Reynolds Number
Added on 2023-04-23
3 Pages1243 Words337 Views
1
Reynolds Number
R. Shankar Subramanian
Department of Chemical and Biomolecular Engineering
Clarkson University
We encountered some interesting dimensionless groups when performing dimensional analysis
of fluid mechanical problems. The most prominent dimensionless group that emerges from these
analyses is the Reynolds number, named after Osborne Reynolds who made several important
contributions to fluid mechanics. One problem Reynolds investigated experimentally is the
transition of flow from the orderly kind that we call “laminar flow” to the more chaotic type of
flow termed “turbulent flow.” Reynolds published the results of his study in 1883 in an article
(1) that is regarded as one of the most important contributions in the field of fluid mechanics.
This study changed the way in which knowledge about the transition between the two types of
flows, namely, laminar and turbulent, is organized. It was known from earlier studies that
turbulent flow occurs in conduits of large cross-sectional dimensions and flows at high
velocities, whereas laminar flow occurs in slow flows in conduits of relatively small cross-
sectional dimensions. The role of viscosity and density in affecting the type of motion was not as
well-characterized. In laminar flow, the pressure drop for flow is linear in the average velocity
of the fluid, as we learned earlier, whereas in turbulent flow Reynolds observed that it was
approximately proportional to 1.72
V , where V is the average velocity, in his experiments. The
actual dependence of the pressure drop on the velocity for turbulent flow in circular tubes is
more complicated. For instance the roughness of the interior pipe wall in contact with the fluid
profoundly affects the pressure drop, even if it is so minute as not to be visible to the naked eye.
We shall learn more about this topic soon in this course.
Through careful experimentation, Reynolds established that the change in the nature of the flow
occurs when a certain combination of the parameters in the flow crosses a threshold. Later, this
combination was named the “Reynolds number.” For flow in a circular tube of diameter D at an
average velocity V , the Reynolds number Re is defined as follows.
Re DV DV
ρ
μ ν
= =
Here,
μ is the dynamic viscosity of the fluid, and
ρ is the density of the fluid. The ratio
ν μ ρ= is termed the kinematic viscosity. For circular tubes, the transition from laminar to
turbulent flow occurs over a range of Reynolds numbers from approximately 2,300 to 4,000,
regardless of the nature of the fluid or the dimensions of the pipe or the average velocity. All that
matters is that this specific combination of the parameters, known as the Reynolds number, fall
in the range indicated. So, when the Reynolds number is below 2,300, we can expect the flow to
be laminar, and when it is above approximately 4,000, the flow will be turbulent. In between
these two limits, the flow is termed “transition flow.”
Reynolds Number
R. Shankar Subramanian
Department of Chemical and Biomolecular Engineering
Clarkson University
We encountered some interesting dimensionless groups when performing dimensional analysis
of fluid mechanical problems. The most prominent dimensionless group that emerges from these
analyses is the Reynolds number, named after Osborne Reynolds who made several important
contributions to fluid mechanics. One problem Reynolds investigated experimentally is the
transition of flow from the orderly kind that we call “laminar flow” to the more chaotic type of
flow termed “turbulent flow.” Reynolds published the results of his study in 1883 in an article
(1) that is regarded as one of the most important contributions in the field of fluid mechanics.
This study changed the way in which knowledge about the transition between the two types of
flows, namely, laminar and turbulent, is organized. It was known from earlier studies that
turbulent flow occurs in conduits of large cross-sectional dimensions and flows at high
velocities, whereas laminar flow occurs in slow flows in conduits of relatively small cross-
sectional dimensions. The role of viscosity and density in affecting the type of motion was not as
well-characterized. In laminar flow, the pressure drop for flow is linear in the average velocity
of the fluid, as we learned earlier, whereas in turbulent flow Reynolds observed that it was
approximately proportional to 1.72
V , where V is the average velocity, in his experiments. The
actual dependence of the pressure drop on the velocity for turbulent flow in circular tubes is
more complicated. For instance the roughness of the interior pipe wall in contact with the fluid
profoundly affects the pressure drop, even if it is so minute as not to be visible to the naked eye.
We shall learn more about this topic soon in this course.
Through careful experimentation, Reynolds established that the change in the nature of the flow
occurs when a certain combination of the parameters in the flow crosses a threshold. Later, this
combination was named the “Reynolds number.” For flow in a circular tube of diameter D at an
average velocity V , the Reynolds number Re is defined as follows.
Re DV DV
ρ
μ ν
= =
Here,
μ is the dynamic viscosity of the fluid, and
ρ is the density of the fluid. The ratio
ν μ ρ= is termed the kinematic viscosity. For circular tubes, the transition from laminar to
turbulent flow occurs over a range of Reynolds numbers from approximately 2,300 to 4,000,
regardless of the nature of the fluid or the dimensions of the pipe or the average velocity. All that
matters is that this specific combination of the parameters, known as the Reynolds number, fall
in the range indicated. So, when the Reynolds number is below 2,300, we can expect the flow to
be laminar, and when it is above approximately 4,000, the flow will be turbulent. In between
these two limits, the flow is termed “transition flow.”
End of preview
Want to access all the pages? Upload your documents or become a member.
Related Documents
Laminar and Turbulent Pipe Flow: Introduction, Method, Resultslg...
|19
|3534
|172
Fluid Mechanics for Chemical Engineeringlg...
|8
|1735
|11
Calculation of Wind Tunnel Speed and Drag Force on a Full-Size Carlg...
|7
|1637
|342
Hydraulics for Civil Engineeringlg...
|11
|1470
|27
Heat Transfer and Combustion Assignmentlg...
|13
|1575
|167