Velocity is usually expressed in distance travelled per unit time, such as in cm/sec or m/sec, whereas flow is usually expressed in ml/sec., gal/sec, etc. The mean velocity of blood flow can be calculated if you know the volume flow per sec. and the cross-sectional area. For example, if the volume flow is 100 ml/sec (6 l/min) and the area is 3 square cm. - then the velocity is about 33 cm/sec. If the cross-sectional area decreased to 1 square cm., then volocity of flow in the tube would triple, to 100 cm/sec.
The cross-section of the blood vessel is assumed to be a circle, thus the area is equal to pie r2. Conversely, if you know the velocity and the area, you can determine the volume flow. The velocity profile of flow is assumed to be cylindrical, whereas, in fact, it is a parabaloid, since flow is maximal on the axis and least near the wall.
Note: Please don't confuse the increase in velocity with decrease in cross-sectional area of a single tube with what occurs in the whole circulation when we look at velocity, for example, in the aorta vs. a capillary. While the cross-sectional area of a single capillary is a tiny fraction that of the aorta, the total cross-sectional area of all of the capillaries in the body are several hundred times that of the one aorta, thus blood velocity in the capillaries must be a small fraction of that in the aorta. See Figure 7.03.
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