Question

5. (a) Consider the uniform potential flow around a circular cylinder with and without circulation. Calculate in detail for both cases the resultant force acting on the cylinder (by integrating the pressure distribution and also by using the complex potential and Blasius theorem), (b) Calculate the drag force on a plane half-body placed in a uniform flow.

Answer 1

Answer :-

Given data :-

5.a) The potential flow around a cylinder is a classical for the flow of an incompressible fluid arounf a cylinder that is transverse to the flow.

- The flow is undirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow.

- The goal is to find the steady velocity vector v and pressure p in a plane, subject to the condition that far from the cylinder and the velocity vector is.

The boundary of the cylinder is :

The flow remains without vorticity or said to be irrotational with.

In polar co-ordinates, laplace equation is :

b) In the field of fluid dynamiv a half body is a feature of fluid flow discovered by scottish physicist and engineer william rankin that is formed when a fluid source is added to a fluid undergoing potential flow.