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Thus, the flow is rotational. At this time we define irrotational flows as those where w = 0 at each point in the flow. Rotational flows are those where w = 0 at points in the flow.

The normal strain rates give the rate of stretching or shrinking of the two lines shown in figure 2.14, while the shear strain rates give rate of change of angularity of the two lines. What's left of the relative motion must be rigid body motion. Thus the expression | (— dy) is actually more than just average rotation of the line segments about the z axis. It represent the rigid body angular velocity uz of the line segments about the z axis.

A development of rotation in a fluid particle in an initially irrotational flow would require shear stress to be present on the particle surface. Thus the shear stress(Newton'sss viscosity law) in such flows and in more general flows will depend on the viscosity of the fluid and the rate of variation of the velocity in region. For fluids with small viscosity such as water and air, assumption of irrotational flow is valid for great part of the flow except region with large velocity gradient. Thus the boundary layer regions are the places that element of fluid rotates. Irrotational analysis may be carried out if the boundary layer thickness is small in comparison with the scale of the fluid.

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