What height of oil (density = 800 kg/m3) is required to produce the same pressure effect of 1 m of mercury (density = 13594 kg/m3)? Express your answer in m.
Question
What height of oil (density = 800 kg/m3) is required to produce the same pressure effect of 1 m of mercury (density = 13594 kg/m3)? Express your answer in m.
Solution
Sure, let's break this down step by step:
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First, we need to understand that the pressure at a certain depth in a fluid is given by the equation P = ρgh, where:
- P is the pressure,
- ρ is the density of the fluid,
- g is the acceleration due to gravity, and
- h is the height of the fluid above the point in question.
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We want the pressure effect of 1 m of mercury to be the same as the pressure effect of a certain height of oil. So, we can set up the equation as follows:
- ρ_mercury * g * h_mercury = ρ_oil * g * h_oil
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We know that the density of mercury (ρ_mercury) is 13594 kg/m3, the density of oil (ρ_oil) is 800 kg/m3, and the height of the mercury (h_mercury) is 1 m. We want to find the height of the oil (h_oil).
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We can cancel out the g on both sides of the equation because it's the same for both fluids. So, the equation becomes:
- ρ_mercury * h_mercury = ρ_oil * h_oil
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Now, we can solve for h_oil:
- h_oil = (ρ_mercury * h_mercury) / ρ_oil
- h_oil = (13594 kg/m3 * 1 m) / 800 kg/m3
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If you do the math, you'll find that h_oil is approximately 17 m.
So, a height of approximately 17 m of oil is required to produce the same pressure effect as 1 m of mercury.
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