# Tag Info

1 vote

### Incompressible flow condition intuition

As you have said it is derived from the continuity equation (which is one of Euler fluid equations) $$\frac{\partial \rho}{\partial t}+\nabla\cdot(\rho \mathbf u)=0$$ if the density of the fluid $\rho$...
• 5,568
Accepted

### Incompressible flow condition intuition

An intuitive explanation comes from the meaning of the word divergence itself. If the divergence of the velocity is zero, it means that there is no (net) inflow or outflow of fluid from a given volume....

### Incompressible flow condition intuition

You ask"How is there a relation between the density of the fluid and its speed"? There is none $\nabla u=0$ says only that the velocity does not change for example in x direction .
• 6,362

### Stress/forces on elements in continuum mechanics

In continuum mechanics, the stress tensor is a point function, and all 9 components exist at each point. When you do a force balance in a fluid parcel, the stress vector is evaluated locally at each ...
• 34.1k
Accepted

### Why is the strain tensor of a rod under uniform torsion the same everywhere along the rod?

Axial $z$-coordinate is homogeneous (and thus the solution doesn't depend on $z$) for: slender beams, if one excludes the region close to the extreme sections of the beam; with no distributed loads ...
• 10.7k
1 vote
Accepted

### Work performed by hydrostatic pressure

With a little less math, the power of a stress distribution $\mathbf{t}_n$ over the boundary of a volume $V$ is $$P(t) = \oint_{\partial V} \mathbf{t}_n \cdot \mathbf{u} \ ,$$ being $\mathbf{u}$ the ...
• 10.7k
1 vote

### Confused about stresses in a small element in solid mechanics

So in the diagram of a stress tensor, the normal and shear stresses on opposite faces of the small cube are equal and opposite. Justified by equilibrium. This is not true. In static conditions, local ...
• 10.7k