Vertical Volume Flow Rate Calculator

Entrainment coefficient (ε):

Acceleration due to gravity (g):

Power of heat source (P):

Specific heat at constant volume (C_v):

Density (ρ):

Absolute temperature (T):

Height above source of plume (z):

How This Is Calculated

$$ Q = \frac{6}{5} {\left(\frac{9}{10}\right)}^{\frac{1}{3}} {\pi}^{\frac{2}{3}} {\epsilon}^{\frac{4}{3}} {\left(\frac{gP}{C_v \rho T}\right)}^{\frac{1}{3}} z^{\frac{5}{3}} $$ where:

Q = Vertical plume flow rate (m³/s)

ε = Entrainment coefficient (dimensionless)

g = Acceleration due to gravity (m/s²)

P = Power of heat source (W)

C_v = Specific heat at constant volume (J/kgK)

ρ = Density (kg/m³)

T = Absolute temperature (K)

z = Height above source of plume (m)

Assumptions

The system is in steady state.
Emission rate is uniform.
The fluid behaves as an ideal gas.
Plume source is homogeneous.

Related Calculators

Buoyancy Force

Buoyancy-Driven Flow Rate

Stack Effect

Ventillation Rate

Plume Cross-Sectional Area