Newton's Parallel Plate Experiment

In this experiment, the apparatus consists of two horizontal parallel plates with a sufficiently large spacing (h) between them. The space is filled by a fluid. Now the top plate is moved with a velocity, U. The distance in the fluid affected by the motion of the upper plate is denoted by . The distance is the penetration depth in the fluid arising from a disturbance on its boundary (the plate movement).The force required to sustain the plate motion is given by,

Now can be approximated as (which you will learn in later chapters). Here is coefficient of momentum transport (kinematic viscosity) that determines the extent of motion transport in a stationary fluid medium. The kinematic viscosity ( ) is related to dynamic viscosity ( ) as

where is the density of the fluid.

So, we can approximate as (upon considering the fluid incompressible). Hence, the force required can be reframed as,

So, this experiment can be used to calculate the coefficient of dynamic viscosity of a fluid for a given value of density of the fluid , velocity of the plate, U and the area of the plate, A and the force applied, F.

                                   u(y) is the velocity profile along the y-axis.