All Questions
Tagged with continuum-mechanicspressure
21 questions
6votes
4answers
1kviews
What is the meaning behind stress distribution in a material, physically?
Why do we even have pressure/stress distributions, why not simply force distributions? Yes, pressure and stress (depending on if we are talking about a fluid, or a solid material's internal forces) is ...
- 79
0votes
0answers
77views
Source of general form of Young-Laplace equation $T^{\alpha\beta}\kappa_{\alpha\beta}=p_\perp$
While studying pressurized lattice spring models of triangulated surfaces, I encountered the following expression: $$T^{\alpha\beta}\kappa_{\alpha\beta}=p_\perp,$$ where $T^{\alpha\beta}$ is the ...
- 353
0votes
1answer
30views
Hydrostatic mean pressure invariance
Does the hydrostatic mean pressure (Cauchy stress trace) remain constant when transforming it to a 2nd Piola-Kirchoff Tensor by using deformation gradient? Thank you Abdoulaye
1vote
2answers
84views
Work performed by hydrostatic pressure
One should be able to show mathematically that the hydrostatic work done by an environment on an object undergoing a volume change $\Delta v$ should be $p \Delta v$, where $p$ is the (constant) ...
- 947
4votes
2answers
461views
What is a general definition of bulk modulus?
For a perfectly elastic body, Bulk modulus always remains constant and is defined as, $$B=-V_i \frac{\Delta P}{\Delta V} \tag{1}$$ Which means, $$B \left(\frac{V_f -V_i}{V_i}\right)= -(P_f-P_i)$$ But, ...
- 261
0votes
2answers
134views
Why doesn't viscosity depend on pressure in the Navier-Stokes equations? [duplicate]
In the incompressible Navier-Stokes equations, we make an assumption on the stress in the fluid: $$ \begin{align*} \frac{Du}{Dt} &= \nabla \cdot \sigma\\ \sigma &= -pI + 2\mu e\\ e &= \...
0votes
1answer
152views
Radial stress of a cylinder that is longitudinally excited
Consider a cylinder that is longitudinally excited on one of its ends and fixed on the other one as shown in the picture below. In the cylindrical coordinate system, the displacement vector $\bf u$ ...
3votes
0answers
93views
Differential geometry and the $P \vec A= \vec F$ equation?
How does one write $$\vec F = P \vec A$$ (where $\vec F$ is the force. $P$ is the pressure and $\vec A$ is the area) in the language of differential forms? I'm confused cause $\vec F$ is a one form ...
- 1,401
6votes
2answers
2kviews
Confusion in Derivation of Excess Pressure in a Cylindrical Drop
I have recently learnt about surface tension and have developed a list of key points to solve problems:- Surface tension acts on the surface where a surface is defined as the interface(flat or curved)...
user329235
1vote
1answer
1kviews
What's the difference between normal viscous stress and pressure?
The stress tensor on a fluid element is the following: The diagonal terms in the two tensors $-p\textbf{I}$ and $2\mu\textbf{e}$ are both stresses that act perpendicular to the faces of the fluid ...
4votes
3answers
2kviews
Why is a force distributed over an area? Why couldn't the stress be directly equal to the force?
So, my question might seem silly. I know in real life when we apply a force with our hand and push on lets say a cylinder , we know the force will be distributed over the cross section of the area, so ...
0votes
1answer
16views
Lower boundary of validity of common gas property models with respect to pressure
In engineering, there are widely used relations for gas properties, e.g., the ideal gas law. Like most (every?) model, there are limits to the validity of those models. For gases, most engineering ...
- 598
0votes
0answers
78views
Pressure in a fluid at rest
I hope this is the right place to post such a question. I'm studying Continuum Mechanics from Gurtin's book, and so far in my class we've seen Cauchy's the about the existence of stress, and nothing ...
- 151
0votes
0answers
29views
Can we say normal stress and pressure are the same? [duplicate]
Now if your Ans is yes then I have one more question to ask. .ie don't u agree that we should not say stress as a tensor of 2nd order rather only tangential stress as tensor of 2nd order and normal ...
0votes
3answers
137views
Why does a fluid flows?
I was reading about viscosity and momentum diffusion in Physical Chemistry and I came up with the title. Suppose we have some amount of liquid inside a container with a piston (initially fixed) in the ...
- 1,718
