8.5 Pipe flow losses
Pipe flow losses
Pipe flow losses occur because of the effect of internal friction. Shear stresses arise as soon as velocity gradients exist.
where
μ = dynamic viscosity [Ns/m²]
v = flow velocity [m/s]
y = coordinate perpendicular to flow direction [m]
The work done by the shear force dissipates heat and adds to the internal heat energy of the liquid. The increase in internal heat energy means that the static pressure becomes a little less than it otherwise would have been. Hence the name pressure loss or pressure drop (see also section 8.6 Head loss>>>).
The flow losses are great wherever the shear stress is great, i.e. where the velocity gradients are great. High velocity gradients occur in the boundary layer, at flow around sharp corners, in strong vortex flow and so on. Viscous flow in pipes is characterized by Reynolds number.
where
v = kinematic viscosity [m²/s]
v = flow velocity [m/s]
d = diameter of pipe [m]
The following relationship exists between kinematic viscosity v and dynamic viscosity μ
v = μ / ρ (Equ. 8.5c)
where
ρ = liquid density (kg/m³)
In the case of low Reynolds numbers (Re <2300) the flow is laminar. The liquid flows in layers with different velocities which do not mix with each other. At Re >2300 the flow is turbulent, that is to say the liquid particles carry on an irregular motion superposed upon the main flow.
Figure 8.5a Laminar and turbulent flow
Since the velocity gradients differ, the shear stress and flow losses Will also differ between the two cases. The critical value of Re number has been stated as Recr ∼2300. lt should be noted, however, that the flow may continue to be laminar at considerably higher values of Re if the flow is very well protected from disturbances. Low values of Reynolds number occur at low flow velocities, at small pipe diameters or at high viscosity.
Figure 8.5b Transition to turbulent flow in pipes
It can be seen from the examples that laminar flow is less usual in practice for liquids with viscosity similar to that of water, but is quite common for oils.