Unsteady Fluid Flow: Incompressible and Stream Function Calculation

Click For Summary
SUMMARY

The discussion focuses on analyzing an unsteady fluid flow characterized by the velocity field q = -1/2 sin(t) (xe^-y, e^-y). It establishes that the flow is incompressible by demonstrating that the divergence of the velocity vector is zero. Additionally, the discussion addresses the calculation of a stream function and the trajectory of a fluid particle starting at the coordinates (1,0) at time t=0. The key takeaway is the necessity of confirming the divergence condition for incompressibility in fluid dynamics.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically incompressible flow.
  • Knowledge of vector calculus, particularly divergence calculations.
  • Familiarity with stream function concepts in fluid mechanics.
  • Basic proficiency in solving differential equations related to fluid motion.
NEXT STEPS
  • Study the mathematical derivation of the divergence of a velocity vector in fluid dynamics.
  • Learn how to calculate stream functions for various flow fields.
  • Explore the concept of particle trajectories in unsteady fluid flows.
  • Review examples of incompressible flow scenarios and their applications in engineering.
USEFUL FOR

Students and professionals in fluid mechanics, engineers working on fluid dynamics problems, and researchers focusing on unsteady flow analysis will benefit from this discussion.

ra_forever8
Messages
106
Reaction score
0
An unsteady fluid flow has velocity field q= - 1/2 sin t ( xe^-y, e^-y).
Show the flow is incompressible and find a stream function.
Find the path of the fluid particle which is at (1,0) at t=0.

I only know it has six faces and the sum of all six terms has to be zero in order to show the flow is incompressible.
Rest i really don't how to slove the problems
 
Physics news on Phys.org
Were you taught that, if the flow is incompressible, then the divergence of the velocity vector must be equal to zero? Do you know the formula for calculating the divergence of a vector?
 

Similar threads

Graduate Why are the Navier-Stokes equations inconsistent in this case?
  • · Replies 18 ·
Replies
18
Views
2K
Navier-Stokes equation for parallel flow
  • · Replies 1 ·
Replies
1
Views
2K
Theoretical Fluid Mechanics - Ideal Fluid Flow
  • · Replies 4 ·
Replies
4
Views
5K
How to Calculate the Volume Flow Rate to Overcome Inertia in Fluid Mechanics?
  • · Replies 4 ·
Replies
4
Views
4K
Fluid Mechanics: Constant Pressure and Incompressible flow
  • · Replies 5 ·
Replies
5
Views
2K
One question about stream function in fluid mechanics
  • · Replies 6 ·
Replies
6
Views
5K
Force Produced from Fluid Motion
  • · Replies 6 ·
Replies
6
Views
2K
Applicability of potential flow theory (fluid dynamics)
  • · Replies 3 ·
Replies
3
Views
3K
Engineering How Does Cup Anemometer Design Utilize Fluid Mechanics Principles?
  • · Replies 4 ·
Replies
4
Views
3K
Flow of air through an open tube with a balloon
  • · Replies 9 ·
Replies
9
Views
4K