MODEL is a mental construction, a set of ideas that help for making mental images of phenomenons, making them easier to be understood.
Free flow happens when the motion of a fluid is not disturbed. Only the internal forces inside the fluid body have a role in the motion distribution of the fluid inside the studied volume.
For the understanding of many concepts, related to fluid dynamics, a moving fluid can be mentally modeled as a joint of layers that can slide one over the others. Imagine something similar to a pile of paper sheets.
Lets suppose a fluid in motion through a channel. The channel dimensions are so big, that the influence of the walls on the central fluid body can be neglected.
Lets forget, by now, why the fluid is moving.
When a layer moves, it drags the layer above and below, and both of them do the same with their sorrounding layers, resulting in a fluid where all layers are moving togheder with the same speed and direction.
If a line is drawn, representing all points of each layer, that are moving with the same speed, a set of parallel lines would be obtained. Those are the stream lines.
Stream lines cannot cross other stream lines. It would mean that those imaginary layers (the paper sheets) are crossing each other.
Lets now suppose that a sand grain is set on one of the layers. If the motion of that grain is followed along time, and a line is drawn, joining all points through which the grain has crossed, we'd get a path line.
Many times, a path line, and a stream line, can be represented by the same draw, but not allways. Will see it later.
How is the motion of a layer transmited to the others ? Just in the same way that it happens in a papers pile, by means of "INTERNAL" dragg.
The difference is that while inside a paper pile, each sheet is a seprated entity, in a fluid, the layers are only a mental model. The whole fluid body is an unique entity.
But its true, and can be observed, that even being a simple whole entity, a fluid whorks as if builded by those layers. There is an internal force that prevent any fluid part from moving with respect to the others.
This internal force is Known as Viscosity. The higher the viscosity, the more diffcult will be to distort the fluid. Viscosity works as a kind of flexible glue.
Imagine an alcohol drop falling along a tilted glass. It can be seen that the drop seems to be attracted by the glass. Having a close view to the drop, it can be realized that the drop shape is distorted by that attraction. In fact, if the tilting angle of the glass is reduced, there will be a given angle, before arriving to the horizontal, when the drop will stop moving. Gravity and that pseudo attraction are balanced.
If the same thing is done with oil, the drop will move slower, and the balance angle will be bigger. It looks that its harder to pour the oil than the alcohol.
This internal force that tries to stuck all parts of the fluid, and the fluid to everything around it, is called VISCOSITY.
The higher the viscosity, the closer will all layers move, becouse the force betwen them is higher.
Why have I chose alcohol and not water ? When a water dop is poured on a glass, other forces are taking part in the motion. Water, in that context, is a very special material.
Lets now approach the bottom of our huge channel, and lets have a look to the fluid layers very, very close to it.
The first layer, that which is in contact with the channel, will be stopped, or almost completly at rest. For all practical applications it is at rest.
The "second" layer is in contacyt with fluid, and not with the walls. A force, that we have not checked by now, is moving the fluid. And another force, viscosity, stucks this layer to the one below. Hence, this second layer will slide over the first, with a speed that will depend on the viscosity and the driving force(The one that is making the fluid flow).
Next layer will be sliding on an already moving layer, and hence, will move faster, and so on, until arriving to a layer where the speed is not affected by the walls. This is the free flow zone.
The higer the viscosity, the bigger the contact area beween fluid and walls, and the bigger any other force, stucking the fluid on the wall, the higher the dragg, and the thicker the affected area.
Lets now have a look to the driving force. In fluids, this driving forces do have no direct effect by themselves. Forces lead to pressure diferences, and fluid moves from higher to lower pressure.
Two areas with quite big pressure differences, will lead to fast motions. If the same areas with the same pressures, are moved appart, to a longer distance, the motion will be slower.
What really minds in a fluid motion is neither pressures nor distances, but the pressure diference that exists along a given distance.
This relation is called the "PRESSURE GRADIENT".
Lets follow the fluid along a given distance, from a high pressure area to a low one.
Along that path, driving pressure will be decreasing, from the higher to the lower pressure values. It can be said that the driving pressure at any point along the path, has a value that is located between the higher and lower values.
This pressure, that corresponds to intermediate points of the fluid along a path, is named "PRESSURE POTENTIAL".
Imagine the fluid in 2D. As a vertical cut through the middle of the channel.
Lets take a very tiny squared portion of the fluid, and lets suppose it as a free body. Whats is the same, isolated from the rest of fluid.
Lets now try to imagine forces, in such a way, that the portion is balanced, and moving as it did when in the fluid.
We have four faces, and hence four forces are required.
For the vertical balance, buoyancy and weight are balanced. One point upwards and the other downward. There is no vertical motion.
For the horizontal motion: Even in that tiny portion, there is a distance beween the right and the left faces, and hence there the pressure potential at each one is different. One pressure points to the left, and the other to the right.
If pressure is different, the square will move from the higher pressure to the lower one.
Lets say it moves to the right.
But there is another force left, that has not been taken into account above.
The upper face, would be in contact with another fluid layer, that would eventually move faster than the square, that belongs to an intermediate layer. The lower face of the square, would be in contact with the layer below it, and hence, there must be two friction forces working, one at the upper and another at the lower face.
Both forces work horizontally, against the speed, but, are not equal. As it was said above, the lower one (in our example) is bigger than the upper. The result is that the square will be distorted. A shear will develop between both faces. This shear stress is another measurement of viscosity.
It must be realized, that all forces are exerted by the fluid body on itself. A portion of fluid influences other portions. That's why, those forces are named. INTERNAL FORCES.
If the explanation of our square, is extended to 3D, turning the square into a cube, and at the same time, the cubic sample is extended to the whole fluid volume under study, we'd arrive to the most commonly used fluid model.
Now, the thing will go around approaching how to guess te behaviour of each of those cubes, when the flow is distorted by any mean.