Question

The diameter of piston of a steam engine is 300 mm and the maximum pressure is 0.7 N/mm 2 . If the maximum permissible compressive strength for piston and material is 40 N/ mm2 .Find size of piston rod

Answer 1

The piston rod size is acceptable if stress (0.699 N/mm²) is below the permissible compressive strength (40 N/mm²). Calculate force using pressure and piston area (70685.834 mm²).

To find the size of the piston rod, we can use the formula for stress:

`\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]`

The force acting on the piston is the product of pressure and the area of the piston. The formula for the area of a piston is:

`\[ \text{Area} = (\pi)/(4) * \text{Diameter}^2 \]`

Now, let's calculate the force on the piston:

`\[ \text{Force} = \text{Pressure} * \text{Area} \]`

Substitute the values into the formulas:

`\[ \text{Area} = (\pi)/(4) * (300 \, \text{mm})^2 \]`

`\[ \text{Force} = 0.7 \, \text{N/mm}^2 * \text{Area} \]`

Next, check if the stress is within the permissible compressive strength for the material:

`\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]`

If
`\(\text{Stress} \leq 40 \, \text{N/mm}^2\),`then the size of the piston rod is acceptable.

Now, let's perform the calculations:

`\[ \text{Area} = (\pi)/(4) * (300 \, \text{mm})^2 \approx 70685.834 \, \text{mm}^2 \]`

`\[ \text{Force} = 0.7 \, \text{N/mm}^2 * 70685.834 \, \text{mm}^2 \approx 49480.083 \, \text{N} \]`

`\[ \text{Stress} = \frac{49480.083 \, \text{N}}{70685.834 \, \text{mm}^2} \approx 0.699 \, \text{N/mm}^2 \]`

ulated stress is less than the permissible compressive strength (40 N/mm²), so the size of the piston rod is acceptable.