You are working with a triple sealed tank with pressure gauges that measure the pressure inside each tank. The gauges report the gauge pressure inside each tank with respect to the pressure in the tank surrounding it. A mercury manometer is connected to the inner most tank, and the other end to the manometer is connected to the atmosphere. All three gauges read -20kPa. What is the reading height of the manometer fluid in mmHg? Please note 1 mmHg = 133.3 Pa)
Question
You are working with a triple sealed tank with pressure gauges that measure the pressure inside each tank. The gauges report the gauge pressure inside each tank with respect to the pressure in the tank surrounding it. A mercury manometer is connected to the inner most tank, and the other end to the manometer is connected to the atmosphere. All three gauges read -20kPa. What is the reading height of the manometer fluid in mmHg? Please note 1 mmHg = 133.3 Pa)
Solution
Step 1: Convert the gauge pressure from kPa to Pa.
-20 kPa * 1000 = -20,000 Pa
Step 2: Convert the gauge pressure from Pa to mmHg.
-20,000 Pa / 133.3 Pa/mmHg = -150 mmHg
Step 3: The negative sign indicates that the pressure inside the tank is lower than the atmospheric pressure. Therefore, the mercury in the manometer will be lower on the side connected to the tank than on the side connected to the atmosphere.
The height of the mercury on the side connected to the tank will be 150 mm lower than the height of the mercury on the side connected to the atmosphere.
So, the reading height of the manometer fluid is -150 mmHg.
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