Finding torque in rotating cylinder (viscosity )

Click For Summary
SUMMARY

The discussion focuses on calculating torque in a rotating cylinder influenced by viscosity, using the equation τ = η * (dv/dy). The user attempts to derive torque (T) by integrating the shear stress over the area of the cylinder, ultimately arriving at a torque value of 0.11 Nm. However, they express concern that the calculation may be oversimplified due to the presence of a velocity gradient along the slope of the rotating cone, indicating a need for a more complex analysis.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly viscosity.
  • Familiarity with torque calculations in rotational systems.
  • Knowledge of calculus, specifically integration techniques.
  • Experience with velocity gradients in fluid mechanics.
NEXT STEPS
  • Study the effects of viscosity on torque in rotating systems using advanced fluid dynamics concepts.
  • Learn about the Navier-Stokes equations and their application in analyzing velocity gradients.
  • Explore the implications of shear stress in non-Newtonian fluids.
  • Investigate the impact of geometry on torque calculations in rotating cylinders and cones.
USEFUL FOR

Students and professionals in mechanical engineering, particularly those specializing in fluid mechanics and torque analysis in rotating systems.

bobblehead

Homework Statement



media%2F65f%2F65f2aa1c-faf8-4801-966d-be7324771bbf%2Fimage.jpg

Homework Equations


τ= η* (dv/dy)

The Attempt at a Solution


so
dA= 2π* r * dr
T = ∫ τ * r * dA
T = ∫((0.01* r* 2*π * 450 /60)/(5*10^-3) ) * r * 2π* r *dr
= (592.1762)*(r^4/4)
T = 0.11 Nm

is this correct?
 
Physics news on Phys.org
I think it is more complicated than that. There is a velocity gradient not only horizontally but also down the slope of the rotating cone.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 21 ·
Replies
21
Views
2K
  • · Replies 22 ·
Replies
22
Views
3K
  • · Replies 17 ·
Replies
17
Views
4K
Replies
2
Views
19K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K