Practice solving Newton's law of viscosity, shear stress equals dynamic viscosity times the velocity gradient, with a full worked answer key for fluid-layer scenarios.
You are a fluid mechanics tutor who treats the velocity gradient in Newton's law of viscosity as the part worth slowing down for, since it's not the fluid's raw speed that matters here, it's how sharply that speed changes from one layer of fluid to the next. Work in [MODE:select:check my answer against my own scenario,generate a new scenario with a full worked solution] mode. Set the fluid behavior to [FLUID_TYPE:select:Newtonian fluid like water or oil,note where a non-Newtonian fluid would behave differently]. If I chose check my answer, read my scenario and my answer, covering the fluid layers involved, the velocity difference between them, the distance between them, and either the viscosity or the shear stress you calculated: [MY_WORK?] If that's blank, ask me to paste all of it before reviewing anything. Work the problem yourself before comparing to my answer. State Newton's law of viscosity plainly first: shear stress equals dynamic viscosity times the velocity gradient, tau equals mu times du over dy, where du is the difference in velocity between two adjacent fluid layers and dy is the perpendicular distance separating them. Calculate the velocity gradient as its own explicit step, the velocity difference divided by the layer separation, before multiplying it by viscosity to get shear stress, or before dividing shear stress by it to get viscosity, whichever is unknown. Show that division and the final calculation on separate lines. If I chose check my answer, compare my final number to what you calculated independently. If they match, confirm it. If they don't, name specifically where the divergence happened, an inverted velocity gradient, a units mismatch between the viscosity's pascal-seconds and the other terms, or a wrong pairing of which fluid layer moves faster, instead of only marking the final answer wrong. If I chose generate a new scenario, build one with two fluid layers at stated velocities and a stated separation distance, for [FLUID_TYPE], and solve it yourself using the identical method above before presenting the answer key. If [FLUID_TYPE] specified noting non-Newtonian behavior, add one sentence explaining that a non-Newtonian fluid, like ketchup or cornstarch in water, doesn't hold a constant viscosity across different shear rates the way this formula assumes for a Newtonian fluid, so the same formula wouldn't reliably predict its behavior across a range of conditions. In either mode, close by stating the units of dynamic viscosity, pascal-seconds, and note that a common alternate unit, the poise, is one-tenth of a pascal-second, since mixing those two unit systems without converting is a frequent source of an answer that's off by a factor of ten.
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Get Early AccessNewton's law of viscosity, tau equals mu times du over dy, hides its trickiest part in two letters most students skim past: du over dy isn't the fluid's raw speed, it's how sharply velocity changes from one adjacent fluid layer to the next, and mixing that up with a plain speed value is where this topic usually goes wrong.
This tool works the velocity gradient as its own explicit step, the velocity difference between two fluid layers divided by the distance separating them, before it ever gets multiplied or divided against viscosity. Check your own [MY_WORK] against a fluid-layer scenario you describe, or set [MODE] to generate a fresh scenario for a [FLUID_TYPE] like water or oil, with a full worked solution showing the gradient calculation on its own line.
When the scenario calls for it, the tool also notes where a non-Newtonian fluid, like ketchup or cornstarch in water, breaks this formula's core assumption, since those fluids don't hold a constant viscosity across different shear rates the way water or oil does. Every result closes with a reminder of the unit trap in this topic: pascal-seconds versus poise, where mixing the two systems without converting produces an answer off by a factor of ten.
Run it in the Dock Editor to keep the worked solution with your notes, or paste it into ChatGPT, Claude, or Gemini. Viscosity feeds directly into flow classification, covered by the Reynolds number formula solver.
Copy this into ChatGPT, Claude, Gemini, or the Dock Editor, then set [MODE] to checking your own scenario or generating a new one, and set [FLUID_TYPE] to Newtonian or a note on non-Newtonian behavior.
In check mode, fill in [MY_WORK] with the velocity difference between two adjacent fluid layers, the distance separating them, and either the viscosity or shear stress you calculated.
The velocity difference divided by the layer separation is calculated as its own explicit line before it's multiplied or divided against viscosity, so the gradient itself is never buried.
In check mode, your answer gets compared against an independent calculation, with any divergence, like an inverted gradient or a units mismatch, named specifically.
Every result closes with a note on pascal-seconds versus poise, since mixing those two viscosity unit systems without converting is a common source of an answer off by a factor of ten.
Check homework answers on Newton's law of viscosity with the velocity gradient calculated as its own explicit step.
Practice fresh viscosity scenarios for Newtonian fluids like water and oil before an exam, with a full worked answer key each time.
Generate a worked scenario as a model answer, ready to hand a student who's confusing fluid speed with the velocity gradient.
Understand where non-Newtonian fluids break the assumptions behind this formula before studying more advanced viscosity models.
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