Question

This question is related to the hoop stress error analysis. Consider a measurement of hoop stress from a thin-walled pressure vessel. The required formula covering pressure (P), radius (r) and wall thickness (t) is given below (Table 2). Determine the Wr/sigma (%) = ? Table 2. Hoop stress error analysis Table 2. Hoop stress error analysis Parameters/Factors Formula P P=100 psi ±5% Pr r r = 3 in ±1/8" ?_{Hoop} = \frac{Pr}{t} t t = 0.15 in ±0.03" Least \omega_{\sigma} = \left[ \left( \frac{\partial \sigma}{\partial P} \omega_{P} \right)^{2} + \left( \frac{\partial \sigma}{\partial r} \omega_{r} \right)^{2} + \left( \frac{\partial \sigma}{\partial t} \omega_{t} \right)^{2} \right]^{1/2} square analysis O a. 28 O b. 6.8 O c. 20.4 O d. 10.4 O e. 15

          This question is related to the hoop stress error analysis. Consider a measurement of hoop stress from a thin-walled pressure vessel. The required formula covering pressure (P), radius (r) and wall thickness (t) is given below (Table 2). Determine the Wr/sigma (%) = ?
Table 2. Hoop stress error analysis
Table 2. Hoop stress error analysis
Parameters/Factors
Formula
P
P=100 psi ±5%
Pr
r
r = 3 in ±1/8"
?_{Hoop} = \frac{Pr}{t}
t
t = 0.15 in ±0.03"
Least
\omega_{\sigma} = \left[ \left( \frac{\partial \sigma}{\partial P} \omega_{P} \right)^{2} + \left( \frac{\partial \sigma}{\partial r} \omega_{r} \right)^{2} + \left( \frac{\partial \sigma}{\partial t} \omega_{t} \right)^{2} \right]^{1/2}
square
analysis
O a. 28
O b. 6.8
O c. 20.4
O d. 10.4
O e. 15

This question is related to the hoop stress error analysis. Consider a measurement of hoop stress from a thin-walled pressure vessel. The required formula covering pressure (P), radius (r) and wall thickness (t) is given below (Table 2). Determine the Wr/sigma (%) = ?
Table 2. Hoop stress error analysis
Table 2. Hoop stress error analysis
Parameters/Factors
Formula
P
P=100 psi ±5%
Pr
r
r = 3 in ±1/8"
?Hoop = (Pr)/(t)
t
t = 0.15 in ±0.03"
Least
ωσ = [ ( (∂σ)/(∂P) ωP )^2 + ( (∂σ)/(∂r) ωr )^2 + ( (∂σ)/(∂t) ωt )^2 ]^1/2
square
analysis
O a. 28
O b. 6.8
O c. 20.4
O d. 10.4
O e. 15

Added by Daniel R.

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