**Characteristics of Fluids and Solids**

- Fluids are able to conform to shape and flow
- Solids are rigid and do not flow. Exert tangential shear forces

**Density **

- ρ = m/v
- Water has a density of of 1 g/cm
^{3}=1000 kg/m^{3} - Weight = FG = ρVg
- The
**Specific gravity**is when density of fluid is compared to that of pure water at 1 atm and 4 degrees Celsius. - SG = ρ/(1g/cm^3)

**Pressure**

- 1.013×10^5 Pa = 760 mmHg = 760 torr = 1 atm
__Atmospheric Pressure:__changes with altitude__Absolute (hydrostatic) Pressure:__total pressure that is exerted on an object that is submerged in a fluid (both gases and liquids).- P = Po + ρgz

- P is the absolute pressure P
_{0}is the ambient pressure, Z is positive downward. __Gauge Pressure:__Pgauge = P-Patm

**Hydrostatics**

- Study of fluids at rest and the forces and pressures associated with standing fluids.
__Pascal’s Principle:__Incompressible fluids transmit pressure equally to all portions of the fluid.__Hydraulic Systems:__F2 = F1(A2/A1)

__Archimedes’ Principle:__a body wholly or partially immersed in a fluid will be buoyed upwards by a force equal to the weight of the fluid that is displaced,**buoyancy**.- Fbuoy = ρfluid*Vfluiddisplaced*g = ρfluid*Vsubmerged*g

- Objects that float have a density less than the fluid and the buoyancy force is equal to the weight of the water.
- The amount of volume submerged of a substance is equal to the specific gravity expressed in percentage. E.g – S.G of ice =0.92 so 92% of ice is submerged in water and 8% at surface.

**Molecular Forces in Liquids**

__Surface Tension__is a strong but thin layer of “skin” at the liquids surface, which is caused by**cohesion**. This is the pulling of the liquid inwards at the surface.__Cohesion__is the attractive force that a molecule of liquid feels toward other molecules of the same liquid.__Adhesion__is the attractive force that molecule of liquid feels towards the molecules of other substances.__E.g. –__forms droplets on windshield, forms**meniscus**(when cohesion>adhesion then there is a convex meniscus; when adhesion>cohesion then there is a concave meniscus)

**Fluid Dynamics**

__Viscosity__: Resistance of a fluid. Increased viscosity of a fluid increases its**viscous drag**- Lower viscosity fluids are said to behave more like ideal fluids which have no viscosity (
**inviscid**). - Units of pascal-second [Pa x s = Ns/m
^{2}]

- Lower viscosity fluids are said to behave more like ideal fluids which have no viscosity (
__Laminar Flow:__Smooth and orderly and is modeled as layers of fluid that flow parallel to each other__Poiseuille’s Law:__for laminar flow through a pipe Q = (πr^4ΔP)/(8ηL)__Turbulence & Speed:__turbulent flow is rough and disorderly and causes the formation of**eddies**which are swirls of fluid of varying sizes occurring typically on the down-stream side of an obstacle.- Occurs after a critical speed is reached. Once reached, laminar flow only occurs in a thin layer of fluid close to the wall called the
**boundary layer**. - Vc = (Reη)/(ρD)

- Occurs after a critical speed is reached. Once reached, laminar flow only occurs in a thin layer of fluid close to the wall called the
__Steamlines:__indicate the pathways followed by tiny fluid elements as they move. Velocity vector of a fluid particle will always be tangential to the streamline at any point.- Flow rate must stay constant in a closed system
- Q = v1A1 = v2A2 known as the continuity equation

__Bernoulli’s Equation:__combines principles of conservation of mass and laminar/ inviscid flow: P is the absolute pressure and v is the linear speed, h is the height of the fluid above datum.- P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2

- Dynamic Pressure is the pressure associated with the movement of a fluid (1/2ρv1^2). This is the kinetic energy divided by volume.
- Pressure can be thought of as
**energy density** - Static pressure is the P+ρgh1 term

**Fluids in Physiology**

__Circulatory System__is a**closed loop**that has a non-constant flow rate. This flow rate is measured as a**pulse**- As blood flows away from the heart, each vessel has a progressively higher resistance until the capillaries, but total resistance of system decreases since the vessels are in parallel with each other.

__Respiratory System__is much the same as the circulatory system.