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4B: Importance of Fluids for the Circulation of Blood, Gas Movement, and Gas Exchange

Pressure, buoyancy, viscosity and the gas laws, animated on the systems that actually run on them: arteries, alveoli and the air above a mountain.

13 topics · 58 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

4B. Density and Specific Gravity

  1. How it worksHow does specific gravity measure a substance against water so that every unit cancels away?
  2. Worked exampleFind the specific gravity of a fluid whose 250 mL sample weighs in at 305 grams.
  3. Common mistakeWhy isn't a denser object automatically the heavier object?
  4. Going furtherWhat happens to a liquid's density as it warms, and why does the warmed layer ride on top?
Your turneasy1 of 3
A fluid of specific gravity 1.327 is poured into a flask that holds 360 mL. Find the mass of fluid the full flask contains.

4B. Hydrostatic Pressure and Pascal's Law

  1. How it worksHow does the weight of the water column standing above a point become the pressure at that point?
  2. How it worksHow does a squeeze on the small piston of a hydraulic jack arrive undiminished at the big one?
  3. Worked exampleFind the gauge pressure ten meters below the surface of a freshwater lake.
  4. Worked exampleFind the output force of a hydraulic lift with pistons of 5 and 250 square centimeters.
  5. Common mistakeWhy isn't the bottom of a skinny tube at a lower pressure than a wide tank filled to the same depth?
Your turneasy1 of 3
Find the gauge pressure 21 m below the surface of a freshwater lake, taking the density of water as 1000 kg/m3 and g = 10 m/s2.

4B. Buoyancy and Archimedes' Principle

  1. How it worksHow does the fluid shoved out of the way turn into the exact upward push on a submerged body?
  2. Worked exampleFind the buoyant force on a block of volume 0.0020 cubic meters held fully under water.
  3. How it worksHow does a floating object settle at the one depth where displaced weight matches its own weight?
  4. Worked exampleFind what fraction of an iceberg sits above water for ice at 0.92 and seawater at 1.03.
  5. Going furtherWhat happens to how high a boat rides when it sails out of a river into salt water?
Your turneasy1 of 3
Find the buoyant force on a block of volume 3634 cubic centimeters held completely under fresh water, taking the density of water as 1000 kg/m3 and g = 10 m/s2.

4B. Surface Tension

  1. How it worksHow do molecules at a liquid's edge end up with lopsided pulls that behave like a stretched skin?
  2. How it worksHow does surfactant in the alveoli cut surface tension and keep the smallest air sacs from collapsing?
  3. Worked exampleFind the inward pressure inside an alveolus of radius 2.0 mm at a surface tension of 0.050 N/m.
  4. Common mistakeWhy isn't surface tension an actual membrane lying across the top of the liquid?
  5. Going furtherWhat happens to the inward pressure inside a bubble as the bubble shrinks?
Your turnmedium1 of 3
An alveolus of radius 3 mm is lined by a fluid of surface tension 0.0654 N/m. Treating it as a sphere with one liquid surface, find the inward pressure the surface tension produces.

4B. Viscosity and Poiseuille Flow

  1. How it worksHow does fluid speed climb from zero at the vessel wall to a peak right down the center line?
  2. How it worksHow does halving a vessel's radius throttle the flow down to one sixteenth of what it was?
  3. Worked exampleFind the factor blood flow changes by when an artery narrows from 2.0 mm to 1.6 mm in radius.
  4. Common mistakeWhy isn't doubling the driving pressure enough to rescue a vessel that lost 20 percent of its radius?
  5. Worked exampleFind how much the resistance of a vessel rises when blood viscosity increases by half.
Your turnmedium1 of 3
An artery narrows from a radius of 3 mm to a radius of 2 mm while the driving pressure is held fixed. Find the factor by which the volume flow rate changes.

4B. The Continuity Equation

  1. How it worksHow does an incompressible fluid force cross-sectional area and speed to trade off exactly?
  2. Worked exampleFind the fluid speed in a 1.0 cm pipe that is fed by a 3.0 cm pipe flowing at 0.40 m/s.
  3. Going furtherWhat happens to blood speed when one aorta fans out into billions of capillaries?
Your turneasy1 of 3
An incompressible fluid moving at 1.45 m/s in a pipe of diameter 5 cm flows on into a pipe of diameter 3 cm. Find the fluid's speed in the second pipe.

4B. Bernoulli's Equation and the Venturi Effect

  1. How it worksHow does Bernoulli's equation split a moving fluid's energy into pressure, height and speed terms?
  2. How it worksHow does a Venturi throat convert a narrowing into a visible drop on a side-arm pressure gauge?
  3. Worked exampleFind the pressure drop when water speeds from 2.0 m/s to 6.0 m/s in a level constriction.
  4. Common mistakeWhy isn't a faster-moving fluid pushing harder against the walls of the pipe it races through?
  5. Ties togetherHow does the Bernoulli pressure drop explain a plaque-narrowed artery clamping down further as flow rises?
Your turnmedium1 of 3
Water of density 1000 kg/m3 speeds up from 3 m/s to 8 m/s through a level constriction. Find the drop in pressure across the constriction.

4B. Turbulence at High Velocities

  1. How it worksHow do neat parallel streamlines shatter into swirling eddies once the speed crosses a threshold?
  2. Worked exampleFind the Reynolds number for blood at 1.0 m/s in a 2.0 cm vessel of density 1060 and viscosity 0.0035.
  3. Common mistakeWhy isn't turbulent flow simply faster flow through the very same vessel?
  4. Going furtherWhat changes about the pressure needed to drive flow the moment the stream goes turbulent?
Your turnhard1 of 3
Blood of density 1061 kg/m3 and viscosity 0.0043 Pa s flows at 1.41 m/s through a vessel of diameter 1.2 cm. Find the Reynolds number for the flow.

4B. The Circulatory System: Pressure and Flow in Arteries and Veins

  1. How it worksHow does the heart's pumping pressure get spent across arterioles, capillaries and veins in turn?
  2. How it worksHow do one-way valves and squeezing leg muscles shove venous blood uphill back to the heart?
  3. Worked exampleFind the mean arterial pressure for a patient whose cuff reads 120 over 80.
  4. Common mistakeWhy isn't blood racing fastest through the capillaries, where each individual vessel is narrowest?
Your turneasy1 of 3
A patient's cuff reads 142 over 83 mmHg. Find the mean arterial pressure.

4B. Pressure, Barometers, and the Kelvin Scale

  1. How it worksHow does one glass tube of mercury weigh the entire atmosphere pressing on a dish?
  2. Worked exampleShow me 25 degrees Celsius turned into kelvin and why a gas law rejects the Celsius number.
  3. Common mistakeWhy isn't zero on the Celsius scale a legal starting point for a gas law ratio?
Your turneasy1 of 3
A gas sample is held at 71 degrees Celsius. Convert that temperature to kelvin.

4B. The Ideal Gas Law: Boyle, Charles, and Avogadro

  1. How it worksHow do Boyle, Charles and Avogadro each turn out to be one corner of PV = nRT?
  2. Worked exampleFind the new volume when 2.0 L of gas is squeezed from 1.0 atm to 2.5 atm at fixed temperature.
  3. How it worksHow does 22.4 liters per mole fall out of PV = nRT at zero degrees Celsius and one atmosphere?
  4. Worked exampleFind how many moles of gas occupy 11.2 L at 273 K and 1.0 atm.
  5. Common mistakeWhy doesn't warming a gas from 20 to 40 degrees Celsius double its volume?
Your turneasy1 of 3
A sealed syringe holds 4 L of gas at 2 atm. The plunger is pushed in until the pressure reads 10 atm, at constant temperature. Find the new volume.

4B. Kinetic Molecular Theory and Deviations from Ideality

  1. How it worksHow does a storm of elastic bounces off the walls add up to one steady pressure reading?
  2. How it worksHow does the spread of molecular speeds slide rightward and flatten when a gas is heated?
  3. Worked exampleFind the average translational kinetic energy of a single ideal gas molecule at 300 K.
  4. Common mistakeWhy isn't every molecule in a warm gas travelling at the same speed?
  5. Going furtherWhat happens to real gas behavior at high pressure and low temperature that van der Waals patches up?
Your turneasy1 of 3
Find the average translational kinetic energy of a single ideal gas molecule at 479 K, taking Boltzmann's constant as 1.38e-23 J/K.

4B. Partial Pressure, Dalton's Law, and Gas Exchange

  1. How it worksHow does each gas in a mixture contribute pressure strictly in proportion to its mole fraction?
  2. Worked exampleFind the partial pressure of oxygen in dry air at 760 mmHg if oxygen is 21 percent of the moles.
  3. Common mistakeWhy isn't a gas with heavier molecules automatically contributing the larger partial pressure?
  4. Going furtherWhat happens to the amount of oxygen dissolved in blood when the gas pressure above it doubles?
  5. Ties togetherHow do partial pressure gradients across the alveolar wall drive the oxygen and carbon dioxide swap?
Your turneasy1 of 3
Dry air at a total pressure of 695 mmHg is 21 percent oxygen by moles. Find the partial pressure of oxygen.

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