Let flat layers of a liquid, located at a distance ∆x, moving with velocity v₁ and v₂ (rice. 10.15). Then the bottom layer will speed up the movement of the middle layer, and the upper layer — slow it down. As a result, under the action of forces of internal friction middle layer will move with velocity v, more v₁, but smaller v₂.

With a uniform change in the rate of movement of the layers in the x direction, the value of grad v is all points of the environment equally and is numerically equal to (v₂—v₁)/∆x, or ∆v/∆x.

Newton showed, that the force of internal friction, acting on the middle layer, directly proportional to the velocity gradient I of the surface area of the layer ∆S. Mathematically, Newton's law for inner friction is expressed by the formula:

The value of η, expressing the dependence of the internal friction forces from such substances and the external environment, is called dynamic viscosity of the medium. Derive the unit of dynamic viscosity η:

The SI unit for η is accepted by the viscosity of a medium, in which the square of the layer in 1 m² the force of internal friction in 1H when the velocity gradient, equal 1 with^-1. The viscosity of the medium depends on its temperature. It is interesting to note, that it gas when heated increases, and liquids is reduced. This indicates, the nature of internal friction in gases and liquids are different.

The viscosity of gases is due to the flight of the molecules from layer to layer as a result of their random motion, they are doing in addition to the directional movement of your layer. Furthermore, the molecules, flying from lower layer to middle (rice. 10.15), accelerate his movement, and molecules, flying from the upper layer in the middle, slow down his movement. As the temperature increases, the speed of random motion of the molecules increases, the viscosity of gases increases when heated.

In liquids, the transition of the molecules from layer to layer also has a place, but the main reason for the liquid viscosity are the forces of mutual attraction of its molecules. Since when heated the liquid expands, the forces of mutual attraction of their molecules with reduced, which explains the decrease in viscosity of liquids with increasing temperature. For example, the viscosity of water at 0°C is 17,75-10^-4 PA*s, at 90°C is 3,20*10^-4 PA*s.

In 1840 g. French scientist L. Poisal showed, what volume of liquid, flowing through a pipe in laminar flow, proportional to the fourth power of the radius of the pipe. Currently the formula Poiseuille flow record in the following form:

V=(πr8/9lη)(p₁-p₂)t

Here V is the volume of liquid, flowing through a pipe with radius r and length l at time t when the differential pressure at the beginning and at the end of the pipe ∆p=p₁—R₂. Formula (10.8) you can compare the viscosity of various liquids, flowing through the same pipe, with the help of the device, called the viscometer.