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Chapter 4: Problem 16

For any steady flow the streamlines and streaklines are the same. For most unsteady flows this is not true. However, there are unsteady flows for which the streamlines and streaklines are the same. Describe a flow field for which this is true.

Short Answer

Expert verified
An unsteady flow where changes are slow compared to the particle flow rate would have the same streamlines and streaklines. An example could be when the rate of fluid flowing out of a tank through a pipe gradually increases from a zero flow rate.

Step by step solution

01

Understanding Steady and Unsteady Flows

Steady flow implies that the flow conditions (velocity, pressure, cross-section, and density) do not change with time. Conversely, unsteady flow means that the fluid control properties modify over time.
02

Identifying Common Characteristic

Streamlines and streaklines invariably coincide in steady flows. In an unsteady flow, these would coincide if the changes in flow are not too abrupt that by the time the particles catch up, the flow pattern has significantly transformed.
03

Describing the Flow Field

A good example is an unsteady flow where sequential change is slow compared to the particle flow rate. For instance, consider the case where the rate of fluid flowing out of a tank through a pipe is gradually (rather than suddenly) increased from a zero flow rate. The flow here is unsteady since the flow rate is changing. However, because the changes occur gradually, the particle released at the beginning from a point in the tank follows a path that the later particles would also follow. Therefore, in this instance, the streamlines and streaklines are the same.

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Most popular questions from this chapter

A certain flow field has the velocity vector $\mathbf{V}=\frac{-2 x y z}{\left(x^{2}+y^{2}\right)^{2}} \mathbf{i}+\frac{\left(x^{2}-y^{2}\right) z}{\left(x^{2}+y^{2}\right)^{2}} \mathbf{j}+\frac{y}{x^{2}+y^{2}} \mathbf{k} .$ Find the acceleration vector for this flow.

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