Non Newtonian Fluid Force Calculator

Calculator Form

Fluid Model

K or Plastic Viscosity

Use Pa.s^n for K or Pa.s for Bingham.

Flow Behavior Index n

Yield Stress

Use Pa. Power law can use zero.

Shear Rate

Use s^-1.

Contact Area

Use m².

Density

Use kg/m³.

Mean Velocity

Use m/s.

Hydraulic Diameter

Use m.

Pipe or Channel Length

Use m.

Safety Factor

Example Data Table

Fluid	Model	K or μp	n	Yield Stress	Shear Rate	Area
Paint	Herschel Bulkley	2.8	0.55	8 Pa	40 s^-1	0.05 m²
Ketchup	Herschel Bulkley	6.0	0.40	22 Pa	20 s^-1	0.03 m²
Corn starch mix	Power Law	1.7	1.35	0 Pa	70 s^-1	0.04 m²
Drilling mud	Bingham Plastic	0.18	1.00	15 Pa	60 s^-1	0.08 m²

Formula Used

Power Law: τ = Kγⁿ

Bingham Plastic: τ = τy + μpγ

Herschel Bulkley: τ = τy + Kγⁿ

Apparent Viscosity: μapp = τ / γ

Force: F = τA

Design Force: Fd = F × safety factor

Reynolds Estimate: Re = ρVD / μapp

Pressure Drop: ΔP = 4τL / D

Hydraulic Power: P = ΔP × Q

How to Use This Calculator

Select the fluid model that matches your material behavior.
Enter K, flow index, yield stress, and shear rate.
Add the contact area for the surface under shear.
Enter density, velocity, diameter, and length for flow estimates.
Add a safety factor for uncertain or rough conditions.
Press Calculate to view force and pressure results.
Use CSV or PDF buttons to save the result.

Understanding Non Newtonian Fluid Force

Non Newtonian fluids do not keep one constant viscosity. Their resistance changes with shear rate, time, or internal structure. This makes force estimation different from water or light oil. Paint, ketchup, blood, slurry, mud, toothpaste, and polymer melts can all behave this way.

Why Shear Rate Matters

The calculator starts with shear rate. Shear rate describes how fast nearby fluid layers slide past each other. A larger value can thin some fluids and thicken others. Shear thinning fluids have a flow index below one. Shear thickening fluids have a flow index above one. The chosen model converts shear rate into shear stress.

Force From Shear Stress

Shear stress is the tangential load per unit area. Once stress is known, force is stress multiplied by contact area. A safety factor can be added when the surface is rough, the sample is uncertain, or the process has spikes. The result is useful for mixer blades, plates, scrapers, pipe walls, nozzles, and moving probes.

Choosing A Model

The power law model is simple and flexible. It works well when yield stress is not important. Bingham plastic fluids resist motion until a yield stress is exceeded. Herschel Bulkley adds both yield stress and non linear shear behavior. These models are estimates, so measured data is always better.

Pressure Drop And Reynolds Value

The tool also estimates pressure drop from wall shear stress. It assumes the entered stress represents the wall condition. The Reynolds estimate uses apparent viscosity at the current shear rate. This helps compare laminar and transitional behavior, but non Newtonian pipe flow can need special corrections.

Using Results Carefully

Non Newtonian calculations depend on temperature, concentration, particle size, and history. A sample mixed for a long time may not match a fresh sample. Use realistic units. Check laboratory rheometer values when available. Compare the result with trial data before choosing motors, pumps, or structural parts.

Practical Design Benefit

This calculator gives fast engineering insight. It links material behavior, shear rate, surface area, and pipe geometry in one place. Exports help store runs, compare cases, and share assumptions. Clear formulas also make the result easy to review in reports or class work during early design reviews too today.

FAQs

What is a non Newtonian fluid?

A non Newtonian fluid changes apparent viscosity with shear rate, time, or stress. It does not behave like water. Common examples include ketchup, paint, blood, slurry, toothpaste, and corn starch suspension.

Which model should I choose?

Use power law for simple shear thinning or thickening fluids. Use Bingham when yield stress and plastic viscosity matter. Use Herschel Bulkley when the fluid has yield stress and non linear shear behavior.

What does K mean?

K is the consistency index for power law and Herschel Bulkley models. Higher K usually means greater resistance. In the Bingham option, the same input is treated as plastic viscosity.

What does flow behavior index mean?

The flow behavior index is n. If n is below one, the fluid is shear thinning. If n is above one, the fluid is shear thickening. If n equals one, behavior is closer to Newtonian flow.

Why is yield stress important?

Yield stress is the stress needed before some fluids start to flow. It matters for pastes, gels, muds, and thick suspensions. Ignoring it can make force estimates too low.

Is the Reynolds value exact?

No. It is an estimate based on apparent viscosity at the entered shear rate. Non Newtonian flow often needs special generalized Reynolds methods for final pipe design.

Can I use this for pump sizing?

You can use it for early estimates. It gives force, pressure drop, and hydraulic power. Final pump sizing should use tested rheology data, fittings, elevation changes, and safety margins.

Why add a safety factor?

A safety factor covers uncertain material data, rough surfaces, temperature shifts, aging, and process spikes. It raises calculated force to a more cautious design value.