Grashof number¶
The Grashof number (Gr) is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It arises in situations involving natural convection and is analogous to the Reynolds number.
Notation:
\(g\) (
g) isacceleration_due_to_gravity.
Links:
- grashof_number¶
grashof_numberof the fluid.
- Symbol:
Gr- Latex:
\(\text{Gr}\)
- Dimension:
dimensionless
- volumetric_expansion_coefficient¶
Volumetric (see
volume)thermal_expansion_coefficientof the body.
- Symbol:
alpha_V- Latex:
\(\alpha_{V}\)
- Dimension:
1/temperature
- surface_temperature¶
temperatureof the surface of the fluid.
- Symbol:
T_s- Latex:
\(T_\text{s}\)
- Dimension:
temperature
- bulk_temperature¶
Average
temperatureof the inside of the fluid.
- Symbol:
T_b- Latex:
\(T_\text{b}\)
- Dimension:
temperature
- characteristic_length¶
characteristic_lengthof the fluid body.
- Symbol:
l_c- Latex:
\(l_\text{c}\)
- Dimension:
length
- kinematic_viscosity¶
kinematic_viscosityof the fluid.
- Symbol:
nu- Latex:
\(\nu\)
- Dimension:
area/time
- law¶
Gr = g * alpha_V * (T_s - T_b) * l_c^3 / nu^2- Latex:
- \[\text{Gr} = \frac{g \alpha_{V} \left(T_\text{s} - T_\text{b}\right) l_\text{c}^{3}}{\nu^{2}}\]