What is the height of a water barometer at atmospheric pressure?

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Welcome back. Everyone in this problem, an oil barometer is used to measure atmospheric pressure. The atmospheric pressure is 1.013 multiplied by 10 to the fifth pascals calculate the height of the oil column in the barometer. If the pressure at the bottom of the column is equal to the atmospheric pressure, use the density of oil row as 850 kg per cubic meter and G as 9.8 m per second squared for our answer choices A says it's 9.8 m. B 12 m c 15 m and D 18 m. Now, here we're trying to figure out the height of the oil column given these conditions given that the pressure at the bottom of the column is equal to the atmospheric pressure. Now, what do we know that can help us? Well, in our problem here, we're given some of the variables we know that the atmospheric pressure which we can call P ATM. OK. Is 1.013 multiplied by 10th of the fifth pasca. We have the density of oil as 850 kg per cubic meter. And we have our acceleration due to gravity G as 9.8 m per second squared. Now, we can also assume that the pressure of the pressure at the surface of the oil p not OK, is going to be zero atmospheres or zero pascals assuming it's at a vacuum, sorry, assuming it's a vacuum at the top of the barometer. Now, what do we know about the height of the oil column that we can relate to our atmospheric pressure? Well, from the formula, from the relationship we are told we can use the hydrostatic pressure equation recall that it tells us that the initial pressure plus the density of the medium multiplied by the acceleration due to gravity multiplied by the height in the column is going to be equal to our atmospheric pressure. Here we know that the pressure at the bottom of the column equals the atmospheric pressure. So in this case, then to find a height, if we do some transposition, that means row GH is going to be equal to the atmospheric pressure minus the initial pressure, which tells us then that h the height is going to be equal to the atmospheric pressure minus the initial pressure divided by the density multiplied by the gravity. Now, in this case, as we said, we know that our initial pressure is zero, pascal the pressure at the surface of the oil. So now that tells us then that our height is going to be equal to our atmospheric pressure 1.013 multiplied by 10 to the fifth pascals divided by our density of oil, 850 kg per cubic meter. Ok? Multiplied by the acceleration due to gravity 9.8 m per second squared. Now, when we go ahead and substitute here, OK. And we go ahead and solve for each, then we should find that to two significant figures. Our answer is 12 m. Therefore that is what the height of the oil column in the barometer will be under these conditions. B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

What is the height of a water barometer at atmospheric pressure?

Verified Solution

Key Concepts

Atmospheric Pressure

Barometer

Hydrostatic Pressure