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# Resistance in a tube

Discover the physics behind fluid resistance! Learn how Dr. Jean Louis Marie Poiseuille's 19th-century equations shed light on why it's harder to blow air through a straw than a tube. Explore how this principle applies to blood flow in our bodies, impacting resistance in our blood vessels. Rishi is a pediatric infectious disease physician and works at Khan Academy. Created by Rishi Desai.

## Want to join the conversation?

• What's the reason for r being raised to the fourth power? I can see why it would be squared (to get the cross sectional area of the tube), but I can't see why it's squared again.
• In laminar flow, the fluid moves quickly near the center of the tube but roughly rests near the walls; this develops a parabolic velocity profile (parabola like x^2 or a quadratic function for the un-initiated). This parabolic velocity profile means that velocity, a symptom of an opposite of resistance, grows with the square of radius. As you mentioned, area also grows with the square of radius. The area (growing with the square of radius) multiplied by the velocity (growing with the square of radius) makes volumetric flow rate grow with r^4.

--- the rest just complicates things more ---
When we say that resistance is 16 times as great for the small tube, this means that 16 small tubes would allow the same amount of airflow as one large tube. Clearly, cross-sectional area plays a less obvious role (unintended pun). While Wikipedia shows the integral leading to the higher power of radius, I suspect that you will be most satisfied with the intuition of the parabolic velocity profile.
Conductivity is flow divided by pressure. Resistance is the reciprocal of conductivity, therefore pressure divided by flow.

Conductivity growing with r^4 means resistance grows proportional to the reciprocal of r^4
• @ Besides taking medications, how do we get the arteries to loosen up and vaso-dilate more naturally?
• By increasing the water intake.

When you become dehydrated, 66% of the water loss is from the cells, 26% is from the fluid held outside the cells and 8% is from the blood. This may not sound like a significant amount, but when you consider that the blood is made up of 94% water, it's enough to make a difference.

The reason the arteries constrict is to take up the slack when the blood volume decreases. Failing a capacity adjustment to the “water volume” by the blood vessels, gases would separate from the blood and fill the space, causing “gas locks”.
• what's viscosity? (This might sound daft, but I'm not a native English speaker, and translating a language's specific vocabulary to another is hard ...)
• Viscosity can be thought of as the "thickness" of a liquid and is a result of the friction between different particles within the fluid. Think about how much easier a fluid like water (with low viscosity) flows than something like ketchup (higher viscosity)
• On the Arterioles, is their a specific name for the smooth muscles surrounding it?
• All arteries have a layer called the "tunica media" which basically means the "middle coat." It is the muscular part of the arteries and is made up of smooth muscle.
• I don't understand. Since the veins are very large, why do they have lower pressure than asteries, which are smaller?
• In general, any pipe with a larger diameter will have a lower pressure. Pressure is the ratio of force divided by the area it is distributed over. So the same force will exert higher pressure in a smaller tube than a big one.

As far as the human body goes, veins are also less pressurized because they have very high capacitance (the ability to stretch), and they're far away from the heart. The arteries on the other hand, have to handle all the high pressure blood being pumped out of the heart. Arteries very close to the heart are very elastic so that they can stretch to accomodate this high pressure without tearing.
• What is the cause of Vaso Constriction?
• Overall, vasoconstriction happens when the smooth muscle cells that are found mostly within the middle layer of your artery get a signal to contract, which "Constricts" or narrows the opening of the vessel.
There are a lot of signals that can tell blood vessels to contract. If they are stretched they can immediately contract as a reflex. They will also contract in response to certain substances produced by the body (such as epinephrine or thromboxane). Or if your body is exposed to cold temperatures, your nervous system can send signals to the blood vessels that are the closest to the skin surface and tell them to contract so that less blood flows through them and you do not loose too much body heat through your skin.
• why do our blood vessels need to contract and relax?
• to regulate blood amount that goes to a specific organ and to adjust our blood pressure
• I'm not understanding nor appreciating the relationship between pressure and resistance. As fluid enters a restriction or smaller radius in a tube, resistance increases (Poiseuille) yet pressure decreases & velocity increases (Bernoulli).

Increased resistance, I'm picturing crammed molecules which is the same thing as increased pressure? Help.
• I had the same question and asked many people. Unfortunately the only answer I got was compliance and elastance.