Pressure field of an irrotational vortex

In summary, the conversation discusses the difficulty in finding definitive verification for the pressure field of an irrotational vortex, with the equation v_theta = 1/r and v_r = 0. The participants mention the use of Bernoulli's equation and the existence of a pressure difference between adjacent streamlines. They also suggest using a force balance to determine the change in pressure.
  • #1
mikeph
1,235
18
time for some revision... I can't find any definitive verification for this

I'm trying to find the pressure field of an irrotational vortex, v_theta = 1/r, v_r = 0; I guess the pressure falls but I'm not sure how since the Bernoulli equation constant only holds over streamlines, and over streamlines of the vortex, velocity is constant!

Thanks for any help
 
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  • #2
There will be a pressure difference between adjacent streamlines. On any finite sized object there will be a suction force drawing the object toward the axis of rotation.
 
  • #3
If the flow is inviscid then the total pressure is the same everywhere so you can use Bernoulli to find the change in pressure across streamlines.

You could also determine this change in pressure by doing a force balance in the direction perpendicular to the motion. Balance the centrifugal force on the fluid element with the pressure force.
 

1. What is an irrotational vortex?

An irrotational vortex is a type of fluid flow in which the fluid particles move in a circular pattern around a center point, without any rotational motion. This type of flow is often found in natural phenomena such as tornadoes and hurricanes.

2. How is the pressure field of an irrotational vortex calculated?

The pressure field of an irrotational vortex can be calculated using Bernoulli's equation, which relates the pressure, velocity, and elevation of a fluid at a specific point. This equation takes into account the density of the fluid, the velocity of the flow, and the acceleration due to gravity.

3. What factors affect the pressure field of an irrotational vortex?

The pressure field of an irrotational vortex is affected by the strength and size of the vortex, as well as the properties of the fluid, such as its density and viscosity. Additionally, any external forces acting on the fluid, such as gravity or air resistance, can also impact the pressure field.

4. What is the significance of the pressure field in an irrotational vortex?

The pressure field in an irrotational vortex is an important factor in determining the behavior and characteristics of the vortex. It can influence the direction and speed of the fluid particles, as well as the overall shape and intensity of the vortex. Understanding the pressure field can also provide insight into the forces at work in natural phenomena such as tornadoes and hurricanes.

5. How is the pressure field of an irrotational vortex visualized?

The pressure field of an irrotational vortex can be visualized using various techniques, such as streamlines and contour plots. These methods show the direction and magnitude of the pressure at different points in the flow. Additionally, experiments and simulations can also be used to observe and analyze the pressure field of an irrotational vortex.

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