Recap - Flows Of Ideal Fluids | Additional Documents & Tests for Civil Engineering (CE) PDF Download

Recap

In this course you have learnt the following

• Irrotationality leads to the condition  which demands , where φ is known as a potential function. For a potential flow  .
• The stream function also obeys the Laplace’s equation    for the potential flows. Laplace’s equation is linear, hence any number of particular solutions of Laplace’ s equation added together will yield another solution. So a complicated flow for an in viscid, incompressible, irrotational condition can be synthesized by adding together a number of elementary flows which are also inviscid, incompressible and irrotational. This is called the method of superposition.
• Some inviscid flow configurations of practical importance are solved by using the method of superposition. The circulation in a flow field is defined as . Subsequently , the velocity may be defined as circulation per unit area . The circulation for a closed path in an irrotational flow field is zero. However , the circulation for a given closed path is an irrotational flow containinga finite number of singular points is a non -zero constant.
• The lift around an immersed body is generated when the flow field processes circulation. The lift around a body of any shape is given by , where ρ is the density and U₀ is the velocity in the streamwise direction.