Blood flows out of your heart through the large vessel called the aorta. From th
ID: 1796105 • Letter: B
Question
Blood flows out of your heart through the large vessel called the aorta. From there, the vessels branch into arteries—multiple smaller vessels. Although the individual arteries have smaller cross sectional areas as you move through the body, the total cross sectional area keeps increasing until you get to the capillaries—the smallest vessels. Their individual cross sections are very small (about a micron in diameter) but there are a lot of them so their total cross sectional area is large. From the capillaries the vessels begin to combine into veins. The cross sectional area of the veins at each stage begins to decrease until they all come together in the vena cava which returns the blood to the heart. This is shown schematically (with total cross-sectional areas indicated) in the figure below.
(a) As the blood comes out of the heart at the maximum pressure of a heartbeat, it has a speed of ~30 cm/s. What is the speed with which it will be moving in an individual capillary? Give your answers for this problem to 2 significant figures.
cm/s
In the vena cava?
cm/s
Explain your reasoning.
(b) The blood pressure through the system is highest at the output of the heart and falls as it moves through the system approximately (for a person lying down) as shown in the figure below. The drop is largest in the capillaries.
Explain why.
(c) When a patient receives an intravenous drip as shown in the figure below, the pressure of the fluid in the needle must be greater than the blood pressure in the vein for the fluid to enter the bloodstream. From the figure in part (b), we can estimate that the pressure in the arm vein is about 2.5 kPa (1 kilopascal = 103 N/m2).
Assuming that the fluid to be introduced is essentially water (saline solution with some chemicals), how high above the arm does it need to be to be certain that the blood doesn't flow out instead of the fluid flowing in? Give your answer for this question to 2 significant figures.
cm
Explain your reasoning.
Explanation / Answer
Using the equation of continuity we know that
A1V1 = A2V2
3 * 30 = 18* V2
V2 = 5 cm/s
b) This similar to water coming through a hole in the dam and then flowing silently afterwards. In the capilaries the net cross sextional area is 300 times the arota. this causes low velocity of the fluid hence low resistence from the capilaries . leading to fall in pressure.
c) to get this much pressure we must have height h, i.e.
rho* g*h = 2500
1000 * 10* h = 2500
h = 25 cm