Experiment to find the fluid resistance on a ball bearing falling through glycerine

Cosmina Oyolola GCSE C

Experiment to find the fluid resistance on a ball bearin falling through glycerine

Planning

Aim

In this experiment I want to investigate the terminal velocity of the ball bearings that are falling through glycerine and the viscosity of the liquid.

Prediction

I predict that the as the balls fall through glycerine, their acceleration will decrease until they will reach their terminal velocity, (due to fluid resistance) and after that they will travel with a constant velocity, because the opposing forces balance.

The bigger the ball, the longer time it needs to reach its terminal velocity, so it will take less time to fall through the fluid than a small ball.

I measured the density of glycerine with a gravity hydrometer and using Stokes’ law I want to find out the viscosity of glycerine.

According to Stokes’ law, ‘when a sphere is falling under streamlined conditions, terminal velocity has the following formula:

(ρs – ρ1)g

Vt = 2r2 9η

In this formula ‘ρs, ρ1 and η are the density of solid, the density of liquid and viscosity of liquid, respectively’.

Another way to calculate, also shown by Stokes, is to find the frictional force which equals: F = 6Πaηv, where a (cm) is the radius of the sphere, η is the coefficient of viscosity (poises) and v (cm/s) is the velocity.

‘When the sphere reaches a constant velocity then F balances the weight of the sphere less the upthrust of the liquid on it.’

mg( 1- ρ ) = 6Πaηv , where ρ is the density of steel and σ is the density of glycerine.

Speed is the distance travelled on time taken. Velocity is the speed of an object in a specific direction.

The viscosity of a fluid is its resistance to flow; the easier the fluid flows, the lower is its viscosity.

“Archimede’s Principle says that the upthrust is always equal to the weight of fluid displaced. A body in water experience an upthrust equal to the weight of the water it displaces. If the upthurst equals the weight of the body, the object does not sink.”

The hydrometer uses this principle to measure the density of a liquid, which is given ‘by the level of the liquid on the float’, then the density is read off the scale.

To find out the density of glycerine I used a hydrometer and I wrote down the value.

I found the density of steel on National Physics Laboratory web site address; steel density = 8.0 gcm-3

I also base my experiment on Newton’s third law of motion: ‘to every action there is an equal and opposite reaction’.

Ball bearings that fall through a fluid accelerate initially due to the force of gravity, but as the balls fall the fluid resistance increases until it balances the gravitational force. When the resultant forces are balanced, the balls fall at their terminal velocity.

Terminal velocity is reached when a ‘falling object stops accelerating and continue to fall at a constant speed, due to balance between gravity on air resistance’ (in my experiment fluid resistance). When this happens the resultant force is equal to zero, because the opposing forces are balanced.

The terminal velocity depends on the size of the fluid resistance force, the shape of the object and its mass.

I used ball bearings because due to their shape the fluid resistance is smaller than it would be with some other shape.

After that I have to calculate the viscosity of glycerine.

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