Fluids: Physics for Life Sciences (Chapter 9) - Structured Study Notes

Fluids in Physics for Life Sciences

Introduction

This chapter explores the physical principles governing fluids, with a focus on biological and life-science applications. Topics include properties of fluids, pressure, buoyancy, surface tension, and fluid dynamics, all of which are essential for understanding processes in living organisms.

Phases of Matter

Classification of Matter

• Solid: Definite volume and shape.

• Liquid: Definite volume, but not a definite shape.

• Gas: Neither definite volume nor shape; unconfined.

Liquids and gases are both considered fluids because they can flow and take the shape of their container.

Properties of Fluids

Definition and Characteristics

• A fluid is a collection of molecules held together by weak cohesive forces and by container walls.

• Fluids take the shape of their container and can flow.

• Both liquids and gases are fluids.

Volume and Density

Key Concepts

• Volume (V): Amount of space a system occupies. SI unit: cubic meter (m3).

• Mass Density (ρ): Characterizes a substance, defined as:

$\rho = \frac{m}{V}$

• SI units: kg/m3; 1 g/cm3 = 1000 kg/m3 = 1 kg/L.

• Mass and volume characterize a specific piece; density characterizes the substance itself.

Density Table

Substance	ρ (kg/m3)
Helium gas (20°C)	0.166
Air (20°C)	1.20
Water (4°C)	1000
Seawater	1030
Blood (whole)	1060
Mercury	13,600

Additional info: For solids and liquids, density is relatively insensitive to pressure and temperature. For gases, density changes markedly with pressure and temperature, as described by the ideal gas law:

$\rho_{gas} = \frac{m}{V} = \frac{MP}{RT}$

where M is the molar mass.

Specific Gravity

Definition

• Specific gravity (SG): Ratio of a substance's density to that of water at 4°C.

$SG = \frac{\rho_{substance}}{\rho_{water\ at\ 4^\circ C}}$

• Dimensionless quantity.

• $\rho_{water\ at\ 4^\circ C} = 1.00\ g/cm^3 = 1.00 \times 10^3\ kg/m^3$

Pressure in Fluids

Definition and Units

• Pressure (p): Ratio of force to area over which the force is exerted.

$p = \frac{F_{\perp}}{A}$

• SI unit: Pascal (Pa) = N/m2

• Other units: psi, atm, bar, torr

Causes of Pressure

• Gravitational contribution: Gravity pulls down on the fluid.

• Thermal contribution: Collisions of molecules with container walls.

Atmospheric Pressure

• Atmospheric pressure decreases with altitude.

• Standard atmosphere: 1 atm = 101,300 Pa.

Pressure in Liquids (Hydrostatic Pressure)

• Pressure is the same in all directions at a given depth for a fluid at rest.

• Hydrostatic pressure is given by:

$p = p_0 + \rho g h$

• Where $p_0$ is the pressure at the surface, $\rho$ is density, $g$ is acceleration due to gravity, and $h$ is depth.

Pascal's Principle

Statement and Application

• If the pressure at one point in an incompressible fluid is changed, the pressure at every other point changes by the same amount.

• Application: Hydraulic lift

$P_1 = \frac{F_1}{A_1} = \frac{F_2}{A_2} = P_2$

Gauge Pressure

Definition

• Gauge pressure (pg): Pressure in excess of atmospheric pressure.

$p_g = p - 1\ atm$

• Hydrostatic gauge pressure: $p_g = \rho_{fluid} g h$

Measuring Pressure

Devices

• Barometer: Measures atmospheric pressure using a column of mercury.

• Manometer: Measures gas pressure, often as gauge pressure.

Barometer equation: $p_0 = \rho_{Hg} g h$

Properties of Liquids in Hydrostatic Equilibrium

Key Points

• Connected liquid rises to the same height in all open regions.

• Pressure is the same at all points on a horizontal line in a connected liquid.

• Pressure depends only on depth, not container shape.

Life-Science Applications of Fluid Physics

Examples

• Circulatory and vascular systems

• Support and size limits of organisms

• Swimming organisms

• Water striders walking on water

Strategy for Solving Hydrostatics Problems

1. Draw a simple picture, indicating all features affecting pressure.

2. Determine the pressure at surfaces (open to air, in contact with gas, or closed surface).

3. Draw a horizontal line; pressure is the same at any point along this line in a connected fluid.

Summary Table: Pressure Units

Unit	Value
Pascal (Pa)	1 N/m2
psi	6.89 × 103 Pa
atm	1.01 × 105 Pa
bar	1.00 × 105 Pa
torr	133 Pa

Example Problems

• Comparing densities of broken glass pieces: Density remains the same regardless of size.

• Hydraulic lift: Calculating platform diameter required to lift a car using Pascal's principle.

Additional info: These notes cover the foundational concepts of fluid mechanics as applied to life sciences, including biological systems and practical measurement techniques.