AutoQuiz: What is the Relationship between Velocity and Reynolds Number Constraints for a Doppler Flowmeter?

Today's 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 information about the CCST program. This question is from the Level III study guide, Domain 1, Calibration. Level III represents a professional who has a 13-year total of education, training, and/or experience.

In order to meet velocity and Reynolds number constraints for a particular Doppler flowmeter sizing application, the following will normally be considered:

a) reduce the size, which increases both the velocity and the Reynolds number
b) reduce the size, which increases the velocity and decreases the Reynolds number
c) fix the size for velocity constraints and neglect Reynolds number
d) try another technology for laminar flow since Reynolds number constraints can preclude the use of Doppler flowmeters
e) none of the above

Recall that Doppler meters measure the frequency shifts caused by liquid flow and that viscosity does not influence their accuracy. Answer B is wrong per this equation, and answers C and D are frivolous and misleading for that purpose alone. The correct answer is A

The Reynolds number is the most important dimensionless number in fluid dynamics. It is the ratio of inertial forces to viscous forces and is used for determining whether a flow will be laminar or turbulent. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion. Turbulent flow occurs at high Reynolds numbers where inertial forces are greatest, producing random eddies, vortices, and other flow fluctuations.

where:

$v$ is the maximum velocity of the object relative to the fluid (SI units: m/s)
$L$ is a characteristic linear dimension, (travelled length of the fluid; hydraulic diameter when dealing with river systems) (m)
$μ$ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
$ν$ (nu) is the kinematic viscosity ( $ν = μ / ρ$ ) (m²/s)
$ρ$ is the density of the fluid (kg/m³)

Click this link for information about the CCST program.