Examples

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• Examples

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Example 2

• A thin cylinder 75 mm internal diameter, 250 mm
  long with walls 2.5 mm thick is subjected to an
  internal pressure of 7 MN/m2. Determine the
  change in internal diameter, the change in
  length, hoop stress longitudinal stress (E
  200 GN/m2 ? 0.3).

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Solution
For thin cylinders
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For thin cylinders
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For thin cylenders
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For thin cylinders
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Example 3

• A cylinder has an internal diameter of 230 mm,
  has walls 5 mm thick and is 1 m long. It is found
  to change in internal volume by 12.0 x 10-6 m3
  when filled with a liquid at a pressure p. If E
  200GN/m2 and ? 0.25, and assuming rigid end
  plates, determine

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• (a) the values of hoop and longitudinal stresses
• (b) the modifications to these values if joint
  efficiencies of 45 (hoop) and 85 (longitudinal)
  are assumed
• (c) the necessary change in pressure p to produce
  a further increase in internal volume of 15 .
  (The liquid may be assumed incompressible).

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Solution

• Check first type of cylinder
• d / t 230 / 5 46
• More than 20, then the cylinder is considered
  Thin cylinder

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• Second step look for the pressure. If the
  pressure is unknown then try to get it by the
  available data.
• In this example the pressure is unknown but the
  change of volume is given. So that you have to
  use the available data to get the unknown
  parameters.

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For thin cylinders
The original volume V is not given but you can
calculate it from the given dimensions of the
cylinder.
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Calculating the original volume V
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For thin cylinders
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For thin cylinders
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b hoop stress acting on the longitudinal joints
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Longitudinal stress (acting on the
circumferential joints)
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• (c) Since the change in volume is directly
  proportional to the pressure, the necessary 15 ,
  then increase in volume is achieved by increasing
  the pressure also by 15 .

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• Necessary increase in pressure
• increase in p
• 0.15 x 1.25 x 106
• 1.86 MN/m2

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• Example (4)
• (a) A sphere, 1 m internal diameter and 6 mm wall
  thickness, is to be pressure-tested for safety
  purposes with water as the pressure medium.
  Assuming that the sphere is initially filled with
  water at atmospheric pressure, what extra volume
  of water is required to be pumped in to produce a
  pressure of 3 MN/m2?
• For water, K 2.1 GN/m2.

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• (b) The sphere is now placed in service and
  filled with gas until there is a volume change of
  72 x 10-6 m3
• Determine the pressure exerted by the gas on the
  walls of the sphere.

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Solution
Where
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Then
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b- Change of volume of the sphere
volume change is given of 72 x10-6 m3
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The required pressure
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Problems
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