Calculating Pressure: Blood Height Above Arm Vein

[clipperdude21]

1. Blood travels from a container hanging at a height H abovethe table into the vein of a persons arm. The blood pressure in the vein is 2000 Pa above 1 atm. Blood has a density of 1 g/cm^2

(a) How high should the container of plasma hang above the patient
(b)Suppose you want to drain blood very slowly from the patient into the container. How high should you hang the container in this case.

Homework Equations

3. I used patm +pgh = 1.01X10^5 + 2000 and got H as .204 meters. For b i thought it would be less than .204 meters

 

[clipperdude21]

bump! please help if you can

 

[ogb p]

, but I am not sure I would like to provide a comprehensive response to the calculations and questions presented. Firstly, it is important to note that the given information is incomplete. The density of blood is typically expressed in units of g/cm^3, not g/cm^2 as stated. Additionally, the units of pressure should be in Pa (Pascal) or mmHg (millimeters of mercury) instead of Pa above 1 atm. These discrepancies could potentially affect the accuracy of the calculations.

(a) To determine the height of the container, we can use the equation pgh = ΔP, where p is the density of blood, g is the acceleration due to gravity (9.8 m/s^2), and ΔP is the difference in pressure between the container and the vein. Rearranging the equation, we get h = ΔP/(pg). Substituting the given values, we get h = (2000 Pa)/(1 g/cm^3 x 9.8 m/s^2) = 20.4 cm or 0.204 meters. Therefore, the container should hang at a height of 0.204 meters above the patient's arm vein.

(b) To drain the blood slowly, we can use the same equation as above, but we need to consider the rate at which the blood is being drained. Let's assume that the desired rate is 1 cm^3/s. Using the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the vein, and v is the velocity of blood flow, we can solve for v. Assuming the cross-sectional area of the vein is 1 cm^2, we get v = Q/A = (1 cm^3/s)/(1 cm^2) = 1 cm/s. Now, using the equation Q = Av and the given density of blood, we can solve for the height of the container. Rearranging the equation, we get h = Q/(pgv). Substituting the known values, we get h = (1 cm^3/s)/(1 g/cm^3 x 9.8 m/s^2 x 1 cm/s) = 0.102 meters. Therefore, the container should hang at a height of 0.102 meters above the patient's arm vein if the blood is to be drained at a rate of 1 cm^3/s.

In conclusion