- #1

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I know that viscosity represents the thickness of a fluid, or its ease of flow, but I don't understand why that is represented by these parameters.

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- Thread starter pa5tabear
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- #1

- 175

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I know that viscosity represents the thickness of a fluid, or its ease of flow, but I don't understand why that is represented by these parameters.

- #2

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[tex]\tau = \mu \nabla \vec{v}[/tex]

where the units are, therefore

[tex][\text{Pa}] = [\text{Pa}\cdot\text{s}]\dfrac{[\text{m}/\text{s}]}{[\text{m}]}[/tex]

- #3

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I don't think such can be found. The two distance measurements that dimensionally cancel are both in the velocity gradient, so a more fundamental question is why a velocity gradient should have dimension of 1/time, or frequency. The two distances are perpendicular to each other, which suggests to me the cancellation has no deep meaning.

Similar coincidences arise, e.g. angular momentum and action; note that one is a vector while the other is a scalar. OTOH, angular momentum is quantised, so maybe there is a deep meaning in that case.

- #4

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I also asked a professor today and he said I should think about it as the relationship between shear stress and shear rate and get the units from that instead of trying to derive a relationship from the units.

- #5

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Then again, I'm saying this because I already know the units.

- #6

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Pascal-seconds is a unit of viscosity. Why?

Be careful- there are two 'flavors' of viscosity, 'kinematic' (typically units of Poise) and 'dynamic' (typically units of Stokes). Viscosity refers to the diffusion of momentum.

Poise has units of M/LT (say, kg/m*s) and is thus equivalent to both pressure*time and momentum/area. Stokes has units of L^2/T, say m^2/s.

- #7

Chestermiller

Mentor

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τ = η (dv/dy)

Shear stress has units of m/(l s

Stress has the same units as pressure.

Shear rate has units of (1/s)

For Newtonian fluids, Newton's law of viscosity in 3D is much more complicated than this (and involves the stress tensor and the rate of deformation tensor), but the general idea and the units are the same.

- #8

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You flipped kinematic and dynamic there, Andy. I figured if just clear that up.

- #9

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You flipped kinematic and dynamic there, Andy. I figured if just clear that up.

Thanks- dyslexic am I.

- #10

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Thanks- dyslexic am I.

Apparently you are as dyslexic as I am a bad typist.

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