Relationship Between Quartz Tube Diameter and Pressure Resistance (Part 5 of 6)

1. Core Relationship (Thin-Wall Theory Formula)

The maximum allowable internal pressure (Pmax) of a quartz tube is inversely proportional to its inner diameter (D).

Τύπος:

• Pmax = Maximum internal pressure (MPa)
• σ = Tensile strength of quartz (~50 MPa, decreases at high temperatures)
• t = Wall thickness (mm)
• D = Inner diameter (mm)

Key Conclusion: Pressure resistance is inversely proportional to the inner diameter.

• Smaller inner diameter → higher pressure resistance (at the same wall thickness).
• Larger inner diameter → significantly reduced pressure resistance.

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2. Pressure Resistance Comparison for Different Inner Diameters (Fixed Wall Thickness = 2 mm)

Inner Diameter D (mm)	Theoretical Pressure (MPa)	Practical Safe Pressure (MPa)
5	40	8–12
10	20	4–6
20	10	2–3
50	4	0.8–1.2

Note: In real applications, a safety factor of 3–5 is required. Therefore, the rated working pressure is always lower than the theoretical value.

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3. Combined Influence of Diameter and Wall Thickness

• Small Diameter Tubes (D < 10 mm):
  • Advantage: Naturally high pressure resistance, suitable for high-pressure experiments (e.g., microreactors, capillary fluid systems).
  • Example: ID 5 mm, wall thickness 2 mm → working pressure 8–12 MPa.
• Large Diameter Tubes (D > 20 mm):
  • Disadvantage: Rapid decline in pressure resistance, requiring much greater wall thickness.
  • Example: ID 50 mm, wall thickness 5 mm → only ~2 MPa.
  • To withstand 10 MPa, wall thickness ≥25 mm would be needed (impractical; recommend alumina or sapphire tubes instead).

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4. Application Case: ID 7.75 mm, 10 MPa Requirement

• Theoretical minimum wall thickness: 0.775 mm.
• Practical requirement with safety factor: ≥3 mm.
• Outer diameter: 7.75 mm + 2 × 3 mm = 13.75 mm.

Conclusion:

• At ID 7.75 mm with 3 mm wall thickness, 10 MPa pressure is achievable.
• If ID increases to 15 mm with the same wall thickness, the pressure resistance drops to ~5 MPa.

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5. Engineering Recommendations for Diameter Selection

1. High-Pressure Applications:
   • Use small inner diameters (5–10 mm) to minimize wall thickness requirements.
2. Large Flow Applications:
   • If large diameters (>20 mm) are required, switch to alumina or sapphire tubes.
3. Vacuum Applications:
   • Large diameters are more prone to buckling and require increased wall thickness or external support.

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6. Extreme Case Comparisons

Inner Diameter D	Wall Thickness t	Theoretical Pressure	Practical Limitation
1 mm	1 mm	100 MPa	Microfluidics feasible, but machining difficult
10 mm	1 mm	10 MPa	Safe limit only 2–3 MPa
100 mm	10 mm	1 MPa	Only for low-pressure/static use

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7. Final Conclusion

• Diameter is the key variable: halving the inner diameter doubles the pressure resistance (at constant wall thickness).
• For ID 7.75 mm, wall thickness 3 mm is a practical balance, ensuring safe operation at 10 MPa.
• Large diameters (>20 mm) make high pressure impractical, so alumina or sapphire tubes should be considered.
• For optimization, consider wall thickness, material purity, and end-sealing methods together.