32 Laminar flow in circular tubes
Consider the laminar, steady, incompressible fully-developed flow of a time-independent fluid in a circular tube of radius, R, as shown in Figure 3.1. Since there is no angular velocity, the force balance on a fluid element situated at distance r, can be written as:
- Figure 3.1 Flow through a horizontal pipe
This shows the familiar linear shear stress distribution across the pipe cross-section, the shear stress being zero at the axis of the tube, as shown in Figure 3.2. Note that equation (3.2) is applicable to both laminar and turbulent flow of any fluid since it is based on a simple force balance and no assumption has been made so far concerning the type of flow or fluid behaviour.
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