Understanding of continuous medium assumptions in macroscopic mechanics, and understanding of the average velocity in fluid mechanics, and the essential differences in mechanics between fluid and solids

Understanding of the continuum hypothesis in macroscopic mechanics:
Macroscopic mechanics (such as fluid mechanics, elasto-plastic mechanics, etc.) are the objects of a large number of molecules, at this time each set constitutes a small micro-body, the whole object is made up of the countless small micro-bodies continuously without gaps in the composition. Because we only need to pay attention to the nature of the objects on each set, such as density, velocity, stress, deformation, etc., do not need to enter the set to search for intermolecular forces, so each set can be regarded as continuous no gap, so that the macroscopic nature of the reflection and the real object is the same macroscopic nature. Only when doing numerical integration or dividing the grid, DX, dy, dz and other spatial dimensions of the self-variable differentiation should be greater than the molecular average free travel of the substance, otherwise the physical properties of the set will change irregularly with time, can not be regarded as a continuous medium, at this time, the use of molecular statistical mechanics to solve.

It can be seen from the data that the molecular average free travel of gas at room temperature and pressure is about 50nm, and the water molecule is 5nm.

Understanding of the average velocity in fluid mechanics:
The speed of each point in the actual Flow field may be different, in order to simplify the calculation, the average speed is defined by the real flow rate, and the mean momentum is expressed by means of the momentum correction coefficient, and the average energy is expressed by the mean velocity, and the energy correction coefficient is used to approximate the real energy.

The essential difference between fluid and solid in mechanics:
The essential difference is that the fluid has fluidity (continuous shear deformation) and the solids do not. Although Bingham fluid needs shear stress exceeding the critical value to start the flow, but once the flow begins, even if the shear stress is constant, the flow will continue; the other three fluids are more likely to continue as long as there is a slight shear stress. and solids do not have this feature, even if some materials (such as steel) into the yield stage will appear (overall) stress does not increase strain will also increase the phenomenon, but that is accounted for a small part of the strain, and into the strengthening phase will show increased stress, strain only increased, the stress is unchanged, the strain will not change the characteristics. So the fluid is continuously deformed under the shear stress, and the solid must increase the stress to increase the deformation.

Understanding of continuous medium assumptions in macroscopic mechanics, and understanding of the average velocity in fluid mechanics, and the essential differences in mechanics between fluid and solids