How do I sketch a flow profile and solve for curl in vector calculus?

In summary, the conversation revolves around sketching the flow profile and solving for curl in a complex function of a complex variable. The speaker is struggling with understanding how to differentiate the function f(y) and is seeking help. They also mention using Wikipedia as a resource and feeling uneasy about their attempt. The conversation also touches on linear mapping and the answer given by a professor.
  • #1
Darsh_22
4
0
Homework Statement
let f(y) = v0 exp(−y^2/L2), with some constant v0 > 0. Make a sketch of the flow
profile. Determine curl v for this case and discuss strength and direction of the local
vorticity. How does shear come into play here? (Hint: Consider a small paddle wheel in
the flow)
Relevant Equations
curl of vector.
Hello,
Can someone explain how to sketch the flow profile in detail. Also, I solved for curl, but I'm getting a zero while the answer is the differentiation of the function f(y). Pls do help me out!
 
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  • #2
I don't see a vector field. Just a scalar function.
 
  • #3
Is this supposed to be a complex function of a complex variable?
 
  • #4
1637669712566.png

this is the entire question. I did (a).
 
  • #5
Please show your attempt!
 
  • #6
Wikipedia quotes the divergence and curl of vector fields in cartesian, cylindrical and spherical coordinates.
 
  • #7
Orodruin said:
Please show your attempt!
1637671753028.png


this is for part B, the one I'm doubtful of. The curl is f'(y), which I don't understand how. Let me know if I'm wrong anywhere.
 
  • #8
Your attempt is OK but you feel uneasy, why?
 
  • #9
Gordianus said:
Your attempt is OK but you feel uneasy, why?
1637678088124.png

Hey Gordianus,
This is the answer given by my professor and that is why I think my answer would be incorrect.
Also, I do not know how to do this linear mapping or sketch the flow profile.
 

1. What is vector calculus?

Vector calculus is a branch of mathematics that deals with vector-valued functions, which are functions that output vectors instead of scalars. It involves the study of vector fields, line and surface integrals, and the gradient, divergence, and curl of vector fields.

2. Why is vector calculus important?

Vector calculus is important because it is used to describe and analyze physical phenomena that involve both magnitude and direction, such as forces, motion, and electromagnetic fields. It is also essential in many fields of science and engineering, including physics, engineering, and computer graphics.

3. What are some common applications of vector calculus?

Vector calculus has many applications in various fields, including physics, engineering, computer science, and economics. Some common applications include calculating electric and magnetic fields, modeling fluid flow, optimizing functions with multiple variables, and analyzing motion in three-dimensional space.

4. What are the main operations in vector calculus?

The main operations in vector calculus are the gradient, divergence, and curl. The gradient is a vector operator that gives the direction and magnitude of the steepest ascent of a scalar field. The divergence measures the tendency of a vector field to originate or converge at a point. The curl measures the tendency of a vector field to rotate around a point.

5. How can I improve my understanding of vector calculus?

To improve your understanding of vector calculus, it is essential to practice solving problems and working with vector-valued functions. You can also read textbooks and watch online lectures to gain a deeper understanding of the concepts. Additionally, seeking help from a tutor or joining a study group can also be beneficial.

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