# Investigating the viscosity of liquids.

Investigating the viscosity of liquids.

Introduction:

All liquids stick to a solid surface so that their velocity gradually decreases to zero as the wall of the pipe or the container is approached. A fluid is therefore sheared when it flows past a solid surface, and the opposition force set up by the fluid is called its viscosity. The speed of flow of liquids is dependent on their viscosity, which controls their resistance to flow. Viscosity can be explained as  internal friction exhibited to some degree by all fluids. A property of a fluid which tends to prevent it from flowing. It arises in liquids because the movement of a molecule relative to neighbouring molecules is opposed by intermolecular forces between them. This resistance acts against the motion of any solid object through the fluid or against motion of the fluid itself past stationary obstacles. Viscosity also acts internally on the fluid between slower and faster moving adjacent layers. High-viscosity fluids have higher resistance to flows and low-viscosity fluids have lower resistance to flows. Generally speaking, the lower the viscosity of a fluid, the ‘runnier’ it is (such as water) and the higher the viscosity of a fluid, the ‘thicker’ it is (such as and syrup).

Measuring Viscosity using Stokes’ law:

It has been decided to use the falling sphere viscometer, in order to find the viscosity or liquids during this investigation. It involves timing a sphere falling at terminal velocity through a fluid. From stokes findings, he was able to quantify viscosity by studying the force exerted on a spherical object as it moves through a fluid. This force is known as the viscous drag force and is described by the relationship known as Stokes’ law:

F = 6πrηv

r is the radius of the sphere, v the terminal velocity of the fluid relative to the sphere, and η the coefficient of viscosity of the fluid (or more commonly known as the viscosity). Viscous drag acts in the opposite direction of travel of the sphere and this force would not exist if the is stationary, equal to how friction works. Now if we rearrange the formula so that it is in terms of η, then would see that it becomes:

η = F / 6πrv

Since 6 and π are constants, the units of viscosity becomes Nsm-2. When a sphere travel down a viscometer tube with a fluid, there are two other forces acting on the sphere as well as the viscous drag. There is also the upthrust or buoyancy force that acts upwards, and the weight of the mass due to gravity that acts downwards as show in the diagram below:

## This can be related to a real life situation, where a skydiver jumps off his plane. The theory of viscous drag can be used to explain ‘air resistance’. When the skydiver first jumps off the plane, he will first accelerate due to a net downward force, where the weight of the skydiver being much greater than the upthrust. But he also experiences a viscous drag force from the air which increases as speed increases. Therefore the net downward force is reduced as speed increases, and eventually when the viscous drag and upthrust balances the weight of the person, the net force reaches zero and the skydiver no longer accelerates. At this moment, the person falls at constant downward velocity or terminal velocity. Terminal velocity will be important in the experiment when the viscosity of glycerol.

The velocity of the falling ball bearing will be measured while the ball bearing reaches terminal velocity, as the velocity of the ball bearing can be simply measured through: speed = distance/ time. Moreover, during constant speed, the net forces acting on the ball bearing is zero, and the following equation is valid and can be applied:

### Upthrust (U)                +        Viscous Drag (F)                =        Weight (W)

4πr3ρfluidg / 3                                6πrηv                        =        4πr3psteel g / 3

r is the radius of the sphere, ρfluid is the density of water, ρsteel is the density of steel, and v is the terminal velocity at which the sphere travels ...