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


  • 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)


  • 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


  • 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.

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