A C.I pipe of 200mm internal diameter and thickness of metal 50mm carries water under a pressure of 7 N/mm². Find the max and minimum intensities of hoop stress, sketch the Variation of hoop stress and radial pressure across the section.
Given:
Internal diameter of C.I pipe, D = 200mm
Thickness of metal, t = 50mm
Pressure of water, P = 7 N/mm²
Hoop stress, σ_h = PD/2t
Maximum hoop stress:
σ_h(max) = P(D + t)/2t
Substitute the values:
σ_h(max) = 7(200 + 50)/2(50)
σ_h(max) = 7(250)/100
σ_h(max) = 17.5 N/mm²
Minimum hoop stress:
σ_h(min) = P(D - t)/2t
Substitute the values:
σ_h(min) = 7(200 - 50)/2(50)
σ_h(min) = 7(150)/100
σ_h(min) = 10.5 N/mm²
Now, let's sketch the Variation of hoop stress and radial pressure across the section:
Hoop stress will be maximum at the inner diameter and gradually decrease towards the outer diameter. The variation of hoop stress will follow a parabolic curve.
Radial pressure will also follow a similar pattern, being maximum at the inner diameter and decreasing towards the outer diameter.
The sketch will show the maximum hoop stress at the inner diameter, the minimum hoop stress at the outer diameter, and the radial pressure decreasing gradually across the section.