The pressure head at level A A is 0.091 m of water, and the unit weights of gas and air are 5.50 and 12.35 N/m^3, respectively. Determine the reading of the water in the U-tube gage that measures the gas pressure at level B in Fig. 2-16.

Question

The pressure head at level A A is 0.091 m of water, and the unit weights of gas and air are 5.50 and 12.35 N/m[latex]^{3}[/latex], respectively. Determine the reading of the water in the U-tube gage that measures the gas pressure at level B in Fig. 2-16.

Accepted Answer

Assume the values of [latex]\gamma[/latex] for air and gas remain constant for the 91 m difference in elevation. Because the unit weights of gas and air are of the same order of magnitude, the change in atmospheric pressure with altitude must be taken into account. The use of absolute pressure units is recommended.

absolute [latex]p_{C}[/latex] = absolute [latex]p_{D}[/latex] (Pa)

atmospheric [latex]p_{E}[/latex] + 9790h = absolute [latex]p_{A}[/latex] - 5.50 x 91 (A)

The absolute pressure at A will next be evaluated in terms of the atmospheric pressure at E, obtaining first the atmospheric pressure at F and then [latex]p_{A}[/latex].

absolute [latex]p_{A}[/latex] = [atmos. [latex]p_{E}[/latex] + (12.35)(h + 91 - 0.091)] + (0.091 x 9790) (Pa)

Substituting this value in (A), canceling atmospheric [latex]p_{E}[/latex], and neglecting very small terms gives

9790h = (91)(12.35 - 5.50) + (0.091)(9790) and h = 0.155 m or 155 mm of water.

Question 2.22: The pressure head at level A A is 0.091 m of water, and the ...

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