David W. Spitzer

Cooling water flows through a 4-inch pipe that is reduced to a 3-inch pipe prior to entering a piece of process equipment. If the velocity in the 4-inch pipe is 1 meter per second, what is the approximate velocity in the 3-inch pipe?

A. 0.75 meters per second
B. 1 meter per second
C. 1.33 meters per second
D. 1.75 meters per second

Commentary

The velocity of a given flow through a 3-inch pipe will be higher than the same flow in a 4-inch pipe. Therefore, Answer A and Answer B are not correct.

Continuity dictates that the volumetric flow (Q) is equal to the velocity (v) times the cross-sectional area of the pipe (A) in each of the pipe sections.

Q = A3 * v3 = A4 * v4

Estimating the pipe internal diameters to be 3 inches and 4 inches, rearranging, substituting A3 = 0.25 π (3)2 and A4 = 0.25 π (4)2, simplifying, and solving for v3 yields:

v3 = (A4 / A3) *v4 = (4/3)2 * 1 = 1.78

Answer D is approximately correct.

Additional complicating factors

Related Content:
“Part I: The Expert Witness” By David W. Spitzer

Precise calculations would require the calculations that use the actual inside pipe diameters that could be obtained if the pipe schedules were known.

David W. Spitzer is a regular contributor to Flow Control magazine and a principal in Spitzer and Boyes, LLC, offering engineering, seminars, strategic, marketing consulting, distribution consulting and expert witness services for manufacturing and automation companies. He has more than 35 years of experience and has written over 10 books and 250 articles about flow measurement, instrumentation and process control.

Mr. Spitzer can be reached at 845-623-1830 or spitzerandboyes.com. Click on the “Products” tab in the navigation menu to find his “Consumer Guides” to various flow and level measurement technologies.