Is My Understanding of Material Derivative Correct?

  • Thread starter Thread starter member 428835
  • Start date Start date
  • Tags Tags
    Derivative Material
AI Thread Summary
The material derivative, represented as Dρ/Dt, describes how a scalar quantity ρ changes over time and as it moves through space. This understanding is affirmed by participants in the discussion, confirming that the material derivative captures both temporal and spatial variations. The concept is crucial in fields like fluid dynamics, where it helps analyze the behavior of quantities within moving fluids. Overall, the explanation provided aligns well with the fundamental principles of the material derivative. Understanding this concept is essential for applying it effectively in various scientific contexts.
member 428835
hey pf! can someone please tell me if my understanding of the material derivative operating over some scalar \rho is correct? basically, from my understanding if we take \frac{ D \rho}{D t} this will tell us how \rho changes as time changes AND how \rho changes as we move our little piece of \rho through space. is this correct?

thanks!
 
Engineering news on Phys.org
Yeah, I would say that's pretty much correct.
 

Thread 'Race car suspension Class'

Posted June 2024 - 15 years after starting this class. I have learned a whole lot. To get to the short course on making your stock car, late model, hobby stock E-mod handle, look at the index below. Read all posts on Roll Center, Jacking effect and Why does car drive straight to the wall when I gas it? Also read You really have two race cars. This will cover 90% of problems you have. Simply put, the car pushes going in and is loose coming out. You do not have enuff downforce on the right...
View full post »
Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'

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...
View full post »

Thread 'Cantilever help'

I'm trying to decide what size and type of galvanized steel I need for 2 cantilever extensions. The cantilever is 5 ft. The space between the two cantilever arms is a 17 ft Gap the center 7 ft of the 17 ft Gap we'll need to Bear approximately 17,000 lb spread evenly from the front of the cantilever to the back of the cantilever over 5 ft. I will put support beams across these cantilever arms to support the load evenly
View full post »

Similar threads

Derive and Solve the Lane-Emden Equation for a Polytropic Gas Sphere
Replies
6
Views
2K
A Dirac's Conservation of Matter: A Closer Look
Replies
7
Views
2K
Poisson ratios for Orthotropic materials (composites)
Replies
1
Views
3K
Confusion on product rule for mass of differential volume element
Replies
4
Views
2K
A Variation of CMFR mass density ##\rho## along a world line
Replies
17
Views
1K
Loss of atoms from the surface of the material: How does it work?
Replies
15
Views
1K
Finding the best height for windmill towers
Replies
5
Views
2K
A Help needed with derivation: solving a complex double integral
Replies
1
Views
2K
I Can interpretation-dependent facts be derived from the axioms?
Replies
10
Views
2K
I Speed of light for a Rindler observer
2
Replies
57
Views
5K

Hot Threads

Recent Insights

Back
Top