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A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200
and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders?
and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders?
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A high pressure cylinder consists of an inner cylinder of inner and ou...
**Solution:**
Given data:
- Inner diameter of the inner cylinder ($d_{1i}$) = 200 mm
- Outer diameter of the inner cylinder ($d_{1o}$) = 300 mm
- Outer diameter of the jacket ($d_{2o}$) = 400 mm
- Difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly ($\delta$) = 0.25 mm
- Elastic modulus of the material ($E$) = 207 GPa (207 kN/mm²)
We need to calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders.
1. **Calculation of the shrinkage pressure:**
The shrinkage pressure is the pressure exerted on the inner cylinder due to the interference fit with the jacket.
The interference fit is the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly, which is given as $\delta$ = 0.25 mm.
The shrinkage pressure can be calculated using the following formula:
$P = \dfrac{\delta \cdot E}{\ln(\dfrac{d_{2o}}{d_{1o}})}$
Substituting the given values, we get:
$P = \dfrac{0.25 \cdot 207}{\ln(\dfrac{400}{300})}$
Calculating the value, we get:
$P \approx 2.12$ MPa
Therefore, the shrinkage pressure is approximately 2.12 MPa.
2. **Calculation of the maximum tensile stress:**
The maximum tensile stress induced in any of the cylinders can be calculated using the following formula:
$\sigma_{max} = \dfrac{P \cdot d_{1o}}{2t}$
where $t$ is the thickness of the cylinder.
To calculate the thickness of the cylinder, we need to subtract the inner diameter of the inner cylinder from the outer diameter of the inner cylinder and divide it by 2.
$t = \dfrac{d_{1o} - d_{1i}}{2} = \dfrac{300 - 200}{2} = 50$ mm
Substituting the values in the formula, we get:
$\sigma_{max} = \dfrac{2.12 \cdot 300}{2 \cdot 50}$
Calculating the value, we get:
$\sigma_{max} \approx 12.72$ MPa
Therefore, the maximum tensile stress induced in any of the cylinders is approximately 12.72 MPa.
Given data:
- Inner diameter of the inner cylinder ($d_{1i}$) = 200 mm
- Outer diameter of the inner cylinder ($d_{1o}$) = 300 mm
- Outer diameter of the jacket ($d_{2o}$) = 400 mm
- Difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly ($\delta$) = 0.25 mm
- Elastic modulus of the material ($E$) = 207 GPa (207 kN/mm²)
We need to calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders.
1. **Calculation of the shrinkage pressure:**
The shrinkage pressure is the pressure exerted on the inner cylinder due to the interference fit with the jacket.
The interference fit is the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly, which is given as $\delta$ = 0.25 mm.
The shrinkage pressure can be calculated using the following formula:
$P = \dfrac{\delta \cdot E}{\ln(\dfrac{d_{2o}}{d_{1o}})}$
Substituting the given values, we get:
$P = \dfrac{0.25 \cdot 207}{\ln(\dfrac{400}{300})}$
Calculating the value, we get:
$P \approx 2.12$ MPa
Therefore, the shrinkage pressure is approximately 2.12 MPa.
2. **Calculation of the maximum tensile stress:**
The maximum tensile stress induced in any of the cylinders can be calculated using the following formula:
$\sigma_{max} = \dfrac{P \cdot d_{1o}}{2t}$
where $t$ is the thickness of the cylinder.
To calculate the thickness of the cylinder, we need to subtract the inner diameter of the inner cylinder from the outer diameter of the inner cylinder and divide it by 2.
$t = \dfrac{d_{1o} - d_{1i}}{2} = \dfrac{300 - 200}{2} = 50$ mm
Substituting the values in the formula, we get:
$\sigma_{max} = \dfrac{2.12 \cdot 300}{2 \cdot 50}$
Calculating the value, we get:
$\sigma_{max} \approx 12.72$ MPa
Therefore, the maximum tensile stress induced in any of the cylinders is approximately 12.72 MPa.
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A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders?
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A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders?.
A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A high pressure cylinder consists of an inner cylinder of inner and outer diameters of 200 and 300 mm respectively. it is jacketed by an outer cylinder with an outside diameter of 400 mm. the difference between the outer diameter of the inner cylinder and the inner diameter of the jacket before assembly is 0.25 mm (e = 207 kn/mm2). calculate the shrinkage pressure and the maximum tensile stress induced in any of the cylinders?.
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