User:Braksb/Blood Pressure Drop Across Major Arteries to Capillaries

Blood pressure is the measurement of force that is applied to the walls of the blood vessels as the heart pumps blood throughout the body. The human circulatory system is 60,000 miles long, and the magnitude of blood pressure is not uniform in all the blood vessels in the human body. The blood pressure is determined by the diameter, flexibility and the amount of blood being pumped through the blood vessel. Blood pressure is also affected by other factors including exercise, stress level, diet and sleep.

The average normal blood pressure in the brachial artery, which is the next direct artery from the aorta, is 120mmHg/80mmHg. Blood pressure readings are measured in millimeters of mercury (mmHg) using sphygmomanometer. Two pressures are measured and recorded namely as systolic and diastolic pressures. Systolic pressure reading is the first reading, which represents the maximum exerted pressure on the vessels when the heart contracts, while the diastolic pressure, the second reading, represents the minimum pressure in the vessels when the heart relaxes. Other major arteries have similar levels of blood pressure recordings indicating very low disparities among major arteries. The innominate artery, the average reading is 110/70mmHg, the right subclavian artery averages 120/80 and the abdominal aorta is 110/70mmHg. The relatively uniform pressure in the arteries indicate that these blood vessels act as a pressure reservoir flow fluids that are transported within them.

Pressure drops gradually as blood flows from the major arteries, through the arterioles, the capillaries until blood is pushed up back into the heart via the venules, the veins through the vena cava with the help of the muscles. At any given pressure drop, the flow rate is determined by the resistance to the blood flow. In the arteries, with the absence of diseases, there is very little or no resistance to blood. The vessel diameter is the most principal determinant to control resistance. Compared to other smaller vessels in the body, the artery has a much bigger diameter (4mm), therefore the resistance is low.

In addition, flow rate (Q) is also the product of the cross-sectional area of the vessel and the average velocity (Q=AV). Flow rate is directly proportional to the pressure drop in a tube or in this case a vessel. ∆P α Q. The relationship is further described by Poisseulle’s equation ∆P=8µlQ/πr^4. As evident in the Poisseulle’s equation, although flow rate is proportional to the pressure drop, there are other factors of blood vessels that contribute towards the difference in pressure drop in bifurcations of blood vessels. These include viscosity, length of the vessel, and radius of the vessel.

Factors that determine the flow’s resistance as described by Poiseuille’s relationship: ∆P=8µlQ/πr^4: ∆P: Pressure drop/gradient µ: Viscosity l: length of tube. In the case of vessels with infinitely long lengths, l is replaced with diameter of the vessel. Q: flow rate of the blood in the vessel r: radius of the vessel

Assuming steady, laminar flow in the vessel, the blood vessels behavior is similar to that of a pipe. For instance if p1 and p2 are pressures are at the ends of the tube, the pressure drop/gradient is (p1-p2)/l =∆P.

In the arterioles blood pressure is lower than in the major arteries. This is due to bifurcations, which cause a drop in pressure. The more bifurcations, the higher the total cross-sectional area, therefore the pressure across the surface drops. This is why the arterioles have the highest pressure-drop. The pressure drop of the arterioles is the product of flow rate and resistance: ∆P=Q xresistance. The high resistance observed in the arterioles, which factor largely in the ∆P is a result of a smaller radius of about 30 µm. The smaller the radius of a tube, the larger the resistance to fluid flow.

Immediately following the arterioles are the capillaries. Following the logic obvserved in the arterioles, we expect the blood pressure to be lower in the capillaries compared to  the arterioles. Since pressure is a function of force per unit area, (P=F/A), the larger the surface area, the lesser the pressure when an external force acts on it. Though the radii of the capillaries are very small, the network of capillaries have the largest surface area in the vascular network. They are known to have the largest surface area (485mm) in the human vascular network. The larger the total cross-sectional area, the lower the mean velocity as well as the pressure.

Reynold’s number also affects the blood flow in capillaries. Due to its smaller radius and lowest velocity compared to other vessels, the Reynold’s number at the capillaries is very low, resulting in laminar instead of turbulent flow.

The Reynold’s number (denoted NR or Re) is a relationship that helps determine the behavior of a fluid in a tube, in this case blood in the vessel. The equation for this dimensionless relationship is written as NR=ρ*v*L/μ where; ρ: density of the blood L: characteristic dimension of the vessel, in this case diameter V: mean velocity of the blood μ: viscosity of blood

The Reynold’s number is directly proportional to the velocity and diameter of the tube. Note that NR is directly proportional to the mean velocity as well as the diameter. A Reynold’s number of less that 2300 is laminar fluid flow, which is characterized by constant flow motion, where as a value of over 4000, is represented as turbulent flow. Turbulent flow is characterized as chaotic and irregular flow.