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Fluid Mechanics - Pressure

The common phases of matter are solid, liquid, and gas. Liquids and gases are fundamentally distinct from solids in their intrinsic inability to maintain a fixed shape. In other words, liquids and gases tend to fill whatever solid containers they are held in. Similarly, both liquids and gases both have the ability to flow, which is why they are collectively called fluids.

Due to their lack of definite shape, fluids tend to disperse any force applied to them. This stands in marked contrast to solids, which tend to transfer force with the direction unchanged. Take for example the force transferred by a nail, from a hammer to a piece of wood:


The impact of the hammer’s blow is directed straight through the solid nail into the wood below. Nothing surprising here. But now consider what a fluid would do when subjected to the same hammer blow:


Given the freedom of a fluid’s molecules to move about, the impact of the hammer blow becomes directed everywhere against the inside surface of the container (the cylinder). This is true for all fluids: liquids and gases alike. The only difference between the behavior of a liquid and a gas in the same scenario is that the gas will compress (i.e. the piston will move down as the hammer struck it), whereas the liquid will not compress (i.e. the piston will remain in its resting position). Gases yield under pressure, liquids do not.

It is very useful to quantify force applied to a fluid in terms of force per unit area, since the force applied to a fluid becomes evenly dispersed in all directions to the surface containing it. This is the definition of pressure (P): how much force (F) is distributed across how much area (A).

In the metric system, the standard unit of pressure is the Pascal (Pa), defined as one Newton (N) of force per square meter (m2) of area. In the British system of measurement, the standard unit of pressure is the PSI : pounds (lb) of force per square inch (in2) of area. Pressure is often expressed in units of kilo-pascals (kPa) when metric units are used because one pascal is a rather low pressure in most engineering applications.

The even distribution of force throughout a fluid has some very practical applications. One application of this principle is the hydraulic lift, which functions somewhat like a fluid lever:


Force applied to the small piston creates a pressure throughout the fluid. That pressure exerts a greater force on the large piston than what is exerted on the small piston, by a factor equal to the ratio of piston areas. If the large piston has five times the area of the small piston, force will be multiplied by five. Just like with the lever, however, there must be a trade-off so we do not violate the Conservation of Energy. The trade-off for increased force is decreased distance, whether in the lever system or in the hydraulic lift system. If the large piston generates a force five times greater than what was input at the small piston, it will move only one-fifth the distance that the small piston does. In this way, energy in equals energy out (remember that work, which is equivalent to energy, is calculated by multiplying force by parallel distance traveled).

For those familiar with electricity, what you see here in either the lever system or the hydraulic lift is analogous to a transformer: we can step AC voltage up, but only by reducing AC current. Being a passive device, a transformer cannot boost power. Therefore, power out can never be greater than power in, and given a perfectly efficient transformer, power out will always be precisely equal to power in:

Power = (Voltage in)(Current in) = (Voltage out)(Current out)
Work = (Force in)(Distance in) = (Force out)(Distance out)

Fluid may be used to transfer power just as electricity is used to transfer power. Such systems are called hydraulic if the fluid is a liquid (usually oil), and pneumatic if the fluid is a gas (usually air). In either case, a machine (pump or compressor) is used to generate a continuous fluid pressure, pipes are used to transfer the pressurized fluid to the point of use, and then the fluid is allowed to exert a force against a piston or a set of pistons to do mechanical work:


To learn more about fluid power systems, click here.


An interesting use of fluid we see in the field of instrumentation is as a signaling medium, to transfer information between places rather than to transfer power between places. This is analogous to using electricity to transmit voice signals in telephone systems, or digital data between computers along copper wire. Here, fluid pressure represents some other quantity, and the principle of force being distributed equally throughout the fluid is exploited to transmit that representation to some distant location, through piping or tubing:


This illustration shows a simple temperature-measuring system called a filled bulb, where an enclosed bulb filled with fluid is exposed to a temperature that we wish to measure. A rise in temperature causes the fluid pressure to increase, which is sent to the gauge far away through the pipe, and registered at the gauge. The purpose of the fluid here is two-fold: first to sense temperature, and second to relay this temperature measurement a long distance away to the gauge. The principle of even pressure distribution allows the fluid to act as a signal medium to convey the information (bulb temperature) to a distant location.

Go Back to Lessons in Instrumentation Table of Contents

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