Calculate the height of the brain above the heart for an animal with an additional blood pressure of 222 mmHg in the heart. Use ρ = 1.055 g/cm3 for the density of blood.
To calculate the height of the brain above the heart for an animal with an additional blood pressure of 222 mmHg, we can use the concept of hydrostatic pressure.
Step 1: Convert the additional blood pressure to units of pressure used for calculating hydrostatic pressure, which is typically done in terms of height of a fluid column. Since 1 mmHg is equal to 13.6 cm of water column, we can convert 222 mmHg to cm of water column:
222 mmHg * 13.6 cm/mmHg = 3025.2 cm of water column
Step 2: Calculate the height of the fluid column using the equation:
Pressure = ρgh
where:
- Pressure is the additional blood pressure in the heart (3025.2 cm of water column)
- ρ is the density of blood (1.055 g/cm3)
- g is the acceleration due to gravity (9.8 m/s2 in this case, since cm is used in the equation)
Now, we need to convert the density of blood from g/cm3 to kg/m3 to ensure consistent units:
1.055 g/cm3 * (1000 kg / 1 g) * (1 m / 100 cm) = 1055 kg/m3
So, the density of blood is 1055 kg/m3.
Step 3: Rearrange the equation to solve for h:
h = Pressure / (ρg)
Plugging in the values:
h = 3025.2 cm / (1055 kg/m3 * 9.8 m/s2)
Converting cm to meters:
h = 30.252 m / (1055 kg/m3 * 9.8 m/s2)
h = 0.00289 m
The height of the brain above the heart is approximately 0.00289 meters, or 2.89 millimeters.