A well of cross-sectional area aw is connected to an inclined tube of cross-sectional area at to form a differential pressure gauge as shown in the figure below. When p1 = p2 the common liquid level is denoted by A. When p1 > p2, the liquid level in the well is depressed to B, and the level in the tube rises by l along its length such that difference in the tube and well levels is hd.The angle of inclination θ of the tube with the horizontal is

• A. \({\sin ^{ - 1}}\left[ {\frac{1}{{{h_d}}} - \frac{{{a_w}}}{{{a_t}}}} \right]\)
• B. \({\sin ^{ - 1}}\left[ {\frac{{{h_d}}}{l} + \frac{{{a_t}}}{{{a_W}}}} \right]\)
• C. \({\sin ^{ - 1}}\left[ {\frac{{{h_d}}}{l} - \frac{{{a_t}}}{{{a_w}}}} \right]\)
• D. \({\sin ^{ - 1}}\left[ {\frac{{{h_d}}}{l} + \frac{{{a_w}}}{{{a_t}}}} \right]\)