B Fluid Continuity Equation in different reference frame

AI Thread Summary
The discussion centers on the application of the continuity equation in fluid dynamics, specifically regarding changes in fluid velocity and cross-sectional area. When fluid velocity increases, the area must decrease to maintain continuity, but switching to a different reference frame complicates this relationship. The key point is that the area constriction is relative to the tube's reference frame, not an arbitrary frame of reference. Understanding this is crucial for correctly applying the continuity equation. The derivation of the continuity equation clarifies these relationships and resolves the apparent violation.
versine
Messages
24
Reaction score
5
If I have fluid with area 10 and velocity 10, if the velocity increases to 20 the area will become 5. But if we switch to a reference frame moving at velocity 1 opposite this motion, then it would be 10 and 11 to 5 and 21, violating the continuity equation. What is wrong?
 
Physics news on Phys.org
If I understand what you ask correctly, the area is constricted because the fluid is moving through some tube. If that's the case, it's the velocity relative to the tube's reference frame that counts. You will see why if you follow the derivation of the continuity equation.
 
Reply
  • Like
Likes vanhees71 and versine
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »
Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

Thread 'Gauss' law seems to imply instantaneous electric field (version 2)'

This argument is another version of my previous post. Imagine that we have two long vertical wires connected either side of a charged sphere. We connect the two wires to the charged sphere simultaneously so that it is discharged by equal and opposite currents. Using the Lorenz gauge ##\nabla\cdot\mathbf{A}+(1/c^2)\partial \phi/\partial t=0##, Maxwell's equations have the following retarded wave solutions in the scalar and vector potentials. Starting from Gauss's law $$\nabla \cdot...
View full post »

Similar threads

A Steady state confined flow field: Is it cyclic?
Replies
9
Views
2K
I Work - Energy Principle Application to Fluid Flow
Replies
35
Views
4K
I Work - Energy Principle Application to Fluid Flow
Replies
48
Views
5K
A Why are the Navier-Stokes equations inconsistent in this case?
Replies
18
Views
2K
A Conservation Laws from Continuity Equations in Fluid Flow
Replies
2
Views
2K
I Reference Frame, Difference in Kinetic Energy, Fuel Consumed
Replies
19
Views
2K
I Question about the velocity of the center of mass reference frame
Replies
21
Views
2K
B What is Mass?
Replies
23
Views
2K
Doublet flow in Fluid Dynamics between two spheres or cylinders
Replies
0
Views
1K
I Laminar-turbulent transition and Reynolds number
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top