14.5 : 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.

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.

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.