Derive an expression for coefficient of viscosity?
Derive an expression for coefficient of viscosity?
Consider a liquid column of height L between the two plates of the contact area of A with the liquid. The upper plate is being pulled by a force F which produces a velocity v as shown in the figure below:
* F is proportional to the area A of the plate. This relationship holds good, since A is directly proportional to the amount of fluid being moved.
* For a given area, greater speeds require larger forces. So the force F is proportional to the speed (v).
* The force is also inversely proportional to the perpendicular distance L between the top and bottom plates (F varies with 1/L). The larger the distance L, the smaller is the force required to achieve a given speed with a given contact area. L is like a lever arm, and the greater the lever arm, the less force that is needed.
And F is directly proportional to the viscous nature of the fluid or coefficient of viscosity, η (eta). The greater the viscosity, the greater the force required to move the fluid.
These 4 dependencies are combined into the equation
F = ηvA /L ………………….(1), which gives us a working definition of fluid viscosity η .
Solving for η, which is called the coefficient of viscosity or simply the viscosity, gives
η= FL/vA ………………………(2)
which defines viscosity in terms of how it is measured. The SI unit of viscosity is N⋅m/[(m/s)m2]=(N/m2)s or Pa⋅s.
From equation 1, we can say that the effort required to move a fluid (like pouring) depends on its viscous nature, labelled by η or coefficient of viscosity.
Consider a liquid column of height L between the two plates of the contact area of A with the liquid. The upper plate is being pulled by a force F which produces a velocity v as shown in the figure below:
* F is proportional to the area A of the plate. This relationship holds good, since A is directly proportional to the amount of fluid being moved.
* For a given area, greater speeds require larger forces. So the force F is proportional to the speed (v).
* The force is also inversely proportional to the perpendicular distance L between the top and bottom plates (F varies with 1/L). The larger the distance L, the smaller is the force required to achieve a given speed with a given contact area. L is like a lever arm, and the greater the lever arm, the less force that is needed.
And F is directly proportional to the viscous nature of the fluid or coefficient of viscosity, η (eta). The greater the viscosity, the greater the force required to move the fluid.
These 4 dependencies are combined into the equation
F = ηvA /L ………………….(1), which gives us a working definition of fluid viscosity η .
Solving for η, which is called the coefficient of viscosity or simply the viscosity, gives
η= FL/vA ………………………(2)
which defines viscosity in terms of how it is measured. The SI unit of viscosity is N⋅m/[(m/s)m2]=(N/m2)s or Pa⋅s.
From equation 1, we can say that the effort required to move a fluid (like pouring) depends on its viscous nature, labelled by η or coefficient of viscosity.
