The assumptions made in this lecture to understand the velocity of blood flow are as follows:

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- 1 meter = 39.37 inches
- 1 millilitre = 1 cubic centimetre
- A cubic centimetre is diagrammed as a small cube which has all its lengths equal to 1 centimetre. Cardiac Output at rest: 5000mL

Let’s assume that the blood vessels are like cylinders and their cross section appear to be circular. Hence, the cross sectional area of a blood vessel is equal to the area of the circle. This can be calculated by the formula A=πr^2.

## Velocity vs. Flow

Velocity is defined as the speed of blood in unit time.

Flow is the amount of blood moving per unit time.

Velocity and Flow can be integrated in the same equation as per the following formula:

V (cm/s) =Q (ml/m)]A (cm^2)

Where: V = velocity

Q = Flow

A = Cross sectional area of the vessel.

This shows that the velocity is inversely proportional to the cross sectional area and directly proportional to the flow of blood in the vessel. This principle is analogous to water pouring out of a water hose. Squeezing the outlet of the hose and making it narrower (decreasing the cross-sectional area) will cause the water to eject with higher than normal speed.

The cross sectional area, of any part of the vasculature is taken as the sum of all the vessels at that level and not of a single vessel individually. Hence, the aorta which is a single vessel, has the smallest cross sectional area of 2.5cm^2. On the other hand, the sum of cross-sectional areas of all the capillaries is calculated to be 3000cm^2.

The calibre of the blood vessels changes as the aorta divides into arteries, arterioles and capillaries during the process of transporting blood to the tissues. The change in vessel calibre is met with a subsequent change in the blood velocity. The aorta, with a cross sectional area of 2.5cm^2 , has blood travelling at a velocity of 20m/min. By the time the blood reaches the capillaries, the velocity of blood drops to 1.6cm/min. This is because the cross sectional area of all the capillaries when summated becomes equal to 3000cm^2, a value which is 1000 folds greater than the cross sectional area of aorta. Following calculations can be used to calculate velocity of blood flowing through the aorta and the capillaries respectively:

## Velocity of the blood flow through Aorta:

- V (cm/s) =Q (ml/min)A (cm^2)

= 5000(ml/min)]2.5(cm^2) {ml and cm^3 can be substituted interchangeably}

= 5000 (cm^3/min)2.5 (cm^2)

= 2000 cm/min

= 20 m/min

= 33 cm/s

## Velocity of the blood flow through the Capillaries:

- V (cm/s) =Q (ml/min)A (cm^2)

= 5000(ml/min)]3000(cm^2) {ml and cm^3 can be substituted interchangeably}

= 5000 (cm^3/min)3000 (cm^2)

= 1.6 cm/min

= 0.016 m/min

= 0.027 cm/s

To summarize, the aorta acts as a conducting vessel as it conducts blood at high velocity to the rest of the body. The capillaries on the other hand, need to contain the blood with minimal velocity which allows for efficient exchange of gases and transport of nutrients and waste products.