# TEP4135: Fluid Mechanics 2

# Incompressible, inviscid flow

## Basic flow elements

### Uniform flow

### Source

### Sink

## Superposition of elements

Superposition combines basic flow elements to create more advanced flow fields. The combination is linear, and the final expressions of the field will be the sum of functions representing the different basic elements

### Rankine half-body

A Rankine half-body is a source added to a uniform flow.

The stagnation point

Pressure distribution is given by

#### Oval rankine half-body

A Rankine oval is a sink and a source in a uniform flow, spaced apart from eachother. The stagnation streamline will then create a boundry between the external streamlines of the uniform flow, and the internal streamlines that starts in the source and ends in the sink.

### Doublet

A doublet is a source added on top of a sink, both equal in strength. Streamlines will then circulate from the center of the sink/source outwards, make a loop, and then end in the center.

The strength of a doublet can be calculated by

Note that this flow elements has directionality, which means it is sensitive to the values provided.

### Line Vortex

A line vortex causes streamlines to move in a circular fashion around a certain point in the field. The flow of a line vortex has no radial movement.

### Flow around cylinder

A flow around a cylinder is built up of doublet placed in a uniform flow.

The pressure distrubution is given by

This gives a symmetric pressure distrubution, resulting in no net forces (which is unphysical).

In reality, drag and lift of a cylinder is given by

The drag is caused by skin friction (viscous effects) and pressure drag. A real cylinder in a flow will have a messy wake.

### Flow around cylinder with circulation

A flow around a cyliner with circulation is modeled by adding a line vortex on top of the flow around of a cylinder.

## Method of images

Method of images is used to represent a solid boundry in a flow field by adding flow elements whose streamlines acts as a solid boundry.