# I Bulk angular momentum

#### dRic2

Gold Member
According to the book "transport phenomena" by Lightfoot, Byron and Stewart if you take the cross product of the equation of motion (for very small element of fluid) and the position vector $r$ you get the equation of change of angular momentum. After some manipulation of vectors and tensors the equation can be written in such a way that a this term shows up:
$$-[ \mathbf \epsilon \mathbf : \mathbf \tau ]$$

Where $\mathbf \epsilon$ is a third-order tensor and $\mathbf \tau$ is the stress-tensor.

Then the authors say:

If, on the other hand, $\mathbf \tau$ is asymmetric, then the last term describes the rate of conversion of bulk angular momentum to internal angular momentum.
What "bulk angular momentum" is? I don't understand, why there are two angular momentum?

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#### ShayanJ

Gold Member
I think bulk angular momentum is the angular momentum the object has as a whole, i.e. $\vec L_b=\vec r_b \times \vec p_b$ where $\vec r_b$ and $\vec p_b$ are the position and momentum vectors of the object itself. Then the internal angular momentum has to be a vector field that tells you what is the angular momentum of a bit of the object at a particular point inside it.

#### dRic2

Gold Member
Thank you. I have some questions left then:

1) how exactly should I "imagine" (or calculate) the total angular momentum of stream of fluid?

2) Why is there a conversion from this two type of angular momentum ?

#### ShayanJ

Gold Member
1) how exactly should I "imagine" (or calculate) the total angular momentum of stream of fluid?
I'm not quite sure. But I suppose if you're talking about ,e.g., a bucket of water, then the motion of that bucket will indicate the motion of the water inside it as a whole. Any motion that changes the shape of the water inside the bucket should be considered as internal motion because it changes the position of those bits of water relative to each other.
2) Why is there a conversion from this two type of angular momentum ?
Well, just take a glass of water and move it, that motion will cause disturbance in the surface of the water. You just converted some bulk momentum to some internal momentum.

#### dRic2

Gold Member
Thanks again. It think it is not very intuitive though (your explanation was clear, I just find it a bit strange)

"Bulk angular momentum"

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