Atlas MCAT Course
Equations & How to Use Them → Equations: Flow
Equations: Flow
Pressure, buoyancy, and fluid flow.
01The idea
Something is exerting pressure, flowing through a tube, or responding to height.
THREAD · Gradients and flow
02Build the model
APressure: how force spreads out over an area
Use when: a force is applied over a surface; comparing sharp vs blunt objects; fluids or tissues experience compression.
Passage cues: “Force distributed”, “Contact area”, “Sharp vs dull”, “Pressure exerted on…”.
Don’t use it for: flowing fluids (use continuity or Poiseuille); depth-dependent pressure (use hydrostatic pressure).
BHydrostatic pressure: how fluid weight creates pressure with depth
Use when: fluids are at rest; pressure depends on depth; columns of liquid are involved.
Passage cues: “At a depth of…”, “Fluid column”, “Height below surface”, “Hydrostatic”.
Don’t use it for: flowing fluids; pressure differences due to motion.
CBuoyant force (Archimedes’ principle): why objects float or sink
Use when: objects are submerged or floating; comparing densities; net force in fluids matters.
Passage cues: “Displaced volume”, “Floats / sinks”, “Submerged”.
Don’t use it for: solid-on-solid contact; situations without fluid displacement.
DContinuity equation: how flow speed changes with area
Use when: fluid flows steadily; cross-sectional area changes; incompressible fluid (liquids).
Passage cues: “Narrowing”, “Widening”, “Constricted vessel”, “Steady flow”.
Don’t use it for: compressible gases (unless approximated); non-steady flow.
EBernoulli’s equation: how pressure, speed, and height trade off
Use when: fluid is flowing; comparing pressure at two points; velocity and pressure change together.
Passage cues: “Venturi effect”, “Flow speed increases”, “Pressure drop”, “Same streamline”.
Don’t use it for: viscous flow with large friction losses; turbulent or discontinuous flow.
FPoiseuille’s law: what controls resistance to flow
Use when: flow through tubes (especially blood vessels); viscosity matters; radius changes dominate flow.
Passage cues: “Resistance”, “Vessel radius”, “Viscosity”, “Laminar flow”.
Don’t use it for: turbulent flow; open containers; non-cylindrical systems.
GFluid resistance (analogy to circuits): pressure drives flow like voltage drives current
Use when: comparing flow through multiple vessels; series vs parallel vessels; pressure drop matters.
Passage cues: “Resistance”, “Flow rate”, “Pressure difference”.
Don’t use it for: compressible gases; non-laminar flow.
03See the connections
The lesson names these links itself. Read the map left to right.
At rest
- P = F/A
- P = P₀ + ρgh
- Buoyancy
Flowing
- Continuity
- Bernoulli
Resistance
- Poiseuille (r⁴)
- ΔP = QR
Next: charge equations.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
A blood vessel narrows, with steady flow. Which equation tells you the blood speeds up there?
Think first.
A diver goes from 5 m to 10 m deep. Which equation tells you how pressure changes?
Think first.
A vessel’s radius halves. Which equation predicts a roughly 16-fold drop in flow?
Think first.
Air speeds up over a curved surface. What happens to its pressure there?
05MCAT lens
MCAT shortcuts
Same force, smaller area → bigger pressure
Deeper = more pressure
Buoyancy depends on fluid, not the object
Squeeze the pipe → fluid speeds up
Faster flow → lower pressure
Small radius change → massive flow change
06Common traps
Trap 1: Confusing pressure with force
Misconception
Pressure depends on area, force does not.
Correct model
P = F/A.
Trap 2: Assuming faster flow means higher pressure
Misconception
It’s the opposite (Bernoulli).
Correct model
Faster flow → lower pressure.
Trap 3: Underestimating radius effects
Misconception
Radius changes dominate everything in vessels.
Correct model
Flow ∝ r⁴.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
When to use P = F/A vs ρgh
Check against 02 · A and B.
How continuity and Bernoulli work together
Check against 02 · D and E.
Why radius dominates flow
Check against 02 · F.
How fluids mirror circuits
Check against 02 · G.
If something feels unclear, the missing idea is usually thisAt rest, depth sets pressure; in motion, area, speed, and radius set flow.
08Remember
REMEMBER · if you keep only a few things
- P = F/A.
- P = P₀ + ρgh.
- F_b = ρ_fluid g V_displaced.
- A₁v₁ = A₂v₂.
- P + ½ρv² + ρgh = constant.
- Q ∝ ΔP r⁴ / ηL; ΔP = QR.
09Forward hook
Block II connects forward to circuits: pressure difference drives flow just as voltage drives current.
Which equation applies when charges move, fields exist, or energy is transferred electrically?
That leads to the charge equations.
Next lessonEquations: Charge→