Solve Complex Potential: Streamfunction from Velocity Potential

  • Thread starter Thread starter Lucus
  • Start date Start date
  • Tags Tags
    Complex Potential
AI Thread Summary
To find the streamfunction from the complex potential F(z)=U(z^2 + 4a^2)^(1/2), separate the real and imaginary parts by expressing it as U*R^(1/2)*e^(i*theta/2). Define z as x + iy to derive R and theta. Utilize the identity k*e^(i*theta) = k*(cos(theta) + i*sin(theta) ) to isolate the velocity potential as k*cos(theta) and the streamfunction as k*sin(theta). The discussion highlights the importance of correctly separating these components for clarity in fluid dynamics analysis. The provided method effectively aids in achieving the desired separation.
Lucus
Messages
3
Reaction score
0
I need to find the streamfunction of the complex potential
F(z)=U(z^2 + 4a^2)^1/2, where U and a are constants and z=x+iy. I can't figure out how to separate the real and imaginary parts in order to isolate the streamfunction from the velocity potential. Thanks in advance for any help!
 
Engineering news on Phys.org
Just write the equation as

U*R^(1/2)*e^(i*theta/2)

Just write out z and you will find R and theta.

then use the identity k*e^(i*theta) = k*(cos(theta) + i*sin(theta))

that way you separate the potential = k*cos(theta)
and the streamfunction is k*sin(theta)

Sorry that I didn't use latex, it can get confusing
let me know if this helped you out or not
Jaap
 
Thank you, Jaap de Vries, for responding to my question. Your answer is very helpful. Thanks again!
 
How did you find PF?: Via Google search Hi, I have a vessel I 3D printed to investigate single bubble rise. The vessel has a 4 mm gap separated by acrylic panels. This is essentially my viewing chamber where I can record the bubble motion. The vessel is open to atmosphere. The bubble generation mechanism is composed of a syringe pump and glass capillary tube (Internal Diameter of 0.45 mm). I connect a 1/4” air line hose from the syringe to the capillary The bubble is formed at the tip...
Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'
Scenario 1 (figure 1) A continuous loop of elastic material is stretched around two metal bars. The top bar is attached to a load cell that reads force. The lower bar can be moved downwards to stretch the elastic material. The lower bar is moved downwards until the two bars are 1190mm apart, stretching the elastic material. The bars are 5mm thick, so the total internal loop length is 1200mm (1190mm + 5mm + 5mm). At this level of stretch, the load cell reads 45N tensile force. Key numbers...
I'd like to create a thread with links to 3-D Printer resources, including printers and software package suggestions. My motivations are selfish, as I have a 3-D printed project that I'm working on, and I'd like to buy a simple printer and use low cost software to make the first prototype. There are some previous threads about 3-D printing like this: https://www.physicsforums.com/threads/are-3d-printers-easy-to-use-yet.917489/ but none that address the overall topic (unless I've missed...

Similar threads

Back
Top