It's intuitive for me that BP is lowest in the veins...but how does this relate to the continuity equation, which says that since capillaries have the greatest surface area they should have the lowest velocity?

That was a badly prased question, so I'll try again: Maybe another way of phrasing my question is, if blood WERE an ideal fluid, what would be the differences in pressure gradients throughout the cardiovascular system?

It's intuitive for me that BP is lowest in the veins...but how does this relate to the continuity equation, which says that since capillaries have the greatest surface area they should have the lowest velocity?

That was a badly prased question, so I'll try again: Maybe another way of phrasing my question is, if blood WERE an ideal fluid, what would be the differences in pressure gradients throughout the cardiovascular system?

Equations for fluid dynamics can't really appropriately be applied to the cardiovascular system because blood is not an ideal fluid. For example, Bernoulli's equation states that pressure would be highest when velocity is the lowest. However, in capillaries, where the velocity is the lowest, the pressure is also low. According to Bernoulli's equation/concept, the pressure should be pretty high in the capillaries, since the velocity is low. However, that is not the case. Blood is an ideal fluid, and we can't really make the same assumptions for it as we do with other fluids in following the physics of fluid dynamics.

It's intuitive for me that BP is lowest in the veins...but how does this relate to the continuity equation, which says that since capillaries have the greatest surface area they should have the lowest velocity?

That was a badly prased question, so I'll try again: Maybe another way of phrasing my question is, if blood WERE an ideal fluid, what would be the differences in pressure gradients throughout the cardiovascular system?

The continuity equation is cross-sectional area, not surface area.

The capillaries do have the greatest cross-sectional area. You have the aorta which is a large artery going into many small capillaries. The total cross-sectional area of all the capillaries is much much greater then that of the aorta.

So you are increasing area and decreasing velocity in the capillaries.

Equations for fluid dynamics can't really appropriately be applied to the cardiovascular system because blood is not an ideal fluid. For example, Bernoulli's equation states that pressure would be highest when velocity is the lowest. However, in capillaries, where the velocity is the lowest, the pressure is also low. According to Bernoulli's equation/concept, the pressure should be pretty high in the capillaries, since the velocity is low. However, that is not the case. Blood is an ideal fluid, and we can't really make the same assumptions for it as we do with other fluids in following the physics of fluid dynamics.

The continuity equation is cross-sectional area, not surface area.

The capillaries do have the greatest cross-sectional area. You have the aorta which is a large artery going into many small capillaries. The total cross-sectional area of all the capillaries is much much greater then that of the aorta.

So you are increasing area and decreasing velocity in the capillaries.

I am not so sure that I understand cross-sectional and surface area argument. The Bernoulli equation should work for any cross-sectional size since it use only local variables as density, speed and pressure. (No surface or diameter variables there).
I would guess that Bernoulli use another assumption that make it not applicable in this case. It assumes that kinetic energy is constant. But friction and viscosity make this assumption invalid. The more surface area of capillary we get, the more friction will eat kinetic energy. The less diameter of pipes, the more losses of energy due to viscosity.

Just to clear something up, the BP in veins is practically ZERO correct? And its not like theres enough negative pressure in the heart to pull blood up from the legs....

I think I read somewhere that vein blood mainly moves due to nearby skeletal contractions correct?

Just to clear something up, the BP in veins is practically ZERO correct? And its not like theres enough negative pressure in the heart to pull blood up from the legs....

I think I read somewhere that vein blood mainly moves due to nearby skeletal contractions correct?

Correct skeletal muscles push it along via contractions and one way valves in the veins. Intherthoracic pressure from breathing also helps move blood into the right Atrium.

For a moment forget the formulas and think about it. You have a wide high pressure pipe called the aorta feeding smaller pipes that reduce in size until they become capillaries and then the pipe widens up into veinules and then into bigger veins. Since the size keeps expanding and only a small amount of liquid / blood can get through the cap's the pressure has to decrease.

PS according to Costanzo the pressure in the Vena Cava is 4 mmHg while it is 2 mmHg in the relaxed right atrium.

capillaries: slowest velocity, intermediate pressure, largest cross sectional area
veins: faster but not as fast as arteries, lowest pressure, intermediate cross sectional area

capillaries: slowest velocity, intermediate pressure, largest cross sectional area
veins: faster but not as fast as arteries, lowest pressure, intermediate cross sectional area