Answer:
16.9816 psia
Explanation:
To determine the absolute pressure at the tube's bottom, we must add atmospheric pressure to gauge pressure.
Gauge pressure accounts for contributions from water columns () and mercury (
), allowing us to derive the contribution of each as:
(*)
where represents density, g is gravity, and h is height.
With all necessary data available to apply the above equations (, height, and density of each fluid), we must be diligent about unit consistency.
For clarity, we can express all pressure contributions in mmHg ( ,
, and
). The units "x" mmHg indicate the pressure at the bottom of a mercury column that is "x" mm tall. In this case, a 12.1 cm Hg column equals 121 mmHg (conversion from cm to mm requires multiplying by 10) showing the pressure exerted is 121 mmHg.
For a water pressure at 5.6 cm (56 mm), it equals 56 mm of water. However, this differs from mmHg because water's density is less than mercury's, resulting in 1 mm of water exerting less pressure than 1 mm of Hg. The conversion between mmHg and mm of water relies on their densities.
Thus, water pressure in mmHg is calculated as
The absolute pressure is computed as:
To convert to dyn/cm^2 units, we will utilize equation (*)
Note: It is essential to maintain cm Hg for uniformity.
Next, to convert from dyn/ to kN/
(or kPa), we must remember that 1 dyn equals
kN and that 1
is
.
Finally, transitioning from kN/ to psia, we must take into account that 1 psia equals 6.89476.