at a given instant, the blood pressure in the heart is 1.9 x 10^4 Pa. if an artery in the brain is 0.53m above the heart, what is the pressure in the artery?
To find the pressure in the artery at the brain, we need to account for the pressure difference due to the elevation difference between the heart and the brain. To do this, we can use the following equation:
P2 = P1 + ρgh
Where:
- P2 is the pressure in the artery at the brain (Pa)
- P1 is the pressure in the heart (1.9 x 10^4 Pa)
- ρ (rho) is the density of blood (~1060 kg/m^3)
- g is the acceleration due to gravity (9.81 m/s^2)
- h is the elevation difference between the heart and brain (0.53 m)
Plugging in the values:
P2 = 1.9 x 10^4 Pa + (1060 kg/m^3)(9.81 m/s^2)(0.53 m)
P2 = 1.9 x 10^4 Pa + 5498.698 Pa
P2 = 24498.698 Pa
So, the pressure in the artery at the brain is roughly 24500 Pa (rounding to the nearest whole number).