How Rankine oval is formed?

How Rankine oval is formed?

A Rankine oval is formed by combining a source-sink pair, each having a strength of 33 ft2/s and separated by a distance of 13 ft along the x axis, with a uniform velocity of 10 ft/s (in the positive x direction).

What is Rankine oval and Rankine Halfbody?

In the field of fluid dynamics, a Rankine half body is a feature of fluid flow discovered by Scottish physicist and engineer William Rankine that is formed when a fluid source is added to a fluid undergoing potential flow. Superposition of uniform flow and source flow yields the rankine half body flow.

What is flow past a Rankine oval body?

Figure 4.26: Flow past a Rankine Oval When the streamlines for this flow are plotted (Fig.4.26) one discovers that the one given by (shown in red) forms a closed curve. This obviously forms the “body”, i.e., the stream function we have written describes the flow about this body.

What is half body in fluid mechanics?

Superimposing a uniform flow and a source will allow us to determine the streamlines of a fluid moving around a half body. In turn, the streamlines can be seen on the second picture of the image above. It is called a half body because the body is open at the down stream end.

What is doublet flow?

A doublet is a result of construction of a flow field using the superposition of a source and a sink that are placed very close to each other. The superposition of these two will result in flow leaving the source and entering the sink.

How could flow past a circular cylinder be simulated as a combination?

Flow about a rotating cylinder is equivalent to the combination of flow past a cylinder and a vortex. As such in addition to superimposed uniform flow and a doublet, a vortex is thrown at the doublet centre which will simulate a rotating cylinder in uniform stream.

What is a complex potential function?

The complex potential F(z)=Ue−iαz. corresponds to uniform flow at speed U in a direction making an angle with the x-axis. Here we are interested in finding the velocity field V=(u(x,y),v(x,y)). But first we need to obtain the stream funcion ψ, which is the imaginary component of (1).

What is uniform stream?

: flow of a fluid in which each particle moves along its line of flow with constant speed and in which the cross section of each stream tube remains unchanged — compare steady flow.

Is Rankine Oval an ellipse?

Yes, you are correct, this oval is not an ellipse for any finite choice of the parameters. However, in the above limit of x0→0, mx0=K the oval becomes a circle.

What is sink flow?

Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source.

What is source and sink flow?

Source and Sink Flow Sink Flow Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source.

What is source and sink in fluid mechanics?

Sink flow is literally opposite to the source flow. In sink flow, fluid moves radially inward (or absorbs fluid) towards a point known as sink, and fluid disappear at sink at a constant rate. The equation of radial velocity in sink flow is similar but with a sign change to q.