Fluids

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/cm³=1000 kg/m³ 
• 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 P₀ 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/m²]
• 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)
• 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.