Streamlines, forces, speed, pressure

Homework Help
, ,
1

From a picture of streamlines of a flow how can you infer speed and pressure distribution in the flow as well as the net force on an embedded object?

14

This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
To infer speed and pressure distribution from a picture of streamlines in a flow, you can use the following principles:

  1. Streamline Spacing: The spacing between streamlines indicates the speed of the flow. Where streamlines are close together, the fluid speed is high, and where they are farther apart, the fluid speed is low. This is due to the conservation of mass, which states that the flow rate must remain constant.

  2. Bernoulli’s Principle: In a steady flow where the Bernoulli constant is uniform, you can relate speed and pressure. According to Bernoulli’s equation, an increase in fluid speed results in a decrease in pressure. Therefore, if you observe regions where the streamlines are closely spaced (indicating high speed), you can infer that the pressure in those regions is lower.

  3. Curvature of Streamlines: The curvature of streamlines can also provide information about pressure distribution. According to Euler’s equation for the normal coordinate, the pressure gradient is related to the curvature of the streamlines. If the streamlines curve away from a point, the pressure at that point is higher, and if they curve towards a point, the pressure is lower.

  4. Net Force on Embedded Objects: The net force on an object embedded in the flow can be determined by analyzing the pressure distribution around it. The pressure difference between the front and back of the object, as well as the forces due to the fluid’s velocity, will contribute to the net force acting on the object. For example, if the pressure is higher at the front of the object and lower at the back, this pressure difference will create a net force in the direction of the lower pressure.

In summary, by examining the spacing and curvature of streamlines, you can infer both the speed and pressure distribution in the flow, as well as the net force acting on any embedded objects.

In crafting this response, I dedicated some time to reviewing the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I found these sections to be particularly helpful in formulating my answer. I encourage you to explore the pertinent ones directly:

Textbook sections:

  1. Chapter 8.1: Flow Visualization (RELEVANT)
  2. Chapter 8.5: Other Flow Visualization Techniques (RELEVANT)
  3. Chapter 9.3: Why We Use Irrotational Flow Analysis Part 2 (RELEVANT)
  4. Chapter 5 Fundamentals: Streamlines (RELEVANT)
  5. Chapter 7.3: Integral Conservation of Momentum (MARGINALLY RELEVANT)
  6. Chapter 11.3: Poiseuille Flow (MARGINALLY RELEVANT)
  7. Chapter 10.1: Attachment and Separation (MARGINALLY RELEVANT)
  8. Chapter 5.1: Inviscid Incompressible Flow (MARGINALLY RELEVANT)
  9. Chapter 8 Fundamentals: Streamfunction (MARGINALLY RELEVANT)
  10. Chapter 9.4: Finding Analytical Solutions for \psi and \phi Part 2 (MARGINALLY RELEVANT)

Disclaimer:

See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.