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.

Sure, let's break this down step by step:

1. 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.

2. 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

3. 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).

4. 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

5. 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

6. 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.