For a given fluid and a given distance between plates in a system like that shown in Fig. 4.5, velocity ν₀ must be large enough to counteract the effect of gravity; other- wise, some of the fluid will flow downward. In a particular system, the distance between plates is 1 mm, and the fluid is an oil with a density of 900 kg/m³ and a viscosity of 50 mPa-s. The pressure drop dp/dy is negligible compared with the term ρg.

Fig. 4.5

(a) What is the minimum upward velocity of the moving plate so that all the fluid moves upward? 

(b) If ν₀ is set at this minimum value, what is the fluid velocity midway between the plates?

(c) What is the shear rate in the fluid at the stationary plate, at the moving plate, at the midway plate, and midway between them? Use the equations in Example 4.3.

Example 4.3

 A newtonian fluid is confined between two broad parallel vertical plates, separated by a distance B. as shown in Fig. 4.5. The plate on the left is stationary; that on the right is moving vertically upward at a constant velocity ν_0. Assuming that the flow is laminar, find the equation for the steady-state velocity profile in the fluid. 

 

Transcribed Image Text:

8 FIGURE 4.5 Flow between vertical plates in Example 4.3.