Comprehensive Study Notes on Fluids, Density, and Pressure

In physics, a fluid is any material that flows. Fluid is used for both liquids, like water, and gases, like air.

• Solids: These cannot flow. They keep their shape.

• Liquids: Liquids flow and change shape to fit their container.

• Gases: Gases also flow.

Fluid mechanics studies both gases and liquids.

Conceptual Underpinnings of Density

Density helps describe how much mass a substance has in a given space.

• The Bread Example:

  • If you squish bread, the mass stays the same, but the volume gets smaller.

  • Thus, its density increases since the mass is now in less space.

• Definition of Density: Density is how much mass is in a unit of volume.

  • High density means more mass in less space.

  • Low density means less mass in more space.

• Density Formula:   $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Symbolically:   $D = \frac{m}{V}$

Standard Densities and Comparisons

• Water: Water has a density of $1\,g/mL$.

  • This comes from its historical definition in metric units.

  • A cubic centimeter is the same as one milliliter.

  • Therefore, $50\,mL$ of water weighs $50\,g$.

• Relative Densities:

  • Ethyl Alcohol: $0.81\,g/cm^3$ (floats on water).

  • Ice: $0.92\,g/cm^3$ (ice floats on water).

  • Lead: $11.3\,g/cm^3$ (very dense).

  • Mercury: $13.6\,g/cm^3$ (liquid metal).

  • Platinum: $21.1\,g/cm^3$ (very dense metal).

  • Iridium: $22.6\,g/cm^3$ (the most dense element).

Weight Density

Weight density involves gravity with the mass density.

• Weight Density Formula:   $\text{Weight Density} = \frac{\text{Weight}}{\text{Volume}}$

The Mechanics of Pressure

Pressure comes from a force spread over an area.

• Pressure Formula:   $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

• Example: A book lying flat exerts less pressure than standing up, even though the weight is the same due to different areas.

Fluid Pressure in Liquids

Liquid pressure depends on its density and depth.

• Liquid Pressure Formula:   $\text{Pressure in a Liquid} = \text{Weight Density} \times \text{Depth}$

• Depth Matters: The deeper you go in a liquid, the more pressure you feel. It does not depend on the total volume of liquid.

Atmospheric and Total Pressure

We live in air, which has pressure because of its weight pushing down.

• At sea level, air pressure is around $15\,lb/in^2$.

• Total Pressure Underwater: If submerged, total pressure equals the fluid pressure plus atmospheric pressure above it.

In physics, a fluid is any material that flows. Fluid is used for both liquids, like water, and gases, like air.

Solids: These cannot flow. They keep their shape.

Liquids: Liquids flow and change shape to fit their container.

Gases: Gases also flow.

Fluid mechanics studies both gases and liquids.

Conceptual Underpinnings of Density

Density helps describe how much mass a substance has in a given space.

The Bread Example:

If you squish bread, the mass stays the same, but the volume gets smaller.

Thus, its density increases since the mass is now in less space.

Definition of Density: Density is how much mass is in a unit of volume.

High density means more mass in less space.

Low density means less mass in more space.

Density Formula:

Density

=

Mass

Volume

Density=

Volume

Mass

​

Symbolically:

D

=

m

V

D=

V

m

​

Standard Densities and Comparisons

Water: Water has a density of

1

g

/

m

L

1g/mL.

This comes from its historical definition in metric units.

A cubic centimeter is the same as one milliliter.

Therefore,

50

m

L

50mL of water weighs

50

g

50g.

Relative Densities:

Ethyl Alcohol:

0.81

g

/

c

m

3

0.81g/cm

3

(floats on water).

Ice:

0.92

g

/

c

m

3

0.92g/cm

3

(ice floats on water).

Lead:

11.3

g

/

c

m

3

11.3g/cm

3

(very dense).

Mercury:

13.6

g

/

c

m

3

13.6g/cm

3

(liquid metal).

Platinum:

21.1

g

/

c

m

3

21.1g/cm

3

(very dense metal).

Iridium:

22.6

g

/

c

m

3

22.6g/cm

3

(the most dense element).

Weight Density

Weight density involves gravity with the mass density.

Weight Density Formula:

Weight Density

=

Weight

Volume

Weight Density=

Volume

Weight

​

The Mechanics of Pressure

Pressure comes from a force spread over an area.

Pressure Formula:

Pressure

=

Force

Area

Pressure=

Area

Force

​

Example: A book lying flat exerts less pressure than standing up, even though the weight is the same due to different areas.

Fluid Pressure in Liquids

Liquid pressure depends on its density and depth.

Liquid Pressure Formula:

Pressure in a Liquid

=

Weight Density

×

Depth

Pressure in a Liquid=Weight Density×Depth

Depth Matters: The deeper you go in a liquid, the more pressure you feel. It does not depend on the total volume of liquid.

Atmospheric and Total Pressure

We live in air, which has pressure because of its weight pushing down.

At sea level, air pressure is around

15

l

b

/

i

n

2

15lb/in

2

.

Total Pressure Underwater: If submerged, total pressure equals the fluid pressure plus atmospheric pressure above it.