A bag of blood with a density of 1050 kg/m3 is raised 1.37 m higher than the level of a patient’s arm. How much greater is the blood pressure at the patient’s arm than it would be if the bag were at the same height as the arm? Assume there is no change in drip speed at the different heights. The acceleration of gravity is 9.81 m/s2.Answer in units of Pa
To solve this problem, we need to calculate the difference in blood pressure between two levels: at the arm level and at the level of the raised bag.
We can start by determining the difference in height between the two levels. Given that the bag is raised 1.37 m higher than the arm, the height difference is 1.37 m.
Next, we need to calculate the difference in pressure due to the difference in height. The pressure difference is given by:
ΔP = ρgh
Where:
ΔP is the pressure difference,
ρ is the density of the fluid (in this case, blood) = 1050 kg/m³,
g is the acceleration due to gravity = 9.81 m/s², and
h is the height difference = 1.37 m.
Plugging in the given values, we have:
ΔP = (1050 kg/m³)(9.81 m/s²)(1.37 m)
Calculating this expression gives us the pressure difference:
ΔP = 15,718.255 Pa
Therefore, the blood pressure at the patient's arm is 15,718.255 Pa (or 15.7 kPa) greater than it would be if the bag were at the same height as the arm.