How do Pressure Gauges Work?

The pressure at both points A and B is the same since both have the same amount of atmosphere above them. The glass tube, which contains a column of mercury, protects the top of the column from feeling the pressure of the atmosphere. The very top of the column is approximately empty.

We measure the height of the mercury column and find it to be some number h. Remember from last lecture we found:

P2

� P1

�

pgh

Since there essentially no gas above the column in the tube, P1 = 0. This means the pressure of the atmosphere, P2 is directly proportional to the height of the mercury column (you know both ρ and g).

Pascal's Principle

Book's definition:Any change in the pressure applied to a completely enclosed fluid is

transmitted undiminished to all parts of the fluid and the enclosing walls.

Translation: If you have a fluid contained in some way so there is not a volume of

gas trapped in the container, then whatever pressure the fluid provides to one part of the container, it provides to all parts of the container.

This is a very useful idea and is the principle behind hydraulic cylinders!

Pascal's Principle (2)

Remember that pressure is a force per area. Also remember Pascal's Principle states the pressure on the sides of the container (including the two pistons) is uniform throughout the container. Also, there is a height difference between piston 1 and piston 2 measured as h.

Find F2 for a given F

1. F2

A2

� P2

This should be the same as:F1

A1

��� gh

therefore:

F2

� F1

A1

��� gh A2

Archimedes' Principle

Book's definition:Any fluid applies a buoyant force to an object that is partially or completely

immersed in it; the magnitude of the buoyant force equals the weight of the fluid that the object displaces.

Mathematically this is given by:

F B

Magnitude of buoyant force� W fluid

Weight of displaced fluid

Example Problem

A cube of some material is floating in a volume of water so exactly ½ of its volume is sticking out of the water. The cube is exactly 1 cm3 in volume. Water has a density of 1.000 × 103 kg/m3.

How heavy is the cube?

Fluids in Motion

First, let's define some terms which relate to fluids:

Flow: The motion of individual particles which make up the fluid.

Steady Flow: The velocity of every particle passing a given point is the same. This does not change with time.

Unsteady Flow: The velocity of particles passing a given point does change with time.

Turbulent Flow:An extremely unsteady flow.

Viscosity: How resistant the fluid is to flowing. Can also be thought of as the "thickness" of the fluid.

Compressibility: How easily the fluid can change its density with a change in pressure upon it.

Continuity of Fluid Flow

The physical principle involved here is conservation of mass!

Bernoulli's Equation

This is defined mathematically (for the steady flow of a non-compressible fluid of density ρ) as:

P1

� 12

� v12 � � gy1

P2

� 12

� v22 � � gy2

Recall the work-energy theorem:

W nc

E f

Ei

12

m v f2 �

mgy f

12

m vi2 mgyi

Rearrange Bernoulli's Equation to identify the terms:

P1

P2 1

2� v2

2 v12 � � g y2

y1

Bernoulli's Equation used to describe a Physical System

P1

� P2

12

� v22 � v1

2 � g y2

� y1

Everyday Uses of Bernoulli's Equation

Another Everyday Use