12.5 The Onset of Turbulence
3 min read•june 18, 2024
explores how liquids and gases move. The is key, helping us predict if flow will be smooth or chaotic. It's calculated using fluid properties and flow conditions, guiding our understanding of real-world situations.
Knowing the difference between laminar and is crucial. Factors like , obstructions, and fluid properties affect when turbulence starts. This knowledge helps engineers design better pipes, planes, and other systems involving fluid flow.
Fluid Dynamics and Turbulence
Reynolds number calculation
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- Reynolds number () dimensionless quantity characterizes fluid flow behavior
- Determines whether flow is laminar (smooth, parallel layers) or turbulent (chaotic, irregular motion)
- Formula:
- : fluid density (kg/m³)
- : average fluid velocity (m/s)
- : tube diameter (m)
- : fluid (Pa·s)
- Calculating involves identifying values for , , , and
- Substitute values into the formula and compute the result
- Example: Water flowing through a pipe (density 1000 kg/m³, velocity 0.5 m/s, diameter 0.02 m, 0.001 Pa·s) has
Laminar vs turbulent flow classification
- occurs at low Reynolds numbers (typically )
- Fluid moves in smooth, parallel layers without mixing between layers
- Examples: Slow-moving, viscous fluids (honey, oil)
- Turbulent flow occurs at high Reynolds numbers (typically )
- Chaotic and irregular fluid motion with mixing between layers
- Examples: Fast-moving, low-viscosity fluids (air, water in pipes)
- between laminar and turbulent flow (typically )
- Flow exhibits characteristics of both laminar and turbulent flow
- Difficult to predict exact behavior in this range
Factors affecting turbulence onset
- Surface roughness promotes turbulence by introducing disturbances in the fluid flow
- Rough surfaces cause fluid layers to mix and become turbulent
- Smooth surfaces delay the onset of turbulence by minimizing disturbances
- Examples: Rough pipe walls vs smooth glass tubes
- Obstructions in the fluid path can trigger turbulence by disrupting smooth, parallel flow
- Obstacles cause fluid layers to mix and become turbulent
- Examples: Valves, bends, and fittings in pipes
- Higher fluid velocities increase the likelihood of turbulence
- Increased relative to promote mixing between layers
- Examples: Fast-flowing rivers vs slow-moving streams
- Higher viscosity fluids are more resistant to turbulence
- Stronger viscous forces dampen disturbances and maintain laminar flow
- Lower viscosity fluids are more prone to turbulence
- Examples: Honey (high viscosity) vs water (low viscosity)
Boundary Layer and Flow Characteristics
- : Region of fluid near a solid surface where fluid velocity changes from zero at the surface to the free-stream velocity
- Thickness of the boundary layer affects the onset of turbulence
- : Measure of local rotation in a fluid flow, often associated with turbulent motion
- : Force per unit area exerted parallel to the flow direction, influencing boundary layer behavior
- occurs when the boundary layer detaches from the surface, potentially leading to turbulence
- : Speed at which flow transitions from laminar to turbulent (related to the Reynolds number)
Key Terms to Review (15)
Boundary Layer: The boundary layer is a thin layer of fluid that forms along the surface of an object moving through a fluid, such as air or water. It is characterized by a gradual transition in velocity and other properties between the object's surface and the free stream of the surrounding fluid.
Critical Velocity: Critical velocity is the velocity at which the flow of a fluid, such as air or water, transitions from a smooth, laminar flow to a turbulent, chaotic flow. This transition point is a crucial concept in the study of fluid dynamics and the onset of turbulence.
Flow Separation: Flow separation is a phenomenon that occurs when a fluid, such as air or water, flowing along a surface abruptly detaches from that surface, creating a region of recirculating flow. This separation of the fluid from the surface is a crucial aspect in the understanding of the onset of turbulence in fluid dynamics.
Fluid dynamics: Fluid dynamics is the branch of physics that studies the behavior of fluids (liquids and gases) in motion. It examines how forces affect the flow and movement of these substances, encompassing concepts like pressure, velocity, and viscosity, which are crucial in understanding phenomena in both natural and engineered systems.
Inertial Forces: Inertial forces are fictitious forces that appear to act on objects in a non-inertial reference frame, such as a frame that is accelerating or rotating. These forces arise due to the relative motion between the object and the non-inertial frame, and they are necessary to maintain the object's motion in accordance with Newton's laws.
Laminar Flow: Laminar flow is a type of fluid flow where the fluid travels in smooth, parallel layers with no disruption between the layers. It is characterized by a high degree of order and predictability in the fluid's movement.
Reynolds number: Reynolds number is a dimensionless quantity used to predict the flow regime in fluid dynamics. It indicates whether flow will be laminar or turbulent based on the ratio of inertial forces to viscous forces.
Shear Stress: Shear stress is the component of stress coplanar with a material cross-section. It is the stress which acts tangentially to the face of the section. Shear stress is an important concept in the study of elasticity, fluid mechanics, and the motion of objects in viscous fluids.
Surface Roughness: Surface roughness is a measure of the texture or irregularity of a surface, which can have significant impacts on various physical phenomena, including friction and the onset of turbulence. It is a fundamental concept in the fields of tribology and fluid dynamics.
Transition Region: The transition region refers to the area between the laminar and turbulent flow regimes in fluid dynamics. It is a critical zone where the flow pattern shifts from smooth, orderly laminar flow to chaotic, unpredictable turbulent flow, marking the onset of turbulence.
Turbulent Flow: Turbulent flow is a type of fluid flow characterized by chaotic and unpredictable fluctuations in the velocity and pressure of the fluid. This is in contrast to laminar flow, where the fluid moves in smooth, parallel layers. Turbulent flow is an important concept in understanding various physical phenomena, including drag forces, pressures in the body, flow rate, and the motion of objects in viscous fluids.
Viscosity: Viscosity is a measure of a fluid's resistance to deformation or flow. It quantifies the internal friction within the fluid when it is in motion.
Viscosity: Viscosity is a measure of the resistance of a fluid to flow. It describes the internal friction within a fluid that causes it to resist motion and flow. Viscosity is a crucial property that affects the behavior of fluids in various contexts, including fluid dynamics, heat transfer, and transport processes.
Viscous Forces: Viscous forces are the frictional forces that arise due to the viscosity, or resistance to flow, of a fluid. These forces act to oppose the relative motion between a solid object and the surrounding fluid, or between layers of fluid moving at different velocities.
Vorticity: Vorticity is a measure of the local spinning or rotation of a fluid element within a flow field. It quantifies the tendency of a fluid to undergo rotational motion and is a fundamental concept in the study of fluid dynamics, particularly in the analysis of turbulent flows.