Final answer:
In Figures 12.12 and 12.13, a Newtonian fluid's viscosity is measured by the force required to keep a top plate moving at a constant velocity, which is influenced by the velocity, plate area, distance between plates, and the fluid's coefficient of viscosity.
Step-by-step explanation:
The concept of viscosity and how it is measured involves understanding the behavior of a Newtonian fluid confined between two parallel plates. If we consider Figure 12.12 or Figure 12.13, for instance, they show that a Newtonian fluid is placed between two plates of area A, where the bottom plate is fixed, and the top plate is moved horizontally. This motion drags the fluid with it, illustrating the principle of laminar flow. The fluid layers move at different speeds, with the top layer moving at speed v due to the motion of the plate, while the layer in contact with the stationary bottom plate remains at rest, creating a gradient of velocities in the fluid from v to 0.
To maintain a constant velocity v of the top plate, a force F is required, and this force is dependent on certain parameters: it is directly proportional to the velocity v, the area A of the moving plate, and the coefficient of viscosity n, while being inversely proportional to the distance L between the plates. This relationship is crucial in understanding how viscosity affects the flow of fluids and how external forces interact with fluid dynamics.