Vertical Volume Flow Rate Calculator

Vertical Volume Flow Rate Equation

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

Calculator

Property to Calculate:

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):

Equation Assumptions

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