Atlas MCAT Course
Physical Foundations → Fluids
Fluids
Mechanics with constraints.
01The idea
Fluids don’t resist shear the way solids do. That single fact changes everything.
If you understand those three, fluids become predictable.
THREAD · Gradients and flow
02Build the model
ADensity: the foundational property
Density links mass, volume, pressure, and buoyancy. It shows up everywhere in fluid equations.
BPressure: force distributed over area
Pressure is a scalar, acts equally in all directions at a point, and transmits force through fluids.
CHydrostatic pressure: depth matters
In a fluid at rest:
Here P₀ is surface pressure, ρ is fluid density, and h is depth. Deeper means higher pressure. The shape of the container doesn’t matter — only depth matters.
DGauge vs. absolute pressure
Absolute pressure includes atmospheric pressure; gauge pressure excludes it. Many MCAT problems implicitly use gauge pressure unless stated otherwise.
EBuoyancy: pressure differences create force
This comes directly from pressure differences with depth.
FFluid flow: when fluids move
Flow occurs due to pressure differences. Flow rate is volume per time:
GContinuity equation: conservation of mass
For incompressible fluids:
A narrower cross-section gives faster flow; slower flow means a wider region. This explains blood flow changes, nozzle behavior, and pipe constrictions.
HBernoulli’s equation: energy conservation in fluids
Each term is energy per unit volume: P is pressure energy, ½ρv² is kinetic energy, and ρgh is gravitational potential energy. If height is constant, faster flow means lower pressure. If speed is constant, higher elevation means lower pressure.
IViscosity: resistance to flow
Real fluids resist motion internally. For laminar flow through a tube:
You don’t need the full derivation, but note the r⁴ dependence: small radius changes make huge flow changes, which explains vascular resistance.
JLaminar vs. turbulent flow
Laminar flow is smooth, orderly layers; turbulent flow is chaotic, with energy loss. Bernoulli applies best to laminar flow.
KFluids and physiology (context lock-in)
These equations explain blood pressure changes, aneurysm risk, flow resistance, and filtration and reabsorption. Physics → physiology is now airtight.
03See the connections
The lesson names these links itself. Read the map left to right.
At rest
- P = P₀ + ρgh
- Buoyancy: ρ_fluid g V
Moving
- Continuity: A₁v₁ = A₂v₂
- Bernoulli: P + ½ρv² + ρgh
Real fluids
- Viscosity, r⁴
- Laminar vs turbulent
Next: electrostatics and circuits.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
Two containers of water have different shapes but the same depth. How do the pressures at their bottoms compare?
Think first.
Blood flows from a wide vessel into a narrowed segment at the same height. What happens in the narrow part?
Think first.
What does the buoyant force on a submerged object depend on?
Think first.
A vessel’s radius is halved. Roughly what happens to laminar flow, all else equal?
05MCAT lens
Equation-level checks
Hydrostatic: P = P₀ + ρgh; only depth matters
Continuity: narrower → faster
Bernoulli: faster → lower pressure (same height)
Flow ∝ r⁴: radius dominates resistance
06Common traps
Trap 1: Container shape changes pressure at the bottom
Misconception
Only depth matters.
Correct model
P = P₀ + ρgh.
Trap 2: Faster flow means higher pressure
Misconception
Bernoulli says the reverse.
Correct model
At the same height, faster flow means lower pressure.
Trap 3: Buoyancy depends on the object’s density
Misconception
It depends on the fluid and the displaced volume.
Correct model
F_b = ρ_fluid g V_displaced.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
Why pressure increases with depth
Check against 02 · C: P = P₀ + ρgh.
Why flow speeds up in narrow regions
Check against 02 · G: continuity.
Why fast flow lowers pressure
Check against 02 · H: Bernoulli.
Why radius dominates resistance
Check against 02 · I: r⁴.
If something feels unclear, the missing idea is usually thisFluid motion is energy redistribution under mass conservation.
08Remember
REMEMBER · if you keep only a few things
- ρ = m/V; P = F/A.
- P = P₀ + ρgh: depth, not shape.
- F_b = ρ_fluid g V_displaced.
- A₁v₁ = A₂v₂: narrower is faster.
- Bernoulli: faster flow, lower pressure.
- Flow ∝ r⁴.
09Forward hook
Fluids complete the mechanics layer. The same pressure–flow logic carries over to electricity.
How do fields, potential, and resistance control the flow of charge?
That leads to electrostatics and circuits.
Next lessonKinetic Molecular Theory & Gas Laws→