Reference ID: MET-E5AB | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
A gravity settling tank is the simplest device for separating dispersed phases (drops, bubbles, or solid particles) from a continuous fluid. Its capacity design answers the question: “What volumetric throughput \(Q\) can a tank of given plan area \(A\) handle while guaranteeing that all particles larger than a specified cut-off diameter \(d_{min}\) are removed?” The answer is governed by two independent velocities:
The terminal settling velocity \(v_t\) of the particle in the continuous phase.
The superficial velocity \(v_s\) of the continuous phase, defined as the volumetric flow rate divided by the tank’s horizontal cross-section, \(v_s = Q/A\).
Because these velocities are independent, the design criterion is purely kinematic: the settling velocity must exceed the superficial velocity. No further numerical calculation is required once \(v_t\) is known from Stokes’ or Newton’s laws. The method is ubiquitous in water treatment, oil–water separation, decanter design, and dust chambers.
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Step 1 – Identify the flow regime
The drag coefficient \(C_D\) depends on the particle Reynolds number \(Re_p = \dfrac{\rho_f v_t d}{\mu}\). Select the appropriate correlation:
Step 2 – Apply the capacity criterion
For complete removal of particles of diameter \(d\), the superficial velocity must satisfy:
\[
v_s \le v_t \quad \Rightarrow \quad \dfrac{Q}{A} \le v_t
\]
Hence, the minimum plan area required for a given flow rate is:
\[
A_{min} = \dfrac{Q}{v_t}
\]
and the corresponding nominal residence time is:
\[
\tau = \dfrac{H}{v_t}
\]
where \(H\) is the vertical height of the dispersion band.
Step 3 – Check for hindered settling (optional)
If the dispersed-phase volume fraction \(\phi\) exceeds 1%, correct the terminal velocity using the Richardson–Zaki relation:
\[
v_t(\phi) = v_t(0)(1 - \phi)^n
\]
with exponent \(n\) between 2.4 (Stokes) and 4.8 (Newton).
The required settling area is governed by the overflow rate (settling velocity of the target particle) and the design flow rate. Use the relation:
Settling area A = Q / vt
Q = maximum anticipated flow rate (m³ h⁻¹)
vt = terminal settling velocity of the smallest particle to be removed (m h⁻¹)
Include a safety factor of 1.25–1.5 on the calculated area to cover flow surges and inlet turbulence.
Residence time is set by the chosen overflow rate and tank depth, not by an arbitrary rule-of-thumb.
Calculate nominal residence time t = V / Q = (A · h) / Q = h / vt
Typical depths for industrial settlers are 1.5–3 m; deeper tanks increase residence time but raise construction and sludge-raking costs.
Verify that the resulting t is ≥ the time needed for particles to settle the full liquid depth at vt; otherwise enlarge the area or accept lower removal efficiency.
Poor inlet hydraulics create turbulence and short-circuiting, effectively reducing the usable settling area.
Use a flocculated inlet zone or perforated baffle to dissipate momentum and spread flow evenly across the tank width.
Keep inlet velocity below 0.15 m s⁻¹ to minimise re-entrainment of settled solids.
Install a stilling chamber or feedwell when influent contains > 300 mg L⁻¹ suspended solids or when temperature differences can cause density currents.
Build in physical and hydraulic margins early; retro-fitting settlers is expensive.
Provide 25–50% extra plan area by lengthening the tank rather than deepening it, so vt remains unchanged.
Size launder weirs for at least 1.5× the present peak flow to avoid hydraulic bottlenecking.
Allow freeboard of 0.3–0.5 m above maximum water level to absorb flow surges and foam.
Specify rake drives and sludge pumps for 2× the design solids loading to cope with higher influent concentrations.
Worked Example – Sizing a Gravity Settling Tank for a Small Brewery
A craft-brewery wants to remove spent yeast from post-fermentation beer before filtration. A horizontal gravity settling tank will be installed to operate at ambient temperature. The design target is to reduce the yeast concentration from 2.5 g L-1 to 0.1 g L-1 with a continuous overflow rate that matches the downstream filtration capacity.
Particle (yeast) density, ρp = 1 050 kg m-3
Beer density, ρf = 1 010 kg m-3
Beer viscosity, μ = 1.8 × 10-3 Pa·s
Smallest yeast diameter to be removed, d = 6 µm = 6 × 10-6 m
Determine the minimum surface area required for 100% removal of the 6 µm particles:
\[
A = \frac{Q}{v_g}
\]
\[
A = \frac{3.333\times10^{-4}}{4.36\times10^{-5}}
\]
\[
A = 7.65\ \text{m}^2
\]
Select a practical length-to-width ratio of 3:1 for a horizontal rectangular tank:
\[
A = L\,W \quad \text{with}\ L = 3W
\]
\[
7.65 = 3W^2 \Rightarrow W = 1.60\ \text{m}
\]
\[
L = 4.80\ \text{m}
\]
Check hydraulic retention time:
\[
t = \frac{V}{Q} = \frac{L\,W\,H}{Q}
\]
Choose side water depth H = 1.2 m:
\[
t = \frac{4.80\times1.60\times1.2}{3.333\times10^{-4}} \approx 27\,600\ \text{s} \approx 7.7\ \text{h}
\]
(Acceptable for gentle yeast settling without disturbing the beer quality.)
Final Answer: A horizontal gravity settling tank with 4.8 m length × 1.6 m width × 1.2 m liquid depth provides the required 7.65 m2 surface area and handles the 1.2 m3 h-1 flow while removing 6 µm yeast particles.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
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