Shear stress is defined as

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Consider the expression for shear stress in a Newtonian fluid. The question asks for the defined form of shear stress with respect to a velocity gradient perpendicular to the direction of flow. In Newtonian fluids, shear stress tau is proportional to the rate of shear strain, which in common Cartesian coordinates is the derivative of the streamwise velocity with respect to the transverse coordinate, dU/dy, multiplied by the dynamic viscosity mu. Therefore, tau equals mu times dU/dy. This relationship encapsulates the linear stress–strain behavior characteristic of Newtonian fluids, where mu is constant for a given temperature. Other possible statements that one might confuse with shear stress include ideas like tau depending on pressure, normal stresses, or gravitational terms; those do not describe shear stress in a Newtonian fluid and would involve different physical quantities or assumptions. Since the provided option directly aligns with the standard constitutive equation for Newtonian shear stress, it correctly expresses the relationship tau = mu dU/dy. The form also implies that if either the viscosity mu or the velocity gradient dU/dy is zero, the shear stress vanishes, which matches physical intuition for no deformation or a quiescent flow. Additionally, the equation inherently assumes a constant viscosity and a unidirectional, steady shear between planes separated by a small distance in the y-direction, reinforcing its domain of applicability in laminar shear flows such as simple Couette flow.

BH40A1401 Fluid Mechanics I - Contact teaching, Lappeenranta 6.1.2025-23.2.2025 Quiz 1

Shear stress is defined as

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