Shear Stress in Fluid Flow formula |
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| \( \tau \;=\; \mu \cdot \dfrac{ du }{ dy } \) | ||
| Symbol | English | Metric |
| \( \tau \) (Greek Symbol tau) = Shear Stress in Fluid Flow | \(lbf \;/\; ft^2\) | \(Pa\) |
| \( \mu \) (Greek symbol mu) = Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \(Pa-s \) |
| \( \dfrac{ du }{ dy } \) = Velocity Gradient Perpendicular to the Direction of Flow | \(ft\;/\;sec\) | \(m\;/\;s\) |
Shear stress in fluid flow, abbreviated as \(\tau\), is a measure of the force per unit area exerted by a fluid as it flows, resulting from the interaction between adjacent layers of the fluid moving at different velocities. When a fluid flows, its layers experience relative motion, creating a tangential force due to the fluid's viscosity, which resists this relative motion. In simpler terms, shear stress arises because faster-moving layers of fluid drag against slower-moving layers, generating internal friction.
For example, in a pipe, fluid near the walls moves slower due to friction with the wall, while fluid in the center moves faster, creating a velocity gradient that produces shear stress. This concept is critical in understanding fluid behavior in applications like pipelines, aerodynamics, and blood flow, as it influences energy losses, drag forces, and the design of systems involving fluid transport. The magnitude of shear stress depends on the fluid's viscosity and the flow conditions, with Newtonian fluids exhibiting a linear relationship between shear stress and shear rate, while non-Newtonian fluids may show more complex behavior.
