The average air pressure at sea-level will support the column of mercury in a mercury barometer to a height of 760 mm (29.92 in.). If water were used in place of mercury in the barometer, what would be the height of the water column at average sea-level pressure? The density of mercury is 13.596 g per cm3 whereas the density of water is 1 g per cm3. (Hint: At a fixed pressure, the height of the fluid in the tube is inversely proportional to the density of the fluid. Hence, X/760 mm=13.596 g cm-3/1 g cm-3.) Answer: _____ m (Round to 2 decimal places, do not include units.)
To find the height of the water column at average sea-level pressure, we can use the information given and the provided hint.
The hint states that the height of the fluid in the tube is inversely proportional to the density of the fluid. So we can set up the following proportion:
X/760 mm = 13.596 g/cm^3 / 1 g/cm^3
To solve for X, we can cross-multiply and then divide:
X = (760 mm) * (1 g/cm^3) / (13.596 g/cm^3)
Now we just need to perform the calculation:
X = (760 mm) * (1 g/cm^3) / (13.596 g/cm^3)
X = 55.95 mm
However, the answer is requested in meters and rounded to two decimal places. To convert mm to meters, we divide by 1000:
X = 55.95 mm / 1000 = 0.056 m
Therefore, the height of the water column at average sea-level pressure would be 0.056 meters.