Understanding Hoop Stress in Microbore Hose Design

By Josh Cosford, Contributing Editor

Hoop stress is a fundamental concept in fluid power, yet it is often overlooked. It represents the circumferential stress exerted on a tube, cylinder, or circular wall when internal pressure pushes outward. Think of the steel hoops that reinforce a wine barrel—similar principles apply to plastic microbore hoses, which can withstand remarkably high pressures.

Hoop stress does not scale linearly with diameter and is inversely proportional to wall thickness, expressed by the equation:
σ = (P × D) / (2 × t)
where σ is stress, P is internal pressure, D is inner diameter, and t is wall thickness.

While the math can be intimidating, the key takeaway is that doubling wall thickness produces the same effect as halving the internal diameter. This relationship holds for tubes, pipes, and hoses, though not for pressure vessels governed by different equations.

Consider a PTFE microbore hose rated for 5,000 psi. It might have an inner diameter of 1/8 in. (0.125 in.) and a wall thickness of only 0.060 in. To double the diameter to 1/4 in., the wall must also double to 0.120 in. For a 1/2 in. diameter hose, a 0.240 in. wall thickness is required.

These numbers illustrate why producing high‑pressure, large‑bore hoses or cylinders becomes impractical. A 12 in. ID PTFE hydraulic hose would demand nearly 6 in. of wall material, resulting in an outside diameter approaching 24 in.—a clear example of the limitations imposed by hoop stress.

Why does wall thickness matter? It’s a surface‑area effect. Visualize a radial ring 2 in. ID and 1 in. wide. Its inner surface area is circumference × width, or 6.28 in². At 3,000 psi, the internal pressure exerts 18,840 lb of outward force on that surface.

Doubling the diameter to 4 in. doubles the circumference, so the outward force rises to approximately 37,699 lb. To maintain a 5,000 psi rating with the same wall thickness, the tube would need a wall roughly 2 in. thick to counter the 63,000 lb force.

In practice, we don’t build 5,000 psi PTFE cylinders; the required wall would be impractical. At Higginson, we use a ¼ in. wall honed steel tube for a 4 in. bore hydraulic cylinder, rated at 3,000 psi with a 4:1 safety factor.

Similarly, an 8 in. bore cylinder would require a ½ in. wall to handle 3,000 psi, and a 16 in. bore cylinder could use a 1 in. wall. These examples confirm that hoop‑stress calculations guide material and wall‑thickness decisions for most cases.

Next time you test a microbore hose, remember that the outward forces are substantial even though the hose diameter is small. Understanding hoop stress ensures you design safely and efficiently.

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