Understanding Air Pressure Limits in Fiberglass Tanks

Fiberglass tanks are widely used in a variety of applications, from industrial uses to household storage. One of the critical factors in the design and usage of such tanks is the air pressure they can safely contain. This article aims to demystify the process of calculating the maximum air pressure that a fiberglass tank with specific dimensions can hold.

Factors Influencing Maximum Pressure

Calculating the maximum air pressure a fiberglass tank can withstand involves several key factors:

Material Properties: The strength and durability of the material. Geometry: The shape and dimensions of the tank. Safety Factors: Engineering standards and guidelines to ensure safety.

Problem Statement

Consider a fiberglass tank with the following specifications: Diameter: 1 foot Radii: 0.5 feet Height: 4 feet Wall thickness: 0.5 inches (approximately 0.04167 feet)

Calculation Steps

1. Calculate the Inner Diameter

The inner diameter is crucial for determining the volume and pressure capacity. We start by subtracting twice the wall thickness from the outer diameter:

Inner Diameter Outer Diameter - 2 times Wall Thickness 1 text{ft} - 2 times 0.04167 text{ft} approx 0.9167 text{ft}

2. Calculate the Inner Radius

The inner radius is half of the inner diameter:

Inner Radius frac{text{Inner Diameter}}{2} approx 0.45835 text{ft}

3. Calculate the Surface Area of the Cylinder

The surface area of the cylindrical wall is essential for stress calculations:

A 2 pi r h approx 2 pi times 0.45835 text{ft} times 4 text{ft} approx 11.5 text{ft}^2

4. Material Properties

The tensile strength of fiberglass is a critical factor. A common value is about 60000 psi. To ensure safety, a safety factor of 3 is applied:

Allowable Stress frac{60000 text{psi}}{3} 20000 text{psi}

5. Calculate the Maximum Pressure

Using the formula for the hoop stress in a thin-walled cylinder:

sigma frac{P cdot r}{t}

Rearranging for P:

P frac{sigma cdot t}{r}

Substituting the values:

P frac{20000 text{psi} cdot 0.04167 text{ft}}{0.45835 text{ft}} approx 1814.7 text{psi}

Conclusion

The fiberglass tank can hold approximately 1814.7 psi of air pressure under the given conditions. However, this is a theoretical maximum. Practical factors such as manufacturing defects, fatigue, and environmental conditions must also be considered. Always consult with a qualified engineer when designing or using pressure vessels.