Particle Terminal Velocity in Fluids Calculator

Stokes regime (Re ≪ 1): $$ v_{Stokes} = \frac{(\rho_p-\rho_f) g d^2}{18 \mu} $$

Force balance: $$ \frac{\pi}{6} d^3 (\rho_p-\rho_f) g = \frac{1}{2} C_d \rho_f \left(\frac{\pi}{4} d^2\right) v_t^2 $$ $$ v_t = \sqrt{ \frac{4 d (\rho_p-\rho_f) g}{3 C_d \rho_f} } $$

Sphere drag (Schiller–Naumann): $$ C_d = \begin{cases} \dfrac{24}{Re}\left(1+0.15\,Re^{0.687}\right), & Re \le 1000 \\[6pt] 0.44, & Re > 1000 \end{cases} $$

Ganser non-spherical drag (sphericity \( \phi \)): $$ Re^\* = Re \, K_1 \, K_2, \quad C_d = \frac{24}{Re^\*}\left(1+0.1118\,{Re^\*}^{0.6567}\right) + \frac{0.4305}{1 + 3305/Re^\*} $$ with $$ K_1 = \left(\tfrac{1}{3} + \tfrac{2}{3}\phi^{-0.5}\right)^{-1}, \qquad K_2 = 10^{\,1.8148\,[ -\log_{10}(\phi) ]^{0.5743}}. $$

Kinematic viscosity: \( \nu = \mu / \rho_f \).

Hindered settling (Richardson–Zaki): $$ v_h = v_t (1-C)^n, \quad \varepsilon = 1-C $$ \( n \) by Garside–Al-Dibouni: \[ n=\begin{cases} 4.65,& Re<0.2\\ 4.4\,Re^{-0.03},& 0.2\le Re<1\\ 4.4\,Re^{-0.10},& 1\le Re<500\\ 2.4,& Re\ge 500 \end{cases} \]

Air density (ideal gas): \( \rho_f = \dfrac{P}{R T} \), with \(R=287.058\) J·kg⁻¹·K⁻¹.

Water density (empirical) (°C): \( \rho_f \approx 1000\left[1 - \frac{(T-3.9863)^2(T+288.9414)}{508929.2\,(T+68.12963)}\right] \) kg/m³.

Assumptions: Newtonian carrier; ideal gas air; water fit near atmospheric pressure; no wall/slip/hindered‑bed corrections beyond R–Z.

1. Select units and fluid preset or set properties.
2. Choose viscosity source and density source; set temperature and pressure.
3. Choose drag model and sphericity; enable R–Z if needed.
4. Click Compute for v, Re, C_d, ν, and v_h.
5. Export table to CSV/PDF or capture the Results card to PNG.

Tips: φ helper suggests typical values by material/shape.