Fluid Properties

Fluid Properties

1. Viscosity - a measure of the importance of friction in fluid flow.

   • Consider a fluid in 2-D steady shear between two infinite plates. The bottom plate is fixed, while the upper plate is moving at a steady speed of V.
     • The velocity profile, u(y) is linear, i.e. u(y) = Vy/h. Also notice that the velocity of the fluid matches that of the wall at both the top and bottom walls. This is known as the no slip condition.
       • The top plate will experience a friction force to the left, since it is doing work trying to drag the fluid alongto the right. The fluid at the top of the channel will experience an equal and opposite force. Similarly the bottom plate will experience a friction force to the right, since the fluid is trying to pull the plate along with it to the right.
       • The fluid at the bottom of the channel will feel an equal and opposite force to the left. In fluid mechanics, shear stress, defined as a tangential force per unit area, is used rather than force itself. Define τ (Greek letter "tau") as the friction force per unit area acting on the fluid
         • In a simple 2-D shear flow such as this, the shear stress is directly proportional to the slope of the velocity profile. In fact, the constant of proportionality is the coefficient of viscosity itself! Mathematically,

2. A block of weight W is sliding down an incline at constant speed V on a thin film of oil of thickness h, as sketched. Find the speed (v)

   • From simple trig, sum the forces in both x and y and set the net force to zero (this is a statics problem since the block is moving at constant speed).
     • A magnified view of the oil film reveals that it is locally the same as our simple shear between plates problem. Thus, the x component of velocity, u is given by u(y) = Vy/h. We also know that for simple 2-D shear
       • Finally, the total viscous force is equal to the shear stress times the surface area, A, in contact between the fluid and the bottom surface of the plate. Therefore

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