Problem №3. Pressure inside steel pipe with inner diameter d=615 mm equal p=3,5 MPa. Find the required pipe wall thickness if the allowable stress for steel σ=158MPa

To find the required pipe wall thickness for a steel pipe with an inner diameter $d = 615$ mm and an internal pressure $p = 3.5$ MPa, using an allowable stress $\sigma = 158$ MPa, we can use Barlow's formula, which is a common method for calculating the required wall thickness of a pipe. Barlow's formula is given by:

$t = \frac{p \cdot (D - 0.5t)}{2 \cdot \sigma}$

where:

• $t$ is the required wall thickness of the pipe,
• $p$ is the internal pressure,
• $D$ is the outside diameter of the pipe,
• $\sigma$ is the allowable stress for the material.

However, we are given the inner diameter $d$ and not the outside diameter $D$. To proceed, we need to determine the outside diameter. Assuming a uniform wall thickness, the outside diameter $D$ can be calculated as $D = d + 2t$, where $t$ is the wall thickness we are trying to find. But since we do not have $t$ yet, we cannot directly apply Barlow's formula.

Instead, we can rearrange Barlow's formula to solve for $t$ when $D$ is expressed in terms of $d$ and $t$:

$t = \frac{p \cdot (2d)}{4 \cdot \sigma}$

Plugging in the given values:

$t = \frac{3.5 \cdot 2 \cdot 615}{4 \cdot 158}$

Now, let's calculate the value of $t$:

$t = \frac{4.2 \cdot 615}{632}$ $t = \frac{2589}{632}$ $t \approx 4.09 \text{ mm}$

This is the minimum required wall thickness to withstand the internal pressure without exceeding the allowable stress for the steel. However, this calculation does not take into account any additional factors such as corrosion allowances, manufacturing tolerances, or safety factors, which are typically considered in real-world applications.23