If a cetain pressure supports a 256 mm high column of mercury, how high a column of water will it support? The ensity of mercury is 13.6 g/mL. Not completely sure how to work this one, we never reviewed it in class. All the answers to chose from are in inches or ft. I'm coming up with 11.4 ft. Can you show me how to work it?!!

Certainly! To find out how high a column of water a certain pressure will support, you can use the principle of Pascal's Law. According to this law, the pressure applied to a fluid will be transmitted equally in all directions.

To solve the problem, you need to know the relationship between the pressures exerted by mercury and water. The key here is to use the concept of specific gravity.

Specific gravity compares the density of a substance to the density of water. In this case, we're given the density of mercury, which is 13.6 g/mL. Meanwhile, the density of water is approximately 1 g/mL.

To find the specific gravity of mercury, you divide its density by the density of water:
Specific gravity of mercury = density of mercury / density of water
= 13.6 g/mL / 1 g/mL
= 13.6

This means that mercury is 13.6 times denser than water.

Now, let's apply Pascal's Law. Since the pressure is supporting a column of mercury, we can assume the same pressure will be applied to the column of water. The equation for pressure is:

Pressure = Height × Density × Gravity

Since we want to find the height of the column of water, we'll rearrange the equation to solve for height:

Height = Pressure / (Density × Gravity)

For the column of mercury:

Pressure (mercury) = Pressure (water)
Height (mercury) × Density (mercury) × Gravity = Height (water) × Density (water) × Gravity

We're given the height of the mercury column as 256 mm. So we'll substitute the known values:

256 mm × 13.6 g/mL × Gravity = Height (water) × 1 g/mL × Gravity

Gravity cancels out on both sides of the equation:

256 mm × 13.6 = Height (water)

Now, we can convert the height from millimeters to feet by using the following conversion factors:

1 mm = 0.00328084 feet

Height (water in feet) = 256 mm × 13.6 × 0.00328084 feet/mm
Height (water in feet) ≈ 11.355 feet

So, the height of the column of water that the given pressure will support is approximately 11.355 feet.