\[\tau=\mu\frac{v}{d}\]
Variables
tauviscous stress (Pa)
mudynamic viscosity (Pa·s)
vrelative velocity (m/s)
dmantle layer thickness (m)
Description
What is this formula?
This formula calculates the viscous shear stress generated within the Earth's mantle due to slow relative motion between adjacent layers.
When to use it
Use this equation in mantle dynamics, tectonics, and fluid deformation studies to estimate stress produced by viscous flow.
Example
Calculate the viscous stress in a mantle layer with a viscosity of 5×10^20 Pa·s, relative velocity of 0.03 m/year, and thickness of 120 km.
Data:
mu = 5×10^20 Pa·s
v = 0.03 m/year = 9.51×10^-10 m/s
d = 1.2×10^5 m
Formula:
tau = (mu*v)/d
Substitution:
tau = (5×10^20*9.51×10^-10)/(1.2×10^5)
Result:
tau = 3.96 × 10^6 Pa
Applications
- Mantle convection analysis
- Plate tectonics
- Lithosphere deformation studies
- Geodynamic simulations
- Earth interior mechanics