LaPlace Relationship confusion

[Ven0m]

KLN 2016 Physiology

LaPlace relationship:
Wall tension is proportional to pressure * radius.
The aorta is the artery with the greatest wall tension (greatest pressure and radius).

I understand that increasing pressure increases wall tension of a vessel.
But how does a larger radius mean a higher wall tension? Does it mean, "increasing radius beyond its normal radius increases wall tension"?
If you had two vessels: each have the same pressure, but one had a large radius and one had a small radius, but both have wall thickness proportional to their radius, why would the larger radius vessel have a greater wall tension?

I fully understand that if you have two deflated balloons, if you inflated one to about 10cm vs one to 50cm, the 50cm one would have way higher wall tension. But this is because you're expanding the radius without increasing the thickness. The aorta does have a larger radius than other arteries but its much thicker than other arteries... so I don't understand how simply having a larger radius increases wall tension.
Like why would a small tube with thin walls (arteries) have lower wall tension than a large tube with thick walls (aorta), if their pressure was the same.

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[Fruit Plant]

KLN 2016 Physiology

LaPlace relationship:
Wall tension is proportional to pressure * radius.
The aorta is the artery with the greatest wall tension (greatest pressure and radius).

I understand that increasing pressure increases wall tension of a vessel.
But how does a larger radius mean a higher wall tension? Does it mean, "increasing radius beyond its normal radius increases wall tension"?
If you had two vessels: each have the same pressure, but one had a large radius and one had a small radius, but both have wall thickness proportional to their radius, why would the larger radius vessel have a greater wall tension?

I fully understand that if you have two deflated balloons, if you inflated one to about 10cm vs one to 50cm, the 50cm one would have way higher wall tension. But this is because you're expanding the radius without increasing the thickness. The aorta does have a larger radius than other arteries but its much thicker than other arteries... so I don't understand how simply having a larger radius increases wall tension.
Like why would a small tube with thin walls (arteries) have lower wall tension than a large tube with thick walls (aorta), if their pressure was the same.

Take a look at this from HyperPhysics (Pressure):

Why does wall tension increase with radius?

If the upward part of the fluid pressure remains the same, then the downward component of the wall tension must remain the same. But if the curvature is less, then the total tension must be greater in order to get that same downward component of tension. For equilibrium of a load hanging on a cable, you can explore the effects of having a smaller angle for the supporting cable tension.

 

[Ven0m]

Take a look at this from HyperPhysics (Pressure):

Why does wall tension increase with radius?

If the upward part of the fluid pressure remains the same, then the downward component of the wall tension must remain the same. But if the curvature is less, then the total tension must be greater in order to get that same downward component of tension. For equilibrium of a load hanging on a cable, you can explore the effects of having a smaller angle for the supporting cable tension.

When it says wall tension increases when radius increases, does this mean that the larger radius, the greater wall tension that must be achieved to achieve the same internal pressure?
For example, they use this principle in the heart. In a dilated cardiomyopathy, the larger radius requires a higher wall tension to be generated in order to generate the same amount of internal pressure (and thus eject blood in a normal fashion).