Density, upthrust and viscosity

Density equation

ρ = m/V

How does the density determine whether an object floats

An object will float in a fluid it is less dense than

Normal pressure equation

p = F/A

Pressure in a fluid equation

p = hρg

Explain why upthrust occurs

The upward force on the bottom of an object submerged in a fluid is greater than the downward force on the top of an object submerged in a fluid, so the resultant force is upwards

Explain why the upwards force below an object submerged in a fluid is greater than the downwards force above that object

There is a greater weight of fluid at the bottom, so the pressure in all directions is increased, including upwards

Archimedes principle

When a body is completely or partially immersed in a fluid, it experiences an upthrust equal to the weight of the fluid it has displaced

Viscous drag

Friction between the surface of an object and a fluid as one of them is in motion

What does Stoke’s law tell you

The force due to viscous drag

Stoke’s Law equation

F = 6πηrv

What does the η symbol mean

Viscosity of the fluid

η units

Nsm^-2

How does increasing temperature affect the viscosity of a liquid

Decreases

How does increasing temperature affect the viscosity of a gas

Increases

Laminar flow

All the parts of a fluid are flowing in the same direction such that the layers do not mix

When does laminar flow occur

When a fluid is flowing slowly or an object is moving slowly through a fluid

Turbulent flow

The layers of a fluid are moving in different directions such that the layers mix

When does turbulent flow occur

A fluid is flowing quickly or an object is moving quickly through a fluid

What does Stoke’s Law apply to

Small, spherical objects moving slowly with laminar flow

Experiment to measure the viscosity of a liquid

1- Drop a ball bearing of known radius and density ρ down a column of liquid of known density σ.

2- There is a series of 3 rubber bands near the bottom of the column at a measured distance apart. When the ball bearing reaches the first at terminal velocity, start a stop watch to calculate the time between the 1st and 2nd and 2nd and 3rd.

3- Repeat with different sized balls.

4- Calculate separate velocity with d/t and find the average for each measurement. Then, calculate viscosity with η = (2r²g(ρ-σ))/9v

Explain how the viscosity equation in the ball bearing experiment can be derived

At terminal velocity F_grav = F_upthrust + F_drag

How should the ball bearing be retrieved from the bottom of the column of liquid

A magnet

Explain why the ball bearing should not fall too close to the wall in the viscosity experiment

The flow will no longer be laminar, so Stoke’s law no longer applies

Explain how submarines float and sink

Large tanks are filled with water to increase weight so it exceeds upthrust to sink. The tanks are filled with compressed air to reduce weight to rise