Neglecting the pressure drop due to resistance, calculate the blood pressure in mmHg in an artery in the brain 32 cm above the heart. The pressure at the heart is 120mmHg and the density of blood is 1.05g/cm3.
To calculate the blood pressure in an artery in the brain, we can use the hydrostatic pressure formula:
Pressure = Density x Gravitational Acceleration x Height
First, let's convert the height from centimeters to meters:
Height = 32 cm / 100 = 0.32 m
Next, we need to convert the density of blood from grams/cm^3 to kg/m^3:
Density = 1.05 g/cm^3 = 1050 kg/m^3
The gravitational acceleration we can assume is 9.8 m/s^2.
Now let's substitute the values into the formula:
Pressure = 1050 kg/m^3 x 9.8 m/s^2 x 0.32 m
Calculating this, we get:
Pressure ≈ 1050 kg/m^3 x 9.8 m/s^2 x 0.32 m ≈ 1029.6 Pa
To convert the pressure from Pascals (Pa) to millimeters of Mercury (mmHg), we can use the conversion factor of 1 mmHg = 133.322 Pa:
Pressure = 1029.6 Pa ÷ 133.322 Pa/mmHg ≈ 7.72 mmHg
Therefore, the blood pressure in an artery in the brain, neglecting the pressure drop due to resistance, is approximately 7.72 mmHg.
To calculate the blood pressure in an artery in the brain 32 cm above the heart, we can use the hydrostatic pressure equation:
P = P₀ + ρgh
where:
P = blood pressure in the artery
P₀ = pressure at the heart
ρ = density of blood
g = acceleration due to gravity (9.8 m/s²)
h = height above the heart
First, we need to convert the given measurements to SI units:
32 cm = 0.32 m
1.05 g/cm³ = 1050 kg/m³ (1 g/cm³ = 1000 kg/m³)
Now we can substitute the values into the equation:
P = 120 mmHg + 1050 kg/m³ × 9.8 m/s² × 0.32 m
Calculating the expression:
P = 120 mmHg + 329.76 mmHg
Adding the pressures together:
P = 120 mmHg + 329.76 mmHg = 449.76 mmHg
Therefore, the blood pressure in the artery in the brain 32 cm above the heart is approximately 449.76 mmHg.