Physics
Viscosity
Viscosity
11
⚡ Quick Summary
Viscosity is a fluid's resistance to flow, like internal friction. It opposes the relative motion between different layers of the fluid.
[]
When a layer of fluid slips or tends to slip on another layer in contact, the two layers exert tangential forces on each other. The directions are such that the relative motion between the layers is opposed. This property of a fluid to oppose relative motion between its layers is called viscosity. The forces between the layers opposing relative motion between them are known as the forces of viscosity. Thus, viscosity may be thought of as the internal friction of a fluid in motion. If a solid surface is kept in contact with a fluid and is moved, forces of viscosity appear between the solid surface and the fluid layer in contact. The fluid in contact is dragged with the solid. If the viscosity is sufficient, the layer moves with the solid and there is no relative slipping.
Viscous Force and Terminal Velocity
11
⚡ Quick Summary
When a body moves through a fluid, it experiences a viscous force proportional to its velocity. As a body accelerates in a fluid, the viscous force increases until it balances the net force due to weight and buoyancy. At this point, the body reaches a constant velocity called the terminal velocity.
['F = k r v η (General form of viscous force)', "F = 6π η r v (Stokes' Law for viscous force on a sphere)", 'v0 = (2 r^2 (ρ - σ) g) / (9 η) (Terminal velocity of a sphere)']
- Viscous Force: The force experienced by a body moving through a fluid, proportional to its velocity.
- Terminal Velocity: The constant velocity attained by a body falling through a fluid when the viscous force equals the net force due to weight and buoyancy.
- Stokes' Law: For a sphere moving through a fluid, the viscous force is given by F = 6πηrv, where η is the coefficient of viscosity, r is the radius of the sphere, and v is the velocity.
Measuring Coefficient of Viscosity by Stokes' Method
11
⚡ Quick Summary
Stokes' method determines the viscosity of a liquid by measuring the terminal velocity of a sphere falling through it. The apparatus involves a test tube containing the liquid, a water bath for temperature control, and markings to measure the time taken by the sphere to travel specific distances.
[]
- Apparatus:
- Test tube (A) containing the experimental liquid.
- Water bath (B) to maintain temperature.
- Thermometer (T) to measure the temperature of the bath.
- Tube (C) to drop the sphere.
- Equidistant marks (P, Q, R) on the test tube.
- Procedure:
- Drop a spherical metal ball into the tube C.
- Measure the time taken by the ball to pass through lengths PQ and QR.
- If the times are equal, the ball has reached terminal velocity.
Viscous Force
11
⚡ Quick Summary
Viscosity is the resistance of a fluid to flow. The tangential force required to maintain a constant speed of a plate moving on a fluid is related to the viscosity, area of the plate, and velocity gradient.
η = (F/A) / (dv/dx)
The viscous force is related to the coefficient of viscosity η, area A, and velocity gradient dv/dx by the formula η = (F/A) / (dv/dx), where F is the tangential force and dv/dx is the velocity gradient.
Shearing Stress in Fluids
11
⚡ Quick Summary
Shearing stress between horizontal layers of fluid is related to the viscosity and the velocity gradient.
τ = η (dv/dx)
The shearing stress is given by τ = η (dv/dx), where η is the coefficient of viscosity and dv/dx is the velocity gradient.
Viscosity
11
⚡ Quick Summary
Viscosity is a measure of a fluid's resistance to flow.
N/A (Conceptual understanding is key)
Viscosity describes a fluid's internal resistance to flow. A fluid with high viscosity resists motion because of its strong intermolecular forces. Viscosity is often denoted by the symbol η (eta). The unit of viscosity is poise (P) or Pascal-second (Pa·s).