Name: newtonian fluid viscosity and shear stress
Uploaded: 2025-02-13T15:43:08.000Z
Duration: 1 min 18 s
Channel: JoVE

A Newtonian fluid has a constant viscosity, meaning the shear stress is directly proportional to the rate of shear strain.
This behavior ensures the fluid responds predictably to applied forces, maintaining a linear relationship between force and flow.
Water, air, and light oils are examples of such fluids, all of which maintain proportionality regardless of the conditions.
Consider a fluid situated between two parallel plates. The upper plate moves constantly, while the lower plate remains stationary.
Given the fluid&#39;s viscosity, the velocity of the moving plate, and the distance between the two plates, the shear stress acting on the stationary lower plate must be determined.
The velocity gradient is determined to calculate the shear stress. The velocity gradient represents the rate of change of the fluid&#39;s velocity from the stationary plate to the moving one.
Once the velocity gradient is known, the shear stress is calculated by multiplying it by the fluid&#39;s viscosity.
The shear stress on the lower plate illustrates the predictable behavior of a Newtonian fluid.

newtonian fluid: problem solving

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with one plate stationary and the other moving at a constant velocity. This gradient represents the rate of change of velocity across the distance separating the plates.
<img alt="Fluid dynamics equation, du/dy=V/h, showing velocity gradient in theoretical analysis." src="/files/ftp_upload/18003/18003_Equation_1.svg" style="text-align: center; height: 35px;" data-altupdatedat="1762173717000" data-alt="Equation 1" />
The shear stress on the stationary plate depends on this velocity gradient and the fluid's viscosity. The velocity of the moving plate is divided by the distance between the plates to determine the velocity gradient. Multiplying the velocity gradient by the fluid's viscosity provides the shear stress acting on the stationary plate.
<img alt="Viscosity formula &#964;=&#956;(du/dy), static equilibrium, fluid dynamics equation." src="/files/ftp_upload/18003/18003_Equation_2.svg" style="text-align: center; height: 48px;" data-altupdatedat="1762173717000" data-alt="Equation 2" />
This calculation highlights the predictable nature of Newtonian fluids, as their constant viscosity ensures the shear stress accurately reflects the applied conditions.
This proportional relationship between shear stress and shear strain rate is fundamental in various applications, including lubrication, fluid transport, and hydraulic systems. Newtonian fluids' behavior allows for precise control and predictable performance in systems that rely on stable and consistent flow characteristics. Their unchanging viscosity under varying conditions makes them indispensable in engineering and scientific applications requiring reliability and precision.

A Newtonian fluid has a constant viscosity, meaning the shear stress is directly proportional to the rate of shear strain.
This behavior ensures the fluid ...

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JoVE Core

Civil Engineering

Unit 1

Fluid Properties

KEY TERMS AND CONCEPTS

newtonian fluid viscosity and shear stress

Newtonian fluids have a constant viscosity, so their shear stress and shear strain rate stay directly proportional. This creates a linear, predictable link between force and flow. Water, air, and light oils are common examples of Newtonian fluids.

A simple way to study this behavior is to place the fluid between two parallel plates. One plate stays still, and the other moves at a constant velocity. The fluid forms a velocity gradient, which is the change in speed across the distance between the plates.

The shear stress on the stationary plate depends on that velocity gradient and the fluid’s viscosity. The velocity of the moving plate is divided by the distance between the plates to find the velocity gradient. Then the gradient is multiplied by the viscosity to calculate the shear stress on the stationary plate.

This relationship shows why Newtonian fluids are so predictable. Their constant viscosity means the shear stress matches the applied conditions in a stable way. That is why they are useful in lubrication, fluid transport, and hydraulic systems. Their steady flow behavior supports precise control and reliable performance in engineering and science.

Newtonian Fluid Viscosity and Shear Stress

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Newtonian fluids have a constant viscosity, so their shear stress and shear strain rate stay directly proportional. This creates a linear, predictable link between force and flow. Water, air, and light oils are common examples of Newtonian fluids. A simple way to study this behavior is to place the fluid between two parallel plates. One plate stays still, and the other moves at a constant velocity. The fluid forms a velocity gradient, which is the change in speed across the distance between...

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key terms and concepts

Explore how Newtonian fluids keep constant viscosity and show a linear link between shear stress and flow. Learn the plate model, gradient, and examples.

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Newtonian Fluid Viscosity and Shear Stress

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