Problem

Water flows through a circular pipe having a constriction in diameter from 1 in. to 0.5...

Water flows through a circular pipe having a constriction in diameter from 1 in. to 0.5 in. The velocity of the water just upstream of the constriction is 4 ft/s. By using the result of Problem P6.35, determine:

(a) The velocity of the water downstream from it.

(b) The pressure drop across the constriction.

Reference: Problem P6.35

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.