Consider the following steady, two-dimensional, incompressible velocity field: V = (u, v) = (1/2ay^2 + b) i + (axy^2 + c) j. Is this flow field irrotational? If so, generate an expression for the velocity potential function.
Added by Ryan L.
Step 1
This means that the curl of the velocity field should be zero. The curl of a two-dimensional vector field is given by: curl(V) = (∂v/∂x - ∂u/∂y) k where k is the unit vector in the z-direction. Applying this formula to our velocity field, we get: curl(V) Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 89 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The velocity field for a two-dimensional flow is $\vec{V}=(A x-B y) t \hat{\imath}-(B x+A y) t \hat{j},$ where $A=1 \mathrm{s}^{-2} B=2 \mathrm{s}^{-2}$ $t$ is in seconds, and the coordinates are measured in meters. Is this a possible incompressible flow? Is the flow steady or unsteady? Show that the flow is irrotational and derive an expression for the velocity potential.
Consider a steady, two-dimensional flow field in the xy-plane whose x-component of velocity is given by u = a + b(x - c)^2 where a, b, and c are constants with appropriate dimensions. Of what form does the y-component of velocity need to be in order for the flow field to be incompressible? In other words, generate an expression for v as a function of x, y, and the constants of the given equation such that the flow is incompressible.
Sahil K.
The u velocity component of a steady, two-dimensional, incompressible flow field is u = 3ax^2 - 2bxy, where a and b are constants. The velocity component is unknown. Generate an expression for the velocity component as a function of x and y.
Sri K.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD