Short Answer:

Bursting pressure is the maximum internal pressure that a thin or thick-walled cylindrical or spherical vessel can safely withstand before it fails or bursts. It represents the failure limit of the material due to excessive hoop (circumferential) stress developed in the wall when subjected to internal pressure.

In simple words, bursting pressure is the pressure at which the stress in the cylinder wall exceeds the material’s ultimate tensile strength. Beyond this limit, the cylinder wall ruptures or cracks. This concept is very important in designing pressure vessels, gas cylinders, boilers, and pipelines for safe operation under internal pressure.

Detailed Explanation:

Bursting Pressure

When a cylindrical or spherical pressure vessel is subjected to internal pressure, it experiences tensile stresses in the wall — mainly hoop stress (acting circumferentially) and longitudinal stress (acting axially). If the internal pressure increases beyond a certain limit, these stresses also increase. When the maximum hoop stress reaches the ultimate tensile strength of the material, the wall of the vessel ruptures or bursts.

The internal pressure corresponding to this condition is called the bursting pressure of the vessel.

It is an important design parameter because it defines the safe working pressure and helps ensure that the vessel will not fail under normal operating conditions. Typically, the working pressure is kept well below the bursting pressure by applying a factor of safety.

Mathematical Expression for Bursting Pressure

For a thin-walled cylinder, where wall thickness is small compared to the diameter (), the hoop stress is assumed to be uniform across the thickness.

The hoop stress () is given by:

At the bursting point, the hoop stress becomes equal to the ultimate tensile stress () of the material. Therefore, the bursting pressure (p_b) can be obtained as:

Where,

•  = bursting pressure,
•  = wall thickness,
•  = ultimate tensile strength of the material,
•  = internal diameter of the cylinder.

This formula gives the theoretical bursting pressure for a thin cylinder. The actual safe working pressure is determined by dividing this value by a factor of safety (F.S.):

Bursting Pressure for Thick Cylinders

For thick-walled cylinders (where ), the stress varies across the thickness. Therefore, Lame’s equations are used to determine the bursting pressure.

The hoop stress at the inner surface (which is maximum) is given by:

At bursting, this stress becomes equal to the ultimate tensile strength ():

From which the bursting pressure for a thick cylinder can be obtained as:

This expression helps determine the pressure at which a thick cylinder will fail due to excessive stress.

Factors Affecting Bursting Pressure

1. Material Strength:
   The higher the ultimate tensile strength of the material, the higher will be the bursting pressure of the cylinder.
2. Wall Thickness:
   Increasing the wall thickness increases the cylinder’s ability to resist internal pressure, thus raising its bursting pressure.
3. Internal Diameter:
   Larger diameters reduce the bursting pressure, as the stress increases with the diameter.
4. Temperature:
   High temperatures decrease the strength of materials, reducing the bursting pressure.
5. Manufacturing Defects:
   Defects like porosity, cracks, or weak welds can lower the actual bursting pressure compared to theoretical values.
6. Type of Loading:
   Static pressure conditions are safer than fluctuating or impact loads, which can cause fatigue and early failure.

Determination of Bursting Pressure (Experimental Method)

Bursting pressure is often determined experimentally through hydrostatic testing.

1. The pressure vessel is filled with an incompressible fluid, such as water.
2. Pressure is increased gradually using a hydraulic pump.
3. The pressure at which the vessel wall ruptures or bursts is recorded as the bursting pressure.
4. For safety, this test is conducted in a controlled environment with proper safety barriers.

This method ensures that the actual bursting pressure matches or exceeds the design requirements.

Applications of Bursting Pressure

1. Pressure Vessel Design:
   Used to determine the safe wall thickness for boilers, tanks, and gas cylinders.
2. Pipeline Engineering:
   Ensures pipelines can safely carry internal pressure without bursting.
3. Hydraulic and Pneumatic Systems:
   Critical in designing cylinders, pumps, and accumulators subjected to high internal pressure.
4. Automotive and Aerospace Components:
   Used for testing fuel tanks, aircraft pressure vessels, and rocket motor casings.
5. Safety Standards:
   Bursting pressure forms the basis for certification and quality control in manufacturing high-pressure components.

Importance of Bursting Pressure in Design

• It defines the upper limit of pressure a vessel can handle before failure.
• Helps determine the factor of safety to ensure safe operation.
• Prevents catastrophic failure, which could lead to property damage and loss of life.
• Enables engineers to select appropriate materials and dimensions during the design phase.

By ensuring that the working pressure is much lower than the bursting pressure, the reliability and safety of pressure equipment are guaranteed.

Conclusion

Bursting pressure is the maximum internal pressure a cylindrical or spherical vessel can withstand before failure occurs. It depends on material strength, wall thickness, and diameter. For thin cylinders, it is given by , and for thick cylinders, by . This concept is essential in designing and testing pressure vessels, ensuring they operate safely within their limits. Accurate determination of bursting pressure helps maintain the safety, efficiency, and reliability of mechanical systems under pressure.