Not quite, if the total cross-sectional area (the sum of the cross-sectional areas of the individual capillaries) increases by a factor of eight hundred and there are nine billion capillaries, each capillary will have a cross-sectional area of how many times than that of the aorta. HINT: You should obtain a number <<1 since a capillary is many times narrower than the aorta. We are of course assuming, as the question states, that each capillary is of the same dimensions.Alcyon said:
Indeed [itex]\frac{800}{9\times 10^9}[/itex]. So the cross-sectional area of an individual capillary is 8.89x10-8 times that of the aorta. Now what happens to the radius of each capillary?Alcyon said:
Indeed, however, you may wish to leave it in terms of r2 (it just takes a further step out of the calculation. So using that information we can form as equation in terms of area exclusively;Alcyon said:
Its my pleasureAlcyon said:(thanks again for your help...really appreciate it.
That is how many times larger the cross-sectional area of a single capillary compared to the aorta. If you substitute that into the last equation for A that will give you the resistance per unit length of a single capillary when compared to the aorta. Do you follow?Alcyon said:
Why would you wish to do this?Alcyon said:
Spot onAlcyon said:
Yes, as each capillary is identical, the resistance of each will also be identical;Alcyon said:
Not quite, you may want to recheck your math there;Alcyon said:
Good luck with your studies, I imagined this was some sort of biophysics course. It was my pleasure to help youAlcyon said:
, an interesting problem; greetings from England.The resistance of the aorta is much lower compared to the resistance of capillaries. This is because the aorta is a large, elastic artery that can expand and contract to accommodate the high pressure and volume of blood coming from the heart, whereas capillaries are much smaller and have a higher resistance due to their narrow diameter.
The main factors that contribute to the change in resistance from the aorta to capillaries are the diameter of the blood vessels and the length of the blood vessels. The aorta has a larger diameter and shorter length compared to the capillaries, resulting in lower resistance. Additionally, the viscosity of blood and the overall health and condition of the blood vessels can also affect resistance.
The change in resistance from the aorta to capillaries creates a gradual decrease in blood flow. This is necessary for the body to efficiently distribute oxygen and nutrients to all of its cells. The high resistance in the capillaries also allows for the exchange of gases and nutrients between the blood and tissues.
The body regulates resistance in the aorta and capillaries through various mechanisms. One of the main ways is through the autonomic nervous system, which can constrict or dilate blood vessels to adjust resistance. Hormones and local chemical signals can also affect resistance by causing vasodilation or vasoconstriction.
There are several disorders and conditions that can affect resistance in the aorta and capillaries. Some examples include hypertension (high blood pressure), atherosclerosis (buildup of plaque in the arteries), and vasculitis (inflammation of blood vessels). These conditions can affect blood flow and lead to serious health complications if left untreated.