183_notes:drag

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183_notes:drag [2015/09/03 20:34] – [Drag] caballero183_notes:drag [2021/02/04 23:39] (current) – [Models of fluid resistance] stumptyl
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 ==== Fluid Resistance ==== ==== Fluid Resistance ====
  
-An object moving in any fluid experiences some form of resistance to its motion due collisions with molecules of the fluid. Each of these little collisions with the surrounding fluid contribute to the overall resistive force that the fluid exerts on a moving object.+//An object moving in any fluid experiences some form of resistance to its motion due collisions with molecules of the fluid.// Each of these little collisions with the surrounding fluid contribute to the overall resistive force that the fluid exerts on a moving object.
  
-Unlike friction forces, which are velocity-independent, fluid resistance depends on the velocity of the object in the fluid. While modeling the molecular collisions with the object can be done, for most purposes, macroscopic models of the fluid drag force are sufficient to model the motion of the object. Below, you will learn about the two most common models: laminar drag and turbulent drag.+//Unlike friction forces, which are velocity-independent, fluid resistance depends on the velocity of the object in the fluid//. While modeling the molecular collisions with the object can be done, for most purposes, macroscopic models of the fluid drag force are sufficient to model the motion of the object. Below, you will learn about the two most common models: laminar drag and turbulent drag.
  
 ==== Models of fluid resistance ==== ==== Models of fluid resistance ====
  
-Which model of fluid resistance is most useful (or valid) depends on the properties of the system in question. Specifically, it depends on the {{http://en.wikipedia.org/wiki/Reynolds_number|Reynolds number}} of the situation. +Which model of fluid resistance is most useful (or valid) depends on the properties of the system in question. Specifically, it depends on the [[http://en.wikipedia.org/wiki/Reynolds_number|Reynolds number]] of the situation. 
  
 A discussion of Reynolds number is beyond the scope of this course, but suffice it to say that an small, slow-moving object in a viscous fluid will have a low Reynolds number. A large, fast moving object in a less viscous fluid will have a high Reynolds number.  A discussion of Reynolds number is beyond the scope of this course, but suffice it to say that an small, slow-moving object in a viscous fluid will have a low Reynolds number. A large, fast moving object in a less viscous fluid will have a high Reynolds number. 
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 === Laminar drag === === Laminar drag ===
  
-For a situation where the Reynolds number is low (e.g., a small, slow-moving object in a viscous fluid), the fluid resistance is proportional to the velocity of the object:+For a situation where the __Reynolds number is low__ (e.g., a small, slow-moving object in a viscous fluid), the fluid resistance is proportional to the velocity of the object:
  
 $$\vec{F}_{drag} = -b\vec{v}$$ $$\vec{F}_{drag} = -b\vec{v}$$
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 $$\vec{F}_{drag} = -6\pi\eta r \vec{v}$$ $$\vec{F}_{drag} = -6\pi\eta r \vec{v}$$
  
-where $\eta$ is the fluid viscosity.+where** $\eta$** is the **fluid viscosity**.
  
 +\\
  
 === Turbulent drag === === Turbulent drag ===
  
-For a situation where the Reynolds number is high (e.g., a large, fast-moving object in a less viscous fluid), the fluid resistance is proportional to the speed of the object squared:+For a situation where the __Reynolds number is high__ (e.g., a large, fast-moving object in a less viscous fluid), the fluid resistance is proportional to the speed of the object squared:
  
 $$\vec{F}_{drag} = -cv^2\hat{v}$$ $$\vec{F}_{drag} = -cv^2\hat{v}$$
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 $$\vec{F}_{drag} = -\dfrac{1}{2} \rho C_d A v^2 \hat{v}$$ $$\vec{F}_{drag} = -\dfrac{1}{2} \rho C_d A v^2 \hat{v}$$
  
-where $\rho$ is the density of the fluid, $A$ is the cross-sectional area of the object in the fluid, and $C_d$ is the drag coefficient of the object, which is often measured experimentally.+where $\rho$ is the// density of the fluid//, $A$ //is the cross-sectional area of the object in the fluid//, and $C_d$ //is the drag coefficient of the object, which is often measured experimentally//.
  
 +\\
 === What about "medium" Reynolds numbers flows? === === What about "medium" Reynolds numbers flows? ===
  
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