Flow in pipelines

The degree of energy loss in a hydraulic system also depends on the type of flow. Flow is divided into laminar and turbulent flow:

In the case of laminar flow, intended stream tube filaments run parallel to the limiting surface. Here the isothermic flow results in a parabolic velocity curve where v_max = 2*v_m (v_m is the mean flow speed). The flow remains below the critical flow speed here. This type of flow is desired in hydraulic systems.

In the case of turbulent flow, the stream tube filaments mix. The velocity profile is flatter and therefore for isothermic flows it becomes v_max = 1.2*v_m.

As of a certain flow speed, which depends on the pipe diameter and the viscosity, the fluid becomes heavily swirled (turbulent) and this results in a high energy loss. This flow should generally be avoided in hydraulic systems.

The transition from laminar to turbulent flow is called the critical flow speed. It is roughly determined by the "Reynolds number" R_e (= critical flow speed). The flow which forms depends on the Reynolds number . As the formation of a laminar flow requires a build-up distance of the fluid flow pattern l_a = 0.03 d_i · R_e (for example 20 mm internal pipe diameter approx. 1.3 m) compared with just 10—20 d_i for turbulent flows, most pipelines have a turbulent flow. (d_i is the inner diameter of the pipeline)

Laminar (a) and turbulent (b) flow

The flow velocity vf through a pipe is calculated from the flow rates Q and the cross sectional area of the line, which results from the diameter df.