Static Mixer Power
Static mixers dissipate energy through headloss as water flows through baffles or orifices. Power depends on the specific weight of the fluid, flow rate, and headloss through the mixer.
P = γ × Q × h
Laminar Impeller Power
In the laminar regime, impeller power depends on the mixing constant, fluid viscosity, rotational speed, and impeller diameter. Used when the Reynolds number is below about 10.
P = k × μ × n² × D³
Turbulent Impeller Power
In the turbulent regime, impeller power depends on the mixing constant, fluid density, rotational speed, and impeller diameter. Used when the Reynolds number exceeds about 10,000.
P = k × ρ × n³ × D⁵
How It Works
Mixing injects energy into water to blend chemicals, suspend solids, or transfer oxygen. This calculator covers six equation families used in wastewater treatment mixing design: static mixer power, laminar and turbulent impeller power, Reynolds number for flow regime classification, and two pneumatic mixing power equations (volume-based and flow-based). Static mixers dissipate energy through headloss as water flows through baffles or orifices. Mechanical impeller mixers operate in either laminar or turbulent regimes, and their power draw depends on rotational speed, impeller diameter, and fluid properties. Pneumatic mixers use compressed air to agitate the liquid.
Example Problem
A static mixer treats 0.2 m³/s of water with a specific weight of 9,810 N/m³ and a headloss of 0.5 m. What power is dissipated?
- P = γ × Q × h = 9,810 × 0.2 × 0.5
- P = 981 W
When to Use Each Variable
- Solve for Static Mixer Power — when you know the flow rate, specific weight, and headloss through the mixer and need the power dissipated.
- Solve for Laminar Impeller Power — when the impeller Reynolds number is below about 10 and you need the power draw from viscosity, speed, and diameter.
- Solve for Turbulent Impeller Power — when the impeller Reynolds number exceeds about 10,000 and you need the power draw from density, speed, and diameter.
Key Concepts
Mixing design determines the energy input required to blend chemicals, suspend solids, or transfer gases in treatment basins. Static mixers use flow energy (headloss) with no moving parts. Mechanical impeller mixers operate in either laminar or turbulent regimes, and the power number (mixing constant k) varies by impeller type and Reynolds number. The velocity gradient G = sqrt(P / (mu x V)) is the key design parameter — rapid mix requires G > 300 s^-1 while slow mix uses G = 20-80 s^-1.
Applications
- Water treatment: designing rapid-mix chambers for coagulant injection and slow-mix basins for flocculation
- Wastewater aeration: sizing mechanical aerators and diffused air systems for activated sludge basins
- Chemical processing: scaling up mixing operations from bench to pilot to full-scale reactors
- Industrial blending: designing mixers for paint, pharmaceutical, and food processing applications
Common Mistakes
- Using the laminar power formula in turbulent flow (or vice versa) — the formulas have different exponents and use viscosity versus density; check the Reynolds number first
- Ignoring impeller type when selecting the mixing constant k — Rushton turbines (k around 5) draw far more power than marine propellers (k around 0.3) at the same speed and diameter
- Sizing mixers using only power without checking the velocity gradient G — adequate power at the wrong G value produces poor mixing quality
Frequently Asked Questions
What is the difference between rapid mix and slow mix?
Rapid mix uses high energy (G > 300 per second) for 10–30 seconds to uniformly distribute coagulant. Slow mix applies gentle energy (G = 20–80 per second) for 20–40 minutes to build flocs without breaking them.
What mixing constant should I use for an impeller?
The mixing constant k depends on impeller type and Reynolds number. For a standard Rushton turbine in turbulent flow, k is about 5.0. Propeller-type impellers in turbulent flow typically use k around 0.3–0.4.
How do I choose between a static mixer and a mechanical mixer?
Static mixers are ideal for rapid blending of chemicals in pressurized pipelines with no moving parts. Mechanical mixers are better for basins where you need adjustable intensity and longer detention times, such as flocculation tanks.
Related Calculators
- Flocculation Calculator -- calculate velocity gradient for the slow-mix stage.
- Ideal Reactor Calculator -- determine required tank volume and detention time.
- Microorganism Disinfection Calculator -- evaluate CT requirements after chemical addition.
- Activated Sludge Calculator — evaluate biological reactor performance downstream of mixing.
- Pump Calculator — size pumps for the power input needed to drive mixing systems.
- Volume Unit Converter — convert between liters, gallons, and cubic meters for tank sizing.
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