how tall must a water filled manometer be to measure blood pressure as high as 300 mm Hg? what do i use for pressure, density and height?
It has to be 13.6 times higher than the maximum mercury column height. (13.6 is the mercury/water density ratio.)
Sorry, still confused. I get that the density for mercury is 13.6x10^3 kg/m^3. All I know is that the answer is 4.08m, I just don't know how to get there. Do I use P=density*gravity*height
h=pressure/density*9.8
but my answer didn't even come close to 4m
If you multiply the mercury manometer maximum reading of 0.3 m by 13.6, which is what I suggested, you get the correct answer. 4.08 meters.
For the same value of P, if liquid density is 1/13.6 as high (as it is with water), H must be 13.6 times higher.
To determine the height of a water-filled manometer required to measure a blood pressure of 300 mm Hg, we can use the equation:
Pressure = Density × Gravitational Acceleration × Height
Here's the breakdown of the information you need:
1. Pressure: The blood pressure given is 300 mm Hg, which stands for millimeters of mercury (mm Hg). This unit can be converted to Pascals (Pa), considering that 1 mm Hg = 133.32 Pa approximately.
So, 300 mm Hg ≈ 300 × 133.32 Pa = 39,996 Pa
2. Density: For water, the density is a constant value, approximately 1000 kg/m³.
3. Gravitational Acceleration: The standard value for gravitational acceleration is approximately 9.81 m/s².
Now that we have all the necessary values, we can rearrange the equation and solve for the height:
Height = Pressure / (Density × Gravitational Acceleration)
Height = 39,996 Pa / (1000 kg/m³ × 9.81 m/s²)
Calculating the above equation, the height of a water-filled manometer required to measure a blood pressure of 300 mm Hg is approximately 4.08 meters.