Shear Force
Shear force is employed for a viscometry experiment. Admittedly, the
connection between the simple model given below, and the viscosity
experiment is not obvious. The model below is shown to illustrate
the math for change in velocity with respect to change in y axis
coordinate.
The above illustration shows equally sized plates, one on top of the
other, and a shear force causes the green plate to slide in the
x direction a certain distance--call it 'd'. The yellow plate travels
2d, the orange plate travels 3d, and the red plate travels 4d. The
blue plate doesn't move with respect to the frame of reference.
With respect to the y axis, we set blue to be at y=0. The green
is at y=1, the yellow at y=2, the orange at y=3 and the red at y=4.
This leaves us with the following table of information:
|
| blue
| | x=0
| | y=0
| | y / x = 0
|
|
| green
| | x=d
| | y=h
| | y / x = h/d
|
|
| yellow
| | x=2d
| | y=2h
| | y / x = h/d
|
|
| orange
| | x=3d
| | y=3h
| | y / x = h/d
|
|
| red
| | x=4d
| | y=4h
| | y /x = h/d
|
|
From this we observe a correlation between position on the y axis, and the
distance travelled along the x-axis.
If we are taking observations with respect to time, then we recall that
that change in distance with respect to time is velocity, and we can
say that the shear force causes a velocity on the red plate twice
that of the velocity produced on the yellow plate (and the velocity of the
blue plate is zero.) The change in velocity as you move up the y-axis
relates to the change in velocity through a constant.
Delta velocity
-------------- = velocity gradient (also called the 'rate of shear')
Delta y
Last Update- August 31, 1995- wld