Blood of density 1010kg/m^3 that is to be administered to a patient is raised about 1.51 m higher than the level of the patient's arm. How much greater is the pressure of the blood than it would be if the container were at the same level of the arm? The acceleration of gravity is 9.8m/s^2. Answer in units of Pa.
Much easier than I thought: Pressure = (1010 kg/m^3) x (1.51 m) x (9.8 m/s^2) = 14,945.98 Pa
Thanks!
14945.98Pa
To solve this problem, we need to calculate the pressure difference between two points. The pressure difference is equal to the difference in height multiplied by the density of the fluid and acceleration due to gravity.
Let's break down the problem step by step:
1. Find the pressure at the level of the arm:
The pressure at the level of the arm is given by the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height.
Here, the height is 0 since the container is at the same level as the arm. So, the pressure at the level of the arm is P₁ = ρgh = 1010 kg/m³ * 9.8 m/s² * 0 = 0 Pa.
2. Find the pressure at the raised level:
The height difference between the raised container and the level of the arm is 1.51 m. So, the pressure at the raised level is P₂ = ρgh = 1010 kg/m³ * 9.8 m/s² * 1.51 m = 15,502.98 Pa.
3. Find the pressure difference:
The pressure difference is the difference between the pressures at the raised level and the level of the arm.
ΔP = P₂ - P₁ = 15,502.98 Pa - 0 Pa = 15,502.98 Pa.
Therefore, the pressure of the blood is 15,502.98 Pa greater than it would be if the container were at the same level as the arm.
In reality, the pressure loss due to the tubing is significant, but well ignore this.
weight of a column blood h height, and area A
weight=density*Volume*g=density*A*h*g
pressure=weight/area=density*g*h