# Roshko Number

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Roshko number, abbreviated as Ro, a dimensionless number, is used in fluid dynamics to characterize the relative importance of rotation to the fluid's velocity in a rotating flow.  It is particularly relevant in the study of rotating machinery and geophysical flows, such as hurricanes and tornadoes.  The Roshko Number provides valuable information about the relative importance of rotation and inertia in fluid flows and is useful in various applications where rotation plays a significant role.

### Key Points about Roshko number

• Rotation vs. Inertia  -  The Roshko number represents the competition between the rotation (angular velocity) of the fluid and the fluid's inertia (characteristic velocity).  It quantifies whether the rotation is significant compared to the fluid's motion.
• Application  -  The Roshko number is commonly used in the analysis of rotating machinery, such as pumps, turbines, and centrifuges, where the effects of rotation on fluid flow must be considered for design and performance evaluation.
• Relationship to Coriolis Force  -  In geophysical and atmospheric flows, the Roshko number is related to the Coriolis force, which deflects moving objects (including air masses) due to the Earth's rotation.  The Roshko number helps quantify the balance between this force and other forces in the system.

### Roshko number Interpretation

• Ro < The angular velocity dominates, and the flow is rotationally dominated.  This often occurs in geophysical flows like hurricanes, where the Coriolis effect (caused by the Earth's rotation) plays a significant role.
• Ro > The characteristic velocity dominates, and the flow is inertially dominated.  In such cases, the fluid's motion is not significantly affected by rotation.

### Roshko Number formula

$$Ro \;=\; f \; l_c^2 \;/\; \nu$$     (Roshko Number)

$$f \;=\; Ro \; \nu \;/\; l_c^2$$

$$l_c \;=\; \sqrt{ Ro \; \nu \;/\; f }$$

$$\nu \;=\; f \; l_c^2 \;/\; Ro$$

Symbol English Metric
$$Ro$$ = Roshko number $$dimensionless$$
$$f$$ = frequency of vortex shedding $$dimensionless$$
$$l_c$$ = characteristic length $$in$$ $$mm$$
$$\nu$$  (Greek symbol nu) = kinematic viscosity $$ft^2\;/\;sec$$ $$m^2\;/\;s$$

Tags: Flow Fluid