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charlies1902
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Are fluid streamlines in an irrotational, but viscous, flow parallel? Or does the flow need to be both irrotational and inviscid?
Oh I see. But if we are strictly talking about streamlines of individual fluid elements, in which case would the streamlines be parallel?boneh3ad said:Streamlines are always parallel to the local velocity. They don't have to be parallel to each other (though they can never cross). For example, if the flow accelerates in a region, streamlines will get closer together, which couldn't happen if they had to be parallel.
charlies1902 said:Oh I see. But if we are strictly talking about streamlines of individual fluid elements, in which case would the streamlines be parallel?
No, streamlines are not always parallel in inviscid and irrotational flow. In inviscid flow, the fluid has no viscosity, meaning there is no internal friction. In irrotational flow, the fluid has no vorticity, meaning there is no swirling motion. While these conditions may make the flow appear to be parallel, there can still be variations in velocity and direction, causing the streamlines to not be perfectly parallel.
The significance of parallel streamlines in inviscid and irrotational flow is that it indicates a state of potential flow. In potential flow, the fluid particles move in a smooth and predictable manner, without any energy loss due to friction or turbulence. This type of flow is often used in theoretical models and calculations in fluid dynamics.
No, streamlines cannot intersect in inviscid and irrotational flow. This is because in irrotational flow, the velocity at any point is determined by the potential function, which is a scalar quantity. Scalar quantities do not have a direction, so the velocity at a specific point can only have one magnitude and direction, meaning the streamlines cannot cross.
In real-world, viscous flow, streamlines often do not remain parallel. This is because there is internal friction and viscosity present in the fluid, causing variations in velocity and direction. These variations can lead to streamlines crossing, converging, or diverging, depending on the specific flow conditions.
Studying parallel streamlines in inviscid and irrotational flow has practical applications in various fields, including aerodynamics, hydrodynamics, and fluid mechanics. Understanding the behavior of potential flow can help engineers design more efficient and streamlined structures, such as airplanes and ships. It can also aid in predicting the behavior of fluids in different scenarios, such as predicting the flow of water in a river or the airflow around a building.