The absolute pressure in the natural gas pipeline is 15.14 psi.
The given parameters:
atmospheric pressure, P₀ = 14.2 Psia (lb/in² atm)
the height of the pipeline, h = 26 in
density of water, ρ = 62.4 lbm/ft³
To find:
- the absolute pressure in the pipeline
The absolute pressure in the pipeline is calculated as follows:
[tex]P_{abs} = P_o + \rho gh\\\\where;\\\\g \ is \ acceleration \ due \ to \ gravity \\\\h \ is \ height = 26 \ in\\\\note: \ 1 \ ft = 12 \ in \\\\pressure \ (psi) = constant \times (\frac{lb}{gallon} ) \times ft\\\\ (\frac{lb}{gallon} ) = \frac{lb}{231 \ in^3} \\\\pressure (psi)= \frac{lb}{231 \ in^3} \times 12 \ in \\\\ pressure(psi)= \frac{12}{231} \ \frac{lb}{in^2}\\\\pressure (psi)= 0.052 \ (\frac{lb}{in^2} )[/tex]
constant = 0.052
To use this constant;
- density must be in lb/gallon and,
- height must be in ft
[tex]density, \rho = 62.4 \frac{lb }{ft^3} \times \frac{1 \ ft^3}{7.48 \ gallon} = 8.342 \ \frac{lb}{gallon} \\\\height, h = 26 \ in \times \frac{1 \ ft}{12 \ in } = 2.167 \ ft[/tex]
The absolute pressure is calculated as:
[tex]P_{abs} = P_o + (constant \times \frac{lb}{gallon} \times feet)\\\\P_{abs} = 14.2 \ psi + (0.052 \times 8.342 \ \frac{lb}{gallon} \times 2.167 \ ft)\\\\P_{abs} = 14.2 \ psi + 0.94 \ psi\\\\P_{abs} = 15.14 \ psi[/tex]
Thus, the absolute pressure in the pipeline is 15.14 psi.
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