If the thickness of the wall of the cylindrical vessel is less than ________ of its internal diameter, the cylindrical vessel is known as a thin cylinder.
Understanding Thin Cylinders and Wall Thickness
In the study of pressure vessels, cylindrical vessels are often classified as either 'thin' or 'thick'. This classification is based on the ratio of the vessel's wall thickness to its internal diameter. This distinction is crucial because the stress distribution within the wall of a thin cylinder is considered relatively uniform, simplifying the analysis compared to thick cylinders where stress varies significantly across the wall thickness.
The generally accepted criterion for classifying a cylindrical vessel as a thin cylinder is when the ratio of its wall thickness (t) to its internal diameter (d) is small. Specifically, if the wall thickness is less than a certain fraction of the internal diameter, the vessel is treated as a thin cylinder for stress analysis purposes.
Condition for a Thin Cylindrical Vessel
For a cylindrical vessel to be considered a thin cylinder, its wall thickness (t) must be significantly smaller than its internal diameter (d). The widely used threshold for this classification is:
- If the ratio of wall thickness to internal diameter, \(\frac{t}{d}\), is less than or equal to a specific value, the cylinder is considered thin.
- Different texts or applications might use slightly different thresholds, but a common value for this limit is 1/20.
Therefore, a cylindrical vessel is classified as a thin cylinder if its wall thickness is less than \(\frac{1}{20}\) of its internal diameter.
Mathematically, this condition is expressed as:
\(\frac{t}{d} < \frac{1}{20}\)
or
\(t < \frac{d}{20}\)
Where:
- \(t\) is the wall thickness of the cylindrical vessel.
- \(d\) is the internal diameter of the cylindrical vessel.
When this condition is met, the stresses (like hoop stress and longitudinal stress) within the wall are assumed to be uniform across the thickness, simplifying the formulas used for their calculation.
Comparing this condition with the given options, the fraction that represents the threshold for a vessel to be considered a thin cylinder is \(\frac{1}{20}\).
Important Questions from Analysis of Thin Cylinder
The longitudinal stress induced in a thin-walled cylindrical vessel of diameter D, thickness t, under pressure P is
If the thin cylindrical shell whose diameter is 'd' is subjected to an internal pressure 'p', then the ratio of longitudinal stress to the hoop stress is-
A seamless pipe is to carry a fluid under a pressure of 2 N/mm2. The thickness of the cylinder is 10 mm. Calculate the diameter of the pipe if the maximum stress allowed is 100 N/mm2.
The circumferential stress is given by:
In a thin cylinder, the hoop stress is:
