the principle behind the operation of such hardware as automotive carburetors and the aspirators that deliver pharmaceutical products to medical patients by inhalation.

Equation 6.13

A₁v₁ = A₂v₂

Equation 6.17

Figure P6.35

2(pi - p:) P2) P(1 - (A/A)*)