# Poiseuille’s Law MCAT (Blood Flow Equation Explained)

Last Updated On: January 1, 2022

When studying for the MCAT, you might be tempted to focus on high-yield and medium-yield topics the most. If you’re short on time, this is a good idea.

However, if you have plenty of time, it’s smart to go through low-yield topics as well.

One such topic is Poiseulle’s Law.

I’ve had countless students come to me struggling to understand this law and how it’s tested on the MCAT.

So, I’ve decided to create my guide on everything students should know about Poiseulle’s Law on the MCAT.

## Poiseuille’s Law for Flow Summary

• Fluids are a medium-yield topic on the MCAT.
• When studying fluids, it’s important to distinguish between laminar and turbulent flows.
• Poiseuille’s flow is related to viscosity and laminar flow.

## Fluid Mechanics

Fluid mechanics studies liquids, plasmas, gases, and the forces they produce [1].

It has applications in many scientific disciplines, such as biological systems, astrophysics, and mechanical and chemical engineering.

Fluid mechanics can be used to explain blood properties and blood flow in arteries, veins, and capillaries.

This is a medium-yield topic on the MCAT, so it’s worth paying attention to.

## What are Fluids?

Fluids are liquids, gasses, or any state of matter that can’t keep form when subjected to shearing or tangential stress.

The flow of fluids is classified in two ways: laminar and turbulent.

### Laminar Flow

Laminar flow happens when the fluid moves in parallel layers in regular paths [2].

There’s no disruption between the layers nor any eddies or swirls.

All particles move in an orderly way, in a straight line parallel to the walls.

Laminar flow is also called streamline or viscous flow.

### Turbulent Flow

Turbulent flow has an irregular movement of particles of the fluid. There are chaotic property changes, such as rapid pressure variations.

Compared to laminar flow, the fluid doesn’t travel in parallel layers but mixes across the tube.

“Laminar flow would be pushing a soccer ball through the pool, and the water flows nicely around it. Then let’s imagine you’re playing water polo, and you shove the ball to your friend at the other side. The water breaks down the layers and eddies around the soccer ball.” MedCat YouTube Channel

There’s a disruption between the layers and eddies and recirculation in a turbulent flow. Also, the speed of the fluid is constantly changing in direction and magnitude.

## Poiseuille Flow

Poiseuille flow is the flow of viscous fluids through a narrow tube, such as a blood vessel or a catheter.

While the fluid that flows through the pipe can have an average velocity, the velocity won’t stay the same at all points in the cross-section of the pipe.

There’s more interaction between the fluid and the walls, so the fluid closer to the walls will move slower compared to the fluid in the center of the pipe.

You can expect Poiseuille flow questions on the MCAT related to blood vessels, as these are modeled as circular pipes.

Note: The flow will increase with the fourth power of the radius but will decrease with the length of the blood vessel.

### Poiseuille Law Formula

Q = π⋅r⁴⋅P / 8⋅η⋅l

Q is flow rate.

Flow is measured in volume over time or m3s.

Note: Flow rate isn’t the same as linear speed or flow velocity, seen in Q=AV.

Q is the flow rate, but v is the linear velocity of the flow you’re looking at. Make sure not to mix up Q and V.

r is the radius of the closed pipe. It’s usually found in the unit of meter.

P is the pressure gradient. This is the reason why the fluid is moving from one place to another. It flows from high to low pressure.

It’s measured in units of pressure, which can be broken into force over area. It can be shown as Nm2=Pa.

8 is a constant.

η is a measure of viscosity. Viscosity unit is Pa x s (Pascals time seconds).

L is the pipe length, and it’s measured in meters.

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### Viscosity

Viscosity is an important part of Poiseuille's formula. It refers to how much resistance a fluid has against stresses.

Flow is proportional to the fluid viscosity. If viscosity increases, the fluid will be thicker and move more slowly, and the other way around.

For example, the blood viscosity increases as the temperature decreases.

So, warming and diluting blood before administration increases its flow rates.

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## Poiseuille’s Law MCAT: Final Thoughts

I’ve covered everything you should know about fluids, how Poiseuille’s Flow is related to fluids and why viscosity is important.

My advice is to study this guide in detail and go over as many practice questions as needed until you get the hang of the fluids and Poiseuille’s formula.

Keep in mind that this is a medium-yield topic, and it’s closely related to blood vessels and blood flow, so chances are you’ll encounter it on the MCAT.

References:

1. https://www.sciencedirect.com/topics/engineering/fluid-mechanics
2. https://www.vapourtec.com/flow-chemistry/laminar-turbulent/