# ISA Interchange

Welcome to the official blog of the International Society of Automation (ISA).

# AutoQuiz: How to Measure Fluid Velocity Through a Pipe

### Subscribe Here!

AutoQuiz is edited by Joel Don, ISA's social media community manager.

This automation industry quiz question comes from the ISA Certified Control Systems Technician (CCST) program. Certified Control System Technicians calibrate, document, troubleshoot, and repair/replace instrumentation for systems that measure and control level, temperature, pressure, flow, and other process variables. Click this link for more information about the CCST program.

### A fluid is flowing through a 10-inch diameter pipe at a velocity of 6 ft/sec. When the pipe reduces to an 8-inch diameter, and all other flowing parameters remain the same, the fluid velocity becomes ________ ft/sec.

a) 2.550
b) 6.075
c) 9.375
d) 12.75
e) none of the above

Flow in a pipe can be expressed as:
Q = A x V,

where

Q = volumetric flow rate, ft3/sec
A = pipe cross-sectional area, ft2
V = fluid velocity, ft/sec

The flow rate of the fluid through the 10-inch pipe (condition 1) is the same as the flow rate through the 8-inch pipe (condition 2), so:

Q1 = Q2

and since Q = A x V,

A1 x V1 = A2 x V2

Solving for V2:

V2 = A1 x V1 / A2  = [A1 / A2 ] x V1

Area is proportional to the square of the pipe diameter (A = Π x D2 / 4), so:

V2 = [(10 in)2 / (8 in)2] x 6 ft/sec

V2 = 9.375 ft/sec

The correct answer is C, 9.375 ft/sec.

Reference: Goettsche, L.D. (Editor), Maintenance of Instruments and Systems, 2nd Edition