Maximum and minimum velocities

The quantitative description of non-dimensional velocity distribution across the channel, depicted by Eq. (26.2a), is shown

in Fig. 26.2b.

• The location of maximum or minimum velocity in the channel is found out by setting =0. From Eq. (26.2a), we can write

Setting gives

26.2b

• It is interesting to note that maximum velocity for P = 1 occurs at y/h = 1 and equals to U . For P > 1, the maximum velocity occurs at a location .
• This means that with P > 1, the fluid particles attain a velocity higher than that of the moving plate at a location somewhere below the moving plate.
• For P = -1, the minimum velocity occurs,  at . For P < -1,  the minimum velocity occurs at a location .
• This means that there occurs a back flow near the fixed plate. The values of maximum and minimum velocities can be determined by substituting the value of y from Eq. (26.2b) into Eq. (26.2a) as

(26.2c)

FIG 26.2b - Velocity distribution of the Couette flow