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Flow is expressed in terms of volume and time. In contrast, velocity is expressed in terms of distance and time. This distinction is important in considering the circulation, where the size of channels varies enormously from the aorta to the capillaries.

The mean velocity of a fluid is flow divided by the cross-sectional area of the channel. As blood passes from the aorta to the microvascular network, there is an enormous increase in the total cross-sectional area and therefore a progressive decrease in velocity, although overall flow remains the same.

Darcy's law of flow relates flow to pressure: blood flows from areas of high pressure to areas of low pressure. This is a simplification; consider the pressures involved when blood flows from the heart to the feet in an upright position.

Mean arterial pressure is typically 95 mmHg in the aorta, but in the foot it is about 180 mmHg (owing to the weight of the column of blood above the foot). However, blood does flow against this apparent gradient. A more general law of flow states that in the steady state there is flow from A to B if there is a difference in mechanical energy from A to B. This relationship was postulated by Bernoulli.

Mechanical energy is the sum of pressure energy, potential energy, and kinetic energy, whic are defined as follows:

1. pressure energy is the product of pressure and volume (PV);

2. potential energy is the capacity of a mass to do work in a gravitational field by virtue of its vertical height above a reference level, i.e. fluid mass (density * volume) * height * gravitational force;

3. kinetic energy is the energy that a moving mass possesses due to its momentum (which increases in proportion to velocity squared).

Returning to the example, it is clear that blood in the aorta has more gravitational potential energy than blood in the foot. The total energy of aortic blood is greater than that in the foot; hence there is an energy gradient relative to the foot.

Kinetic energy, i.e. energy dependent on the momentum of flow, is particularly important in the venous side of the circulation. In the great veins blood velocity is similar to that in the aorta but pressure is much lower. Thus kinetic energy contributes more than pressure energy to the fluid energy in the great veins. When blood reaches the relaxed ventricle, the kinetic energy is almost zero. This gradient of kinetic energy from the veins to the ventricles contributes to ventricular filling.

In this brief description of the physical laws governing the flow of fluids it has been assumed that flow is constant. This is clearly not the case on the arterial side of the circulation where flow is pulsatile. The laws are still useful in considering mean flow, but slightly different rules apply for instantaneous flow. These are beyond the scope of this review.

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