Momentum Flux Calculator

J = β × ρAV² = β × ṁV — momentum per unit time through a cross-section. Used in control-volume force analysis, jet impingement, and thrust calculations.

Fluid Mechanics II

Common fluids — click to auto-fill density

Inputs

Pipe / duct diameter D (mm)

Mean velocity V (m/s)

Fluid density ρ (kg/m³)

Velocity profile (momentum correction factor β)

Uniform (slug) flow(β = 1, α = 1)

Ideal/inviscid, or well-mixed flow

Laminar — parabolic profile(β = 1.333, α = 2)

Re < 2 300, fully developed pipe flow

Turbulent — 1/7 power law(β = 1.02, α = 1.058)

Re > 10 000, fully developed pipe flow

Custom

Enter β and α manually below

Theory

Momentum flux (rate of momentum transport):

J = β × ṁ × V = β × ρ × A × V² [N]

ṁ = ρ × A × V [kg/s]

Kinetic energy flux:

Ek = α × ½ρAV³ = α × ½ṁV² [W]

Momentum and energy correction factors:

Profile	β (momentum)	α (energy)
Uniform (slug) flow	1.000	1.000
Laminar — parabolic	4/3 = 1.333	2.000
Turbulent — 1/7 law	1.020	1.058

Control-volume momentum equation (x-direction):

ΣF_x = J_out − J_in = β₂ṁV₂ − β₁ṁV₁

Includes pressure forces ΣP·A and body forces. For a straight reducing pipe at steady state: F_x + P₁A₁ − P₂A₂ = ṁ(V₂ − V₁).

Where:

J = momentum flux [N = kg·m/s²]
β = momentum correction factor (accounts for non-uniform velocity)
α = kinetic energy correction factor
ṁ = mass flow rate = ρAV [kg/s]
V = cross-sectionally averaged (mean) velocity [m/s]
A = cross-sectional area [m²]
ρ = fluid density [kg/m³]