Module 5: Fluids

Introduction to Fluids

Welcome to Module 5: Fluids, a high-yield chapter of MCAT physics that bridges physical principles with human biology and clinical science. This lesson focuses on the behavior of substances that can flow, namely, liquids and gases, and how they exert pressure, experience, forces, and move through systems.

On the MCAT, fluid principles underpin numerous topics, including blood flow, gas exchange, organ perfusion, lung pressures, and medical instrumentation. Understanding how fluids behave, both at rest and in motion, is essential for interpreting cardiovascular dynamics, respiratory mechanics, and everyday physical phenomena like buoyancy and pressure gradients.

Learning Objectives:

By the end of this module, you should be able to:

Define density and specific gravity and apply them to floating/sinking scenarios.
Use pressure equations to calculate hydrostatic and total pressures in fluids.
Apply Pascal’s Law to hydraulic systems and force multiplication.
Calculate buoyant forces using Archimedes’ Principle and determine whether objects float or sink.
Analyze fluid motion using the continuity equation and Bernoulli’s principle.
Understand how viscosity affects flow rate and how Poiseuille’s Law governs laminar flow in real systems.
Distinguish between ideal and non-ideal fluid behavior and apply appropriate assumptions on the MCAT.

Why Fluids Matter on the MCAT

Fluid dynamics directly translates to MCAT-relevant physiology. Concepts such as blood pressure, cardiac output, pulmonary ventilation, and IV fluid administration are all governed by physical principles of pressure, volume, and flow.

You are expected to:

Calculate how blood flow changes when arteries narrow.
Understand how lung pressures allow air to enter and exit.
Interpret clinical scenarios involving buoyancy, syringes, or catheters.
Apply Bernoulli’s or Poiseuille’s equations to model vascular or respiratory flow.

Approximately 5-10% of MCAT physics questions directly involve fluid statics or dynamics. But their real value lies in their overlap with biology and medicine, making this topic disproportionately important.

Module Overview:

Density and Specific Gravy
Pressure (Pascal’s Principle and Hydrostatics)
Buoyancy and Archimedes’ Principle
Fluid Dynamics: Continuity and Bernoulli’s Equation
Viscosity and Poiseuille’s Law

Density and Specific Gravity

What is Density?

Density is a physical property that describes how compact a substance is, how much mass is packed into a given volume. It combines two measurable physical quantities:

$$
\rho = \frac{m}{V}
$$

Where:

$$
\rho = \text{Density (kilograms per cubic meter, kg/m}^3\text{)}
$$

$$
m = \text{Mass (kilograms, kg)}
$$

$$
V = \text{Volume (cubic meters, m}^3\text{)}
$$

Conceptual Meaning:

A material with high density (like lead) has a lot of mass in a small space.
A material with low density (like Styrofoam) has less mass in a larger volume.

Important MCAT Note:

The MCAT will often give you mass in grams and volume in cm³. That’s okay if you’re consistent. You can leave your answer in g/cm³ or convert to SI units (kg/m³) when needed:

$$
1 \ \text{g/cm}^3 = 1000 \ \text{kg/m}^3
$$

Why Density Matters

Density is one of the most fundamental fluid properties. On the MCAT, it shows up in:

Buoyancy questions (floating/sinking behavior)
Pressure calculations (pressure depends on fluid density)
Circulatory system (blood density vs. plasma)
Diagnostic tools (urine specific gravity tests)
Biochemical separations (centrifugation based on density gradients)

Key Densities to Know

Substance	Density (kg/m³)	Notes
Water	1000	Standard reference point
Blood	~1060	Slightly denser than water
Fat tissue	~900	Floats in water
Bone	~1800 – 2000	Much denser than soft tissue
Air (STP)	~1.2	Very low density

Visualizing Density

Imagine holding two identical-sized blocks:

One is made of solid gold.
The other is made of hollow plastic

Even though their volumes are the same, the gold block is dramatically heavier. That’s because it has more mass per unit volume – greater density.

MCAT Tip: Questions will sometimes disguise density by giving you mass and volume separately. Always be prepared to compute it from the basic formula.

Specific Gravity: The Density Comparison Tool

Specific gravity (SG) is a unitless ratio that compares the density of any substance to the density of water (which is 1000 kg/m³ at 4°C). It tells you how dense something is relative to water:

$$
\text{SG} = \frac{\rho_{\text{object}}}{\rho_{\text{water}}}
$$

Since the density of water is used as the baseline, specific gravity makes it easy to reason about floating or sinking:

SG > 1: Substance is denser than water → it sinks
SG < 1: Substance is less dense than water → it floats
SG = 1: Neutral buoyancy → it suspends in water

Clinical Tip: SG is often used in medicine to assess the concentration of urine (hydration status), blood plasma, or cerebrospinal fluid.

Relationship to Buoyancy

For floating objects, specific gravity directly determines what fraction of the object’s volume is submerged:

$$
\frac{V_{\text{submerged}}}{V_{\text{total}}} = \text{SG}
$$

So if SG = 0.80, the 80% of the object is submerged and 20% floats above the surface.

This relationship is only valid when the object is floating in water and is often tested in MCAT-style questions involving floating cubes, blocks, or biological tissues.

Density vs. Specific Gravity

Property	Density	Specific Gravity
Units	kg/m³	None (unitless)
Absolute/Relative	Absolute measure	Ratio (relative)
Reference	None	Always compared to water
MCAT usage	Used in formulas	Used in reasoning/comparison problems

Key Takeaways

Density is the foundational quantity for all fluid-related problems.
Always match units carefully and convert early if needed.
Specific gravity simplifies float/sink comparisons and is unitless.
Floating objects displace fluid equal to their own weight; the submerged volume is proportional to SG.

Pressure and Hydrostatics

What Is Pressure?

In physics, pressure is the amount of force exerted per unit area. It tells us how concentrated a force is over a surface and is especially important when analyzing fluids (liquids and gases), where forces are applied across boundaries, such as against walls of blood vessels, airways or containers.

$$
P = \frac{F}{A}
$$

Where:

$$
P = \text{Pressure (Pascals, Pa or N/m}^2\text{)}
$$

$$
F = \text{Force applied perpendicular to the surface (Newtons, N)}
$$

$$
A = \text{Area over which the force is applied (square meters, m}^2\text{)}
$$

Units of Pressure:

1 Pascal (Pa) = 1 N/m²

MCAT Often Uses:

1 atm = 101,325 Pa
1 atm = 760 mmHg
1 atm = 101.3 kPa
1 mmHg = 133.3 Pa

Everyday Example: If you press your fingertip (small area) into your palm, it feels more intense than pressing with you palm (larger area) – that’s higher pressure, even with the same force.

Pressure in Fluids: Key Concept

Fluids transmit pressure in all direction – not just downward. This is because molecules within a fluid move freely and exert forces as they collide with each other and with surfaces.

At any given depth in a fluid at rest:

Pressure acts equally in all direction (up, down, sideways)
The greater the depth, the greater the pressure.

This is why scuba divers experience greater pressure the deeper they go.

Hydrostatic Pressure

Pressure Due to the Weight of a Fluid

Hydrostatic pressure is the pressure exerted by a stationary fluid at a certain depth. It comes from the weight of the fluid above the point in question:

$$
P = \rho g h
$$

Where:

$$
P = \text{Pressure at a given depth (Pascals, Pa)}
$$

$$
\rho = \text{Density of the fluid (kg/m}^3\text{)}
$$

$$
g = \text{Gravitational acceleration (9.8 m/s}^2\text{)}
$$

$$
h = \text{Depth below the surface of the fluid (meters, m)}
$$

This pressure increases linearly with depth and is independent of the container’s shape or volume – a key insight on the MCAT.

MCAT Note: Two identical points at the same depth in different containers experience the same pressure, even if one container is wide and the other is narrow.

Total Pressure: Including Atmospheric Pressure

When measuring pressure below the surface of a fluid open to the atmosphere, the total pressure includes both:

The ambient air pressure pushing down from above
The fluid’s hydrostatic pressure beneath the surface

$$
P_{\text{total}} = P_{\text{atm}} + \rho g h
$$

Patm = 101,325 Pa (or 1 atm)
This is often assumed unless the container is sealed or under vacuum

Gauge Pressure

Many devices (e.g., car tires, blood pressure cuffs) measure gauge pressure, which ignores atmospheric pressure:

$$
P_{\text{gauge}} = P_{\text{total}} – P_{\text{atm}} = \rho g h
$$

Where:

$$
P_{\text{gauge}} = \text{Gauge pressure (Pa)}
$$

$$
P_{\text{total}} = \text{Absolute (total) pressure at depth (Pa)}
$$

$$
P_{\text{atm}} = \text{Atmospheric pressure (Pa)}
$$

$$
\rho = \text{Density of the fluid (kg/m}^3\text{)}
$$

$$
g = \text{Gravitational acceleration (9.8 m/s}^2\text{)}
$$

$$
h = \text{Depth below the surface (m)}
$$

So a pressure gauge at the bottom of a pool would real only the water’s contribution to pressure – not the atmosphere’s.

Pascal’s Principle – How Fluids Amplify Force

Pascal’s Principle states:

A change in pressure applied to an enclosed, incompressible fluid is transmitted undiminished throughout the fluid.

This forms the basis for hydraulic systems. If you apply a small force over a small area, the fluid transmits that pressure evenly, and it can produce a larger force over a larger area elsewhere.

$$
\frac{F_1}{A_1} = \frac{F_2}{A_2} \Rightarrow F_2 = F_1 \cdot \frac{A_2}{A_1}
$$

Where:

$$
F_1 = \text{Input force (Newtons, N)}
$$

$$
F_2 = \text{Output force (Newtons, N)}
$$

$$
A_1 = \text{Area over which } F_1 \text{ is applied (m}^2\text{)}
$$

$$
A_2 = \text{Area over which } F_2 \text{ is applied (m}^2\text{)}
$$

Example: In a hydraulic lift, you push a piston with a small force, and the lift pushes up a car using a larger piston – resulting in mechanical advantage without violating conservation of energy.

MCAT Applications of Pressure

Circulatory system: Hydrostatic pressure explains why blood pressure increases in the legs when standing, gravity pulls blood downward, increasing h.
IV drips and syringes: Flow occurs due to a pressure difference between high and low ends.
Lungs and thoracic cavity: Inhalation lowers pressure in the lungs, drawing air in (negative pressure breathing).
Hydraulic equipment: Blood pressure cuffs and ventilators manipulate pressure and volume.

Conceptual Takeaways

Pressure in a fluid increases with depth – not with horizontal position.
Pressure is scalar – its effects are equal in all directions at a given depth.
Total pressure = atmospheric + hydrostatic
Gauge pressure = hydrostatic pressure only
Pascal’s principle allows a small force to lift heavy loads using fluid pressure transmission.

Buoyancy and Archimedes’ Principle

What is Buoyancy?

Buoyancy is the net upward force that a fluid exerts on an object that is immersed in it, either partially (e.g., floating) or fully (e.g., sinking). This force exists because fluid pressure increases with depth. The deeper you go, the greater the pressure pushing upward on the lower surfaces of a submerged object. The result in an unbalanced force, directed upward, known as the buoyant force.

In essence:

The bottom of the object experiences a greater pressure than the top, resulting in a net upward force.
This force is not dependent on the object’s material, but rather on the volume of fluid it displaces and the density of the fluid.

Example in Nature:

Fish maintain depth using a swim bladder, a gas-filled organ that adjusts their average density by changing internal volume and mass balance, illustrating buoyancy control in physiology.

Definition and Equation of Buoyant Force

The buoyant force (F_b) is defined by:

$$
F_b = \rho_{\text{fluid}} \cdot V_{\text{submerged}} \cdot g
$$

Variable	Meaning
F_b	Buoyant force (in netwons, N)
ρ_fluid	Density of the fluid (not the object) in kg/m³
V_sub	Volume of the object that is submerged in the fluid (in m³)
g	Gravitational acceleration, ^~9.8 m/s²

Key Clarification:

The fluid’s density determines the strength of the buoyant force – not the object’s density.
Volume submerged is the only portion of the object contributing to buoyancy.
- Fully submerged objects: V_sub = V_object
- Floating objects: V_sub < V_object

Archimedes’ Principle

Archimedes’ principle states:

"A body wholly or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the body."

Breakdown:

Displacement is key: an object must displace fluid to experience buoyancy.
The greater the volume displaced, the greater the buoyant force.
The denser the fluid, the stronger the upward force for the same displaced volume.

$$
F_b = \text{Weight of displaced fluid} = m_{\text{fluid}} \cdot g = \rho_{\text{fluid}} \cdot V_{\text{sub}} \cdot g
$$

Why Does This Work?

It arises from the pressure gradient in a fluid due to gravity. The derivation uses a vertical force analysis on a submerged object with flat top and bottom surfaces:

Pressure at bottom:

$$
P_{\text{bottom}} = \rho_{\text{fluid}} \cdot g \cdot h_{\text{bottom}}
$$

Pressure at top:

$$
P_{\text{top}} = \rho_{\text{fluid}} \cdot g \cdot h_{\text{top}}
$$

Net force = difference in pressure x area = buoyant force.

Buoyancy in Action: Float vs. Sink vs. Suspend

Condition	Outcome	Explanation
F_b > F_g	Object accelerates upward	Buoyant force exceeds gravity → object rises
F_b = F_g	Object suspended in fluid	Forces are balanced → no net motion (e.g., neutrally buoyant)
F_b < F_g	Object sinks	Gravity wins → object accelerates downward

Where:

$$
F_g = m_{\text{object}} \cdot g = \rho_{\text{object}} \cdot V_{\text{object}} \cdot g
$$

MCAT Insight:

An object floats if its density is less than that of the fluid.
An object sinks if its density is greater than the fluid.
A neutrally buoyant object has equal density to the fluid and remains suspended.

Fraction Submerged: Floating Objects at Equilibrium

When a floating object is at rest, the buoyant force exactly balances the weight of the object. This leads to the equation:

$$
F_b = F_g
$$

$$
\rho_{\text{fluid}} \cdot V_{\text{sub}} \cdot g = \rho_{\text{object}} \cdot V_{\text{object}} \cdot g
$$

Cancel g and solve:

$$
\frac{V_{\text{sub}}}{V_{\text{object}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}}
$$

This gives the fraction of the object’s volume that is submerged.

Apparent Weight in Fluids

The apparent weight is how heavy an object feels when submerged, due to reduction by buoyant force.

$$
W_{\text{apparent}} = W_{\text{true}} – F_b
$$

This concept explains:

Why lifting objects underwater feels easier.
Why a spring scale reads lower underwater.

If the object is fully suspended and stationary (e.g., fish with neutral buoyancy):

$$
W_{\text{apparent}} = 0 \Rightarrow F_b = W
$$

Buoyancy in Gases: Archimedes’ Principle for Air

Archimedes’ Principle is universal to all fluids, including gases.

Example:

A helium balloon rises in air because it displaces air that is heavier than the mass of the balloon plus helium.
The buoyant force equals the weight of displaced air.
If: F_b > W_{balloon+helium} then the balloon accelerates upward.

This same concept applies to:

Weather balloons
Airships
Lung inflation dynamics in respiratory physiology

Common MCAT Traps and Strategic Notes

Trap or Concept	Clarification
Confusing displaced volume with mass	The volume of displaced fluid determines F_b, not the mass of the object
Thinking buoyant force depends on object density	It only depends on fluid density and submerged volume
Misusing the floating fraction equation	Only valid when object is in equilibrium and floating
Forgetting Archimedes applies to gases	MCAT loves sneaky balloon and air-density questions
Ignoring units (g/cm³ vs kg/m³)	Always convert to SI units (kg/m³) for consistency

Fluid Dynamics – Continuity and Bernoulli’s Equation

What is Fluid Dynamics?

Fluid dynamics is the study of fluids in motion, in contrast to hydrostatics, which deals with stationary fluids. On the MCAT, this section primarily focuses on ideal (non-viscous, incompressible, laminar) flow through pipes or open systems.

There are two major equations governing ideal fluid flow:

The Continuity Equation, which expresses conservation of mass.
Bernoulli’s Equation, which expresses conservation of energy in a flowing fluid.

These equations are central to understanding how blood flows through vessels, how air moves through the respiratory tract, and how fluids behave in laboratory or clinical setups.

The Continuity Equation: Conservation of Mass

The Continuity Equation arises from the conservation of mass: for an incompressible fluid, the amount of fluid entering one end of a pipe must equal the amount of fluid exiting the other end per unit time.

$$
A_1 v_1 = A_2 v_2
$$

Where:

$$
A_1, A_2 = \text{Cross-sectional areas at two points in the pipe (m}^2\text{)}
$$

$$
v_1, v_2 = \text{Fluid speeds at those respective points (m/s)}
$$

This product (A) (v) is called volume flow rate, denoted Q, and has units of m³/s.

$$
Q = A v
$$

Thus:

$$
Q_1 = Q_2 \Rightarrow A_1 v_1 = A_2 v_2
$$

Interpretation:

If a pipe narrows, area A decreases → velocity v must increase.
If a pipe widens, area increases → velocity decreases.
The same amound of fluid must pass each point per second, assuming no loss or accumulation.

Bernoulli’s Equation: Conservation of Energy in Fluids

Bernoulli’s Equation is a statement of the conservation of mechanical energy for an ideal, incompressible, non-viscous fluid undergoing steady flow.

It balances:

Kinetic energy (due to motion)
Gravitational potential energy (due to height)
Pressure energy (due to fluid pressure)

$$
P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}
$$

Where:

$$
P = \text{Pressure energy per unit volume (Pascals, Pa)}
$$

$$
\frac{1}{2} \rho v^2 = \text{Kinetic energy per unit volume (Pa)}
$$

$$
\rho g h = \text{Gravitational potential energy per unit volume (Pa)}
$$

$$
\rho = \text{Density of the fluid (kg/m}^3\text{)}
$$

$$
v = \text{Fluid velocity (m/s)}, \quad h = \text{Height above reference (m)}
$$

This equation tells us that in an ideal system, as a fluid gains speed, its pressure or height must decrease to conserve energy – and vice versa.

Physiological Example: Blood Flow in Circulation

As blood passes from aorta to capillaries, cross-sectional area increases greatly → velocity drops.
Pressure also drops along the length of the vessel due to frictional resistance (not captured in ideal Bernoulli’s but important in real physiology.

In arteries:

Narrower arteries can show increased velocity and decreased pressure downstream, consistent with Bernoulli’s principles.
However, viscosity and turbulence (e.g., in aortic stenosis or anemia) complicate ideal behavior.

How to Apply Bernoulli’s Equation

You can treat Bernoulli’s equation as a form of mechanical energy conservation:

Consider Two Points (1 and 2):

$$
P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2
$$

Use this when you have:

Change in height (e.g., vertical pipes or fountains)
Change in velocity (e.g., narrowed or widened pipe)
Pressure measurements (e.g., barometer, manometer, blood pressure)

Bernoulli-Continuity Synthesis: The Venturi Effect

The Venturi Effect is a direct application of Bernoulli + Continuity:

In a narrow region of a tube (small A), fluid speed v increases.
Because v increases, Bernoulli tells us that pressure P must decrease.

Result:

Narrow pipe → fast fluid → low pressure

This principle is exploited in:

Venturi masks for oxygen delivery (low-pressure suction draws in ambient air)
Carburetors, atomizers, aspirators
Measurement of flow rate in Venturi meters

Conceptual Summary Table

Parameter	Narrow Tube	Wider Tube
Cross-sectional Area A	↓	↑
Velocity v	↑	↓
Pressure P	↓ (Venturi effect)	↑
Flow Rate Q = Av	Constant (if ideal flow)	Constant (if ideal flow)

MCAT Strategy Notes and Traps

Common Error	Clarification
Misapplying Bernoulli to non-ideal flows	MCAT assumes ideal fluids unless told otherwise – no friction, viscosity, or turbulence
Confusing pressure drop as energy loss	In ideal fluids, pressure converts into kinetic or potential energy, not lost
Forgetting units	Keep consistent SI units: Pa for pressure, m/s for velocity, m for height

Real-World Analogies

Scenario	How Bernoulli/Continuity Apply
Shower curtain pulls inward	Fast air from shower reduces pressure → curtain drawn inward (Venturi effect)
Blood pressure cuff	Occludes artery, reduces area → blood speed increases → Korotkoff sounds emerge
Compressed garden hose nozzle	Narrower opening → higher velocity stream → pressure inside hose drops
Syringe aspiration	Pulling plunger creates low pressure → fluid enters by atmospheric pressure

Viscosity and Poiseuille’s Law

What is Viscosity?

In real fluids, internal friction exists between adjacent layers of the fluid as they move past one another. This internal resistance to flow is known as viscosity.

Definition:

Viscosity is a measure of a fluid’s resistance to deformation and flow. It quantifies how “thick” or “sticky” a fluid is.

Honey → High viscosity (resists flow)
Water → Low viscosity (flows easily)

Unit:

$$
\text{Viscosity } (\eta) = \text{Pa} \cdot \text{s} = \frac{\text{N} \cdot \text{s}}{\text{m}^2}
$$

Where η is the Greek letter eta, used to denote dynamic viscosity.

Laminar vs. Turbulent Flow

Laminar flow = smooth, orderly flow where adjacent layers slide over each other
Turbulent flow = chaotic, irregular mixing of layers and eddies

For Poiseuille’s Law (below) to apply, the flow must be:

Steady
Incompressible
Newtonian (constant viscosity)
Laminar

In blood flow, large arteries tend to show laminar flow, but turbulence can occur at branch points, plaques, or valve defects.

Poiseuille’s Law: Flow Rate Through a Viscous Pipe

What It Describes:

Poiseuille’s Law quantifies the volume flow rate Q of a viscous fluid through a cylindrical pipe, depending on pressure, radius, length, and viscosity.

$$
Q = \frac{\pi r^4 \Delta P}{8 \eta L}
$$

Where:

$$
Q = \text{Volumetric flow rate (m}^3\text{/s)}
$$

$$
r = \text{Radius of the pipe (meters, m)}
$$

$$
\Delta P = \text{Pressure difference across the pipe (Pascals, Pa)}
$$

$$
\eta = \text{Dynamic viscosity of the fluid (Pa} \cdot \text{s)}
$$

$$
L = \text{Length of the pipe (meters, m)}
$$

Conceptual Takeaways:

Flow rate increases with:
- Higher pressure difference (ΔP)
- Larger radius of pipe → power of 4 dependence is crucial
Flow rate decreases with:
- Higher fluid viscosity (η)
- Longer pipe length

Remember: The radius is the most sensitive variable. Doubling the radius increases flow by a factor of 16!

Clinical Example: Blood Flow Through Vessels

Blood is a viscous, incompressible fluid, and arteries approximate cylindrical pipes.
Atherosclerosis (plaque buildup) reduces radius → drastically reduces flow rate.
Blood doping or dehydration increases blood viscosity → decreases flow.
Vasodilation increases r, enhancing flow to tissues.

Viscosity in Real-World Terms

Fluid	Approximate Viscosity (η)	Comments
Water	1 x 10^-3 (Pa)(s)	Low viscosity; baseline reference
Blood	3-4 x 10^-3 (Pa)(s)	Increases with hematocrit
Olive oil	8 x 10^-2 (Pa)(s)	Much higher than water; thick flow
Glycerol	1.5 (Pa)(s)	Extremely viscous
Air (gas)	1.8 x 10^-5 (Pa)(s)	Very low viscosity; treated as nearly inviscid

Reynolds Number: Predicting Flow Type

While not always tested directly, MCAT students should understand the concept of Reynolds number as a predictor of whether flow is laminar or turbulent:

$$
\text{Re} = \frac{\rho v D}{\eta}
$$

Where:

$$
\text{Re} = \text{Reynolds number (unitless)}
$$

$$
\rho = \text{Density of the fluid (kg/m}^3\text{)}
$$

$$
v = \text{Flow speed of the fluid (m/s)}
$$

$$
D = \text{Characteristic diameter of the pipe or vessel (m)}
$$

$$
\eta = \text{Dynamic viscosity of the fluid (Pa} \cdot \text{s)}
$$

If Re < 2000: flow is laminar

If Re > 3000: flow is turbulent

Transitional range: 2000-3000

Summary of Relationships

Variable	Effect on Flow Rate Q	Types of Relationship
Pressure difference ΔP	↑ leads to ↑ flow	Directly proportional
Radius r	↑ leads to ↑↑↑↑ flow	Proportional to r⁴
Viscosity η	↑ leads to ↓ flow	Inversely proportional
Length L	↑ leads to ↓ flow	Inversely proportional

General MCAT Strategy Recap: When to Use What

Scenario	Use This Equation
Fluid speed increases in a narrowing pipe	Bernoulli + Continuity
Pressure drop in a long, narrow tube	Poiseuille’s Law
Flow rate dependence on radius or viscosity	Poiseuille’s Law
Area-velocity relationships	Continuity Equation: A1v1 = A2v2
Comparing fluid speed and pressures at 2 points	Bernoulli’s Equation