In steady laminar flow, the fluid velocity between the plates varies linearly between 0 and V, and thus the velocity profile and the velocity gradient are: The fluid in contact with the lower plate assumes the velocity of that plate, which is zero (because of the no-slip condition). Note that the fluid layer deforms continuously under the influence of shear stress. Where A is the contact area between the plate and the fluid. The fluid in contact with the upper plate sticks to the plate surface and moves with it at the same velocity, and the shear stress τ acting on this fluid layer is: After the initial transients, it is observed that the upper plate moves continuously under the influence of this force at a constant velocity V. Now a constant parallel force F is applied to the upper plate while the lower plate is held fixed. To obtain a relation for viscosity, consider a fluid layer between two very large parallel plates (or equivalently, two parallel plates immersed in a large body of a fluid) separated by a distance L. The magnitude of the drag force depends, in part, on viscosity. The coefficient of viscosity is a proportionality constant that is unique for each material. The symbol μ is used to represent the coefficient of viscosity, also called the viscous coefficient, dynamic viscosity of a fluid, and absolute viscosity of a fluid. This discussion is limited to dynamic viscosity. Viscosity may be known as either dynamic (absolute) viscosity or kinematic viscosity. For example, the viscosity of oil is higher than that of water, the oil is more viscous than the water. Viscosity represents the internal resistance of a fluid to motion.
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