Pressure in an Oil Storage Tank What is the absolute pressure at the bottom of the cylindrical tank of Fig. E1.3, filled to a depth of H with crude oil, with its free surface exposed to the atmosphere? The specific gravity of the crude oil is 0.846. Give the answers for (a) H = 15.0 ft (pressure in

Question

Pressure in an Oil Storage Tank

What is the absolute pressure at the bottom of the cylindrical tank of Fig. E1.3, filled to a depth of [latex]H[/latex] with crude oil, with its free surface exposed to the atmosphere? The specific gravity of the crude oil is [latex]0.846[/latex]. Give the answers for (a) [latex]H=15.0 \mathrm{ft}[/latex] (pressure in [latex]\mathrm{lb}_{\mathrm{f}} / \mathrm{in}^{2}[/latex] ) and (b) [latex]H=5.0 \mathrm{~m}[/latex] (pressure in Pa and bar). What is the purpose of the surrounding dike?

Accepted Answer

(a) The pressure is that of the atmosphere, [latex]p_{a}[/latex], plus the increase due to a column of depth [latex]H=15.0 \mathrm{ft}[/latex]. Thus, setting [latex]p_{s}=p_{a}[/latex], Eqn. (1.34) gives:

[latex]p =p_{s}+ ho g H[/latex] (1.34)

[latex]\begin{aligned}p &=p_{a}+ ho g H \&=14.7+\frac{0.846 imes 62.3 imes 32.2 imes 15.0}{144 imes 32.2} \&=14.7+5.49=20.2 ext { psia. }\end{aligned}[/latex]

The reader should check the units, noting that the [latex]32.2[/latex] in the numerator is [latex]g[=][/latex] [latex]\mathrm{ft} / \mathrm{s}^{2}[/latex] and that the [latex]32.2[/latex] in the denominator is [latex]\mathrm{g}_{\mathrm{c}}[=] \mathrm{lb}_{\mathrm{m}} \mathrm{ft} / \mathrm{lb}_{\mathrm{f}} \mathrm{s}^{2}[/latex].

(b) For SI units, no conversion factors are needed. Noting that the density of water is [latex]1,000 \mathrm{~kg} / \mathrm{m}^{3}[/latex] and that [latex]p_{a} \doteq 1.01 imes 10^{5} \mathrm{~Pa}[/latex] absolute:

[latex]p=1.01 imes 10^{5}+0.846 imes 1,000 imes 9.81 imes 5.0=1.42 imes 10^{5} \mathrm{~Pa}=1.42[/latex] bar.

In the event of a tank rupture, the dike contains the leaking oil and facilitates prevention of spreading fire and contamination of the environment.

Epilogue

When he arrived at work in an oil refinery one morning, the author saw firsthand the consequences of an inadequately vented oil-storage tank. Rain during the night had caused partial condensation of vapor inside the tank, whose pressure had become sufficiently lowered so that the external atmospheric pressure had crumpled the steel tank just as if it were a flimsy tin can. The refinery manager was not pleased.

Question 1.3: Pressure in an Oil Storage Tank What is the absolute pressur...

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