# What is Newtonian fluid: Definition and 13 Discussions

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly correlated to the local strain rate—the rate of change of its deformation over time. That is equivalent to saying those forces are proportional to the rates of change of the fluid's velocity vector as one moves away from the point in question in various directions.
More precisely, a fluid is Newtonian only if the tensors that describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow. If the fluid is also isotropic (that is, its mechanical properties are the same along any direction), the viscosity tensor reduces to two real coefficients, describing the fluid's resistance to continuous shear deformation and continuous compression or expansion, respectively.
Newtonian fluids are the simplest mathematical models of fluids that account for viscosity. While no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions. However, non-Newtonian fluids are relatively common, and include oobleck (which becomes stiffer when vigorously sheared), or non-drip paint (which becomes thinner when sheared). Other examples include many polymer solutions (which exhibit the Weissenberg effect), molten polymers, many solid suspensions, blood, and most highly viscous fluids.
Understanding whether a fluid is Newtonian or not is important in certain industrial processing industries including food processing and pharmaceutical manufacturing. In these industries, the nature of the fluid being processed, and whether or not its viscosity changes when exposed to force, can affect product attributes such as texture, taste, and appearance.Newtonian fluids are named after Isaac Newton, who first used the differential equation to postulate the relation between the shear strain rate and shear stress for such fluids.

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1. ### Frame indifference and stress tensor in Newtonian fluids

During lecture today, we were given the constitutive equation for the Newtonian fluids, i.e. ##T= - \pi I + 2 \mu D## where ##D=\frac{L + L^T}{2}## is the symmetric part of the velocity gradient ##L##. Dimensionally speaking, this makes sense to me: indeed the units are the one of a pressure...
2. ### Shear and the stress tensor of a Newtonian fluid

Similarly the paper by @buchert and @ehlers https://arxiv.org/abs/astro-ph/9510056 Here the author has defined ##v_{ij}=\frac{\partial v_i}{\partial x_j}=\frac{1}{2}(\frac{\partial v_i}{\partial x_j}+\frac{\partial v_j}{\partial x_i})+\frac{1}{2}((\frac{\partial v_i}{\partial...
3. ### Non Newtonian / Newtonian Fluid interface

Suppose I have a wave tank partially filled with a shear thickening Newtonian fluid (Oobleck), on top of which sits a layer of water (separated by a thin membrane to prevent mixing) If I propagate a surface wave in the water layer how will it conduct itself at the Newtonian/Non Newtonian Fluid...
4. E

### B Liquid Flow Calculation out of a pressurized tank

I am an engineer who needs to help my chemical transport girl friend with a little basic physics. It has been about 35 years since basic physics for me so I am rusty. She wants to understand how to calculate the following: She drives a large tanker (cylindrical) which carries a variety of...
5. ### Energy conservation for a Newtonian fluid?

Homework Statement ρ= density, vi = i-th velocity component, gi=i-th component of gravity vector, p=pressure, μ= viscosity, D/Dt = material derivative Homework Equations Continuity equation: div v = 0 The Attempt at a Solution
6. ### Basic Fluids Viscosity question

1. piston having a diameter of D = 5.48 in. and a length of L = 9.50 in. slides downward with a velocity V through a vertical pipe. The downward motion is resisted by an oil film between the piston and the pipe wall. The film thickness is δ = 0.002 in., and the cylinder weighs W = 0.5 lb...
7. ### Newtonian fluid in compressible flow?

When compressible effects are accounted for, viscosity should vary with temperature. Doesn't this violate the concept of Newtonian fluids, where shear stress is linearly proportional to the strain rate?
8. ### Newtonian fluid mechanics: Navier-Stokes equation

Homework Statement Homework Equations Navier-Stokes The Attempt at a Solution Not really trying to solve a problem, trying to understand what is going on in my textbook. So look at the stuff in red first. I see where all that is coming from, it's clear to me. However, the stuff in green...
9. ### Relation between Cooling rate and Viscosity in Newtonian fluid

Relation between Cooling rate and Viscosity Hi all I have a situation where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. This means, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature...
10. ### Calculating Shearing Stress in a Newtonian Fluid

Homework Statement The velocity distribution for the floe of a Newtonian fluid between 2 wide parallel plates is given by the equation u=3V/2[1-(y/h)^2] where V is the mean velocity. The fluid has a viscosity of 1.915Ns/m^2. When V=0.61m/s and h=5mm, determine: A) the shearing stress acting on...
11. ### Solving Non-Steady Flow of Newtonian Fluid in Circular Pipe

I am to find the velocity distribution where there is non steady flow of a Newtonian fluid in a circular pipe. I did a mass and momentum balance around the system and ended up with the following equation: dp/ds = 4 + 1/e*d/de(e*dp/de) The derivatives in the equation are partial derivatives the...
12. ### Factors that affect viscosity of incompressible Newtonian fluid?

What are the factors that affect viscosity of incompressible Newtonian fluid? Here is what I think: Temperature: When we increase the temperature of a fluid (controlled volume) the frequency ofintermoleculer collisions increases. Does this mean viscosity decreases? And if so, does...
13. ### Flow of a Newtonian fluid down an inclined plane.

I'm basically reading on how the velocity profile is found for a laminar flow of a Newtonian fluid down an inclined plane surface. (x is along the incline, y is perpendicular to the incline) The assumptions being made are - The fluid is Newtonian - It's laminar - It's fully developed - It's...