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.
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.
