# Radial Displacement Thin-wall Section (Internal and External Pressure)

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## Radial Displacement Thin-wall Section (Internal and External Pressure) Formula

$$\large{ \Delta_r = \frac{ 1 \;-\; \mu }{ \lambda } \; \frac{ \left( p_i \;r_i^2 \;-\; p_e \;r_e^2 \right) \; r }{ r_e^2 \;-\; r_i^2 } \;+\; \frac{ 1 \;+\; \mu }{ \lambda } \; \frac{ \left( p_i \;-\; p_e \right) \; r_e^2 \; r_i^2 }{ \left( r_e^2 \;-\; r_i^2 \right) \; r } }$$
Symbol English Metric
$$\large{ \Delta_r }$$ = radius change $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \lambda }$$  (Greek symbol lambda) = elastic modulus $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \mu }$$  (Greek symbol mu) = Poisson's Ratio $$\large{ dimensionless }$$
$$\large{ p_e }$$ = external pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ p_i }$$ = internal pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ p }$$ = pressure under consideration $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ r }$$ = radius to point of intrest $$\large{ in }$$ $$\large{ mm }$$
$$\large{ r_e }$$ = external radius $$\large{ in }$$ $$\large{ mm }$$
$$\large{ r_i }$$ = internal radius $$\large{ in }$$ $$\large{ mm }$$

Tags: Hoop Stress