In this chapter we shall discuss the flow properties of liquids, and derive or state some of the more standard equations of flow. However, our main attention will be directed to a molecular model of viscous flow; this follows closely the theory proposed by Eyring.

Flow in ideal liquids: Bernoulli's equation

As with gases we can assume the existence of ideal liquids in which internal forces play a trivial part, so that they have negligible surface tension or viscosity. Their flow properties are determined solely by their density. Of course, no liquids can have zero internal forces, they would not be liquid if this were so, but they can often behave as ideal liquids in flow if the inertial forces dominate.

Consider the flow of such an idealized liquid and let us follow the path of any particle in it. If it moves in a continuous steady state we may draw a line such that the tangent at any point gives the direction of flow of the particle. Such lines are called streamlines. They are smooth continuous lines throughout the liquid and can never intersect – no fluid particles can flow across from one streamline to another. Let AB represent an imaginary tube in the liquid bounded by streamlines (figure 11.1 (a)). At A the liquid is at height h1 above a reference level, the pressure acting at that point is p1, the cross-sectional area of the tube is α1, and the liquid flow velocity is v1; at B the corresponding quantities are h2, p2, α2, v2. Consider the energy balance during a short time interval dt.