Write the mathematical expression for viscous force. What does the negative sign indicate in the viscous force expression?
Answers
Answer:
Informally, viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them.
Formally, viscosity (represented by the symbol η "eta") is the ratio of the shearing stress (F/A) to the velocity gradient (∆vx/∆z or dvx/dz) in a fluid.
η = F/A
∆vx/∆z
or
η = F/A
dvx/dz
The more usual form of this relationship, called Newton's equation, states that the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton's second law of motion (F = ma) should be apparent.
F = η ∆vx
A ∆z
⇔
F = m ∆v
∆t
Or if you prefer calculus symbols (and who doesn't)…
F = η dvx
A dz
⇔
F = m dv
dt