Human blood consists of plasma, the fluid, and red and white corpuscles are immersed in the plasma. Because blood is a fluid, the laws of physics can be applied to the flow of blood throughout the body. A schematic diagram of the circulatory system, which transport blood and oxygen around the body , is shown in figure.
It consists of
- Heart, which is the pump that is responsible for supplying the pressure to move the blood.
- Lungs, which are the source of oxygen for all the cells of the body.
- Arteries, which are connecting blood vessels that pass the blood from the heart to various parts of the body.
- Capillaries, which are extremely small blood vessels that bring the oxygenated blood down to the layer of human cells.
- Veins, which are blood vessels that return deoxygenated blood to the heart to complete the circulatory system.
The heart is the pump that circulates the blood throughout the body and a diagram of it is shown in figure. Blood, containing carbon dioxide, returns to the heart by the veins and enters the right auricle. It is then pumped from the right ventricle to the pulmonary artery to the lungs where it dumps the waste carbon dioxide and picks up a new supply of oxygen. It then returns to the left auricle of the heart. The left ventricle then pumps this oxygen rich blood to the aorta, the main artery of the body, for distribution to the rest of the body.
For a person at rest, the heart pumps approximately 5.00 liters of blood per minute (8.33 x 10-5 m3/s) at a rate of about 70 beats per minute. For a person engaged in very strenuous exercise the heart can pump up to 25.0 liters of blood per minute (41.7 x 10-5 m3/s) at a rate of about 180 beats per minute. We can determine the speed of the blood as it enters the aorta by an eq.
ΔV/Δt = AAVA
Where ΔV/Δt is the rate at which the blood is flowing from the heart into the aorta, AA is the cross-sectional area of aorta, and VA is the speed of the blood in the aorta. The diameter of the aorta is about 2.00 cm.
So, Area of cross-section of aorta is
Diameter = 2.00 cm
Radius = r = 1.00 cm = 0.01 m
A = πr2
A = 3.14 x ( 0.01 m )2 = 3.14 x 10-4 m2
Hence speed of blood in aorta is
VA = (ΔV/Δt )/AA
= (8.33 x 10-5 m3/s ) / (3.14 x 10-4 m2 )
= 0.265 m/s
= 26.5 cm/s
We can determine the speed of the blood in the capillaries by the continuity eq.
AAVA = AbVb
Where AA is the cross-sectional area of the aorta, which was just determined as
3.14 x 10-4 m2 ; VA is the speed of the blood in the aorta, which was just found to be 26.5 cm/s ; and Ab is the cross-sectional area of a capillary tube, which is quite small.
However, because there are literally billions of these capillaries the effective cross-sectional area of all these capillaries combined approximately 2500 x 10-4 m2. The speed of blood in the capillary becomes
Vb = (AA /Ab) VA
= (3.14 x 10-4 m2 / 2500 x 10-4 m2 ) ( 26.5 cm/s)
Thus, the blood moves relatively slowly at the level of the capillaries.
Finally, we should note that the body controls the flow of blood through the arteries by muscles that surround the arteries. When the muscles contract, the diameter of the artery is reduce. From the equation of continuity, Av = constant. By decreasing the diameter of the artery, the cross-sectional area of the artery decrease and hence the speed of blood must increase through the artery. Alternatively, when the muscles are relaxed, the diameter of the artery increases to its former size, the cross-sectional area increases, and the speed of the blood decreases. With advancing age the arterial muscles lose some of this ability to contract, a situation called hardening of the arteries, and the control of blood flow is somewhat diminished.
A good indication of how well the heart is functioning is obtained by measuring the pressure that heart exerts when pumping blood and when at rest. The device used to measure blood pressure is called sphygmomanometer.
The device consists of an air bag, called a cuff that is wrapped around the upper arm of the patient at the level of the heart. A hand pump is used to inflate the cuff, and the pressure exerted by the cuff on the arm is measured by the mercury manometer. The pressure exerted by the cuff is increased until the pressure is great enough to collapse the brachial artery in the arm, cutting off the blood supply to the rest of the arm. A stethoscope is placed over the brachial artery and the pressure in the cuff is slowly decreased. When the pressure in the cuff becomes low enough, the pressure exerted by heart is large enough to force the artery open and some blood squirts through. This blood flowing through the narrow restriction becomes turbulent and makes a noise as it enters the open portion of the artery. The physician hears this noise through the stethoscope, and simultaneously observes the pressure indicated on the manometer, expressed in terms of mm of Hg. At this point the pressure exerted by the heart, called the systolic pressure, is equal to the pressure exerted by the cuff. A normal systolic pressure is around 120 mm of Hg.
As the pressure in the cuff is decreased the turbulent flow noise is still heard in the stethoscope until the lowest pressure exerted by the heart, the diastolic pressure, is equal to the pressure exerted by the cuff. At this point the artery is completely open and the blood is no longer in turbulent flow and the characteristic noise disappears. The pressure is read from the mercury manometer at this point. This pressure is the pressure that the heart exerts when it is at rest. The combined systolic and diastolic pressures are usually indicated in form 120/80. If the systolic pressure becomes too high, above about 150 mm of Hg, the patient has high blood pressure. If the systolic pressure becomes too large fro a long period of time, damage can be done to the different organs of the body. If the systolic pressure becomes extremely large, arteries in the brain can rupture and the person will have a stroke. If the diastolic pressure exceeds 90 mm of Hg, the person also said to have high blood pressure. This type of high blood pressure causes eventual damage to the heart itself because it is operating under high pressures even while it is supposed to be resting.
Frictional effect between different layers of a fluid is known as viscosity. A fluid in which frictional effects are significant is called a viscous fluid and the fluid flow is referred to as laminar flow, flow in layers. Flow rate is inversely proportional to the coefficient of viscosity of the fluid. Thus, a very viscous fluid flows very slowly compared to a fluid of low viscosity. That is, everything else being equal, molasses flows at a slower rate than water. Human blood is a viscous fluid, the greater the number of red corpuscles in the blood the greater the viscosity. The viscosity of human blood varies from about (1.50 x 10-3 N-s/m2) for plasma, to about 4.00 x 10-3 N-s/m2) for whole blood.
