Does Shear Stress Act in the Direction of Motion for a Downward Moving Plate?

[snakeshadowx]

Homework Statement

A submersed, vertical plate is moving downward. The positive coordinate is downward. Mass is M (per unit area). Shear stress is [tex]\tau[/tex]_w.

Homework Equations

[tex]\Sigma[/tex]F = 0

The Attempt at a Solution

I have [tex]\Sigma[/tex]F = Mg - 2*[tex]\tau[/tex]_w = 0.
(2 for the two sides of the plate)(using unit area, so the shearing term is actually a force).

However, the solutions have Mg + 2*[tex]\tau[/tex]_w = 0. Is the shear stress acting the same direction of the motion? I'm confused.

 

[mark726]

The shear stress is acting in the opposite direction of the motion. This is because the shear stress is caused by the fluid flowing past the plate, and the direction of the shear stress is always perpendicular to the direction of the flow. In this case, the flow is downward, so the shear stress is acting upward on the plate. Therefore, the correct equation is Mg + 2*\tauw = 0.