When you studied rotational motion you learned that in many cases the effect of a force was not determined solely by the magnitude of the force. The rotational effect produced by a force depends not only upon the magnitude of the force, but also upon the lever arm of the force. Similarly there are many situations in which the area to which the force is applied is important in determining the effect of a force. This is the case for fluids. The investigation of the behavior of fluids is made easier by the introduction of the concept of pressure. We define pressure as the force divided by the area over which the force is applied, P = F / A. We give the name Pascal to the pressure unit equal to one Newton per square meter or 1 Pa = 1 N / m². Pressure can be increased by increasing the force or by reducing the area to which a given force is applied. The physical variable pressure is very useful in considering the behavior of fluids, whether those fluids are liquids or gases.

Pascal's principle explains why the concept of pressure is so useful in investigating the behavior of fluids. It states that any change in pressure of a fluid is transmitted uniformly, in all directions, throughout a fluid. As a result of Pascal's principle we do not have to engage in detailed analysis to determine the direction of each force at each point in a fluid, because Pascal's principle tells us that the change in pressure is transmitted uniformly in all directions within the fluid.

Atmospheric pressure represents the effect of the air above the surface of the Earth. Expressed in terms of standard pressure, measured at sea level, atmospheric pressure is 1.01 x 10⁵ N / m² or 101 kPa. You may be more familiar with atmospheric pressure expressed in the British System of Units as 14.7 lb / in² or as approximately 30 inches of mercury. The latter unit refers to the column of mercury that can be supported by a pressure of one standard atmosphere. The effect of the air in the atmosphere on us is the same as carrying 1.01 x 10⁵ Newtons on every square meter or of having a weight of 14.7 pounds upon every square inch of our bodies. Ordinarily we do not notice this "load" because we also have air permeating our bodies pushing back out against this pressure. Perhaps you have ridden in a very fast elevator, or you may have flown in a commercial airliner that was climbing or descending at a rapid rate. If so, you may noticed the difference in pressure on your eardrums as your body was not able to react quickly enough to adjust the inside pressure to be equal to the pressure outside the body.

Gases are compressible, so a column of a gas, such as air, has a greater density near the bottom of the column than it does near the top of the column. In a sense the weight of the column of air causes the portion at the bottom to be squeezed closer together, i.e. to be compressed. Liquids are much less compressible than gases. In most cases we consider a column of a liquid to have the same density throughout its entire height.

Boyle's law states that the product of the pressure times the volume for a gas is equal to a constant. In equation form this is expressed as P₁ V₁ = P₂ V₂ . Boyle's law is really a special case of having the temperature held constant in the more general expression known as the ideal gas law.

A column of liquid will produce a pressure that depends upon the density of the liquid, d, the height of the liquid, h, and the acceleration of gravity, g, according to the equation D P = d h g. Archimedes' principle states that the buoyant force acting on an object that is fully or partially submerged in a fluid is equal to the weight of the fluid that is displaced by the object.

Bernoulli's principle is an expression of the conservation of energy in terms of variables that are more conveniently measured for fluids. It is useful for calculating the pressure or velocity of a fluid in such cases as a fluid moving in a pipe, and it can be used to explain such phenomena as the lift on airplane wings and the deflection of a curve ball.

Bernoulli's principle is derived using the principle of conservation of energy. According to Bernoulli's principle for a level pipe, the sum of the pressure plus the kinetic energy per unit volume of a flowing fluid must remain constant. In equation form this is expressed as P + (1 / 2) d v² = constant, where d is the fluid density. Thus, if the velocity of a fluid increases, as, for example, through a constriction in a horizontal pipe where the equation of continuity requires faster velocity, the pressure must decrease to maintain the equality in Bernoulli's equation.

The lift on airplane wings provides a practical illustration of Bernoulli's principle. The wings are designed so that the airflow is faster past the top of the wings. Bernoulli's principle requires the pressure to be lower where the velocity is higher with the consequence that the pressure is greater on the undersurface of the wing than on the upper surface resulting in the lift that makes flying possible.