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Columbia University Press
viscosity
resistance of a fluid to flow. This resistance acts against the motion of any solid object through the fluid and also against motion of the fluid itself past stationary obstacles. Viscosity also acts internally on the fluid between slower and faster moving adjacent layers.

All fluids, i.e., all liquids and gases, exhibit viscosity to some degree. Viscosity may be thought of as fluid friction, just as the friction between two solids resists the motion of one over the other but also makes possible the acceleration of one relative to the other (e.g., the friction between the wheels of an automobile and a highway), so viscosity resists the motion of a solid through a fluid but also makes it possible for a propeller or other device to accelerate the solid through the fluid.

The Velocity Gradient

When a fluid is moving through a pipe or a solid object is moving through a fluid, the layer of fluid in contact with the sides of the pipe or the surface of the object tends to be in the same state of motion as the object with which it is in contact; that is, the layer of fluid along the side of the pipe is at rest, while that in contact with the moving object is carried along at the same velocity as the object. If the difference in velocity between the fluid at the sides of the pipe and that at the center, or between the moving object and the fluid through which it is moving, is not too great, then the fluid flows in continuous, smooth layers; that is, the flow is laminar.

The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers. To keep one layer of fluid moving at a greater velocity than the adjacent layer, a force F is necessary, resulting in a shearing stress F/A, where A is the area of the surface in contact with the layer being moved.

The Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient is a measure of the viscosity of the fluid and is called the coefficient of viscosity η, or η=Fx/Av. The cgs unit for measuring the coefficient of viscosity is the poise. Experiments have shown that the coefficient of viscosity of liquids decreases with increasing temperature, while the coefficient of viscosity of gases increases with increasing temperature. In liquids an increase in temperature is associated with the weakening of bonds between molecules; since these bonds contribute to viscosity, the coefficient is decreased. On the other hand, intermolecular forces in gases are not as important a factor in viscosity as collisions between the molecules, and an increase in temperature increases the number of collisions, thus increasing the coefficient of viscosity. A striking result of the kinetic theory of gases is that the viscosity of a gas is independent of the density of a gas. Viscosity is the principal factor resisting motion in laminar flow. However, when the velocity has increased to the point at which the flow becomes turbulent, pressure differences resulting from eddy currents rather than viscosity provide the major resistance to motion.