Flow Around a Cylinder

The flow around a cylinder is described by the vector field

defined for .

The corresponding pressure for this flow is

(up to a constant). We can plot the pressure field as follows.

Note the areas of high pressure just before and after
the obstacle; the lowest pressure occurs on the sides where the fluid
moves the fastest.

We can now compute the force that the fluid exerts on the obstacle; . The symmetry of the situation immediately tells us that , and this is easily verified.

This somewhat surprising result is caused by the fact that the absence of viscosity is equivalent to the absence of friction; in particular there is no friction between the fluid and the obstacle, and hence no force is exerted.