FT-10 · External flow and particles

Particle drag and terminal velocity

Evaluates the current operating point and solves implicitly for terminal velocity using the equivalent diameter and sphericity.

Particle, fluid and relative velocity

Equivalent diameter dᵥ · Esfericidad φParticle density · Fluid density · Dynamic viscosity · Current relative velocity · Lift coefficient ClGravedad ·

Terminal velocity

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Cd actual

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Reynolds actual

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Drag force

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Lift force

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Terminal direction

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Reynolds terminal

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Drag coefficient vs. Reynolds number

Balance terminal

\[(\rho_p-\rho)gV_p=\tfrac12\rho C_dA_pv_t^2\]

\[Re=\frac{\rho vd_v}{\mu}\]

C_d(Re,φ) is evaluated with Haider–Levenspiel. d_v is the diameter of a sphere with the same volume as the particle.

Drag coefficient calculator for particles

The drag coefficient captures the effect of shape and flow regime on fluid resistance. For non-spherical particles, sphericity shifts the transition between the Stokes, intermediate and inertial regimes.

Indicative flow regimes

Re	Flow regime	Comportamiento
<0.1	Stokes	Cd ≈ 24/Re for a sphere
0.1–1000	Transitional	Increasing inertia; Cd depends on Re and shape
>1000	Inercial	Cd varies more slowly until further transitions

Terminal velocity

Terminal velocity is reached when apparent weight and drag balance. Because Cd depends on the Reynolds number, the calculation is solved iteratively.

Preguntas frecuentes

What is sphericity?

It is the ratio of the surface area of an equal-volume sphere to the actual particle area; it equals 1 for a sphere.

Is solids concentration taken into account?

No. Concentrated suspensions show hindered settling and need an additional correction.

Does lift change the vertical terminal velocity?

The balance shown uses weight and axial drag; Cl is reported for cross flow but is not included in the basic vertical equilibrium.