Pressure

Pressure is a derived quantity that is the quotient when dividing a applied force by the area over which that force is applied.

Pressure = Force/Area

Units for this quantity in the British Engineering System are lbs/inch^2 (do not use p.s.i.). In the metric system pressure is measured in Newtons/meter^2 which is renamed the Pascal (Pa).

A
barometer is the classic device for measuring atmospheric pressure. It consists of an evacuated tube, open at the bottom, in which atmospheric presssure supports a column of liquid. The height of the liquid is preportional to atmospheric pressure. In this application, units are often given as inches or mm of Mercury.

A manometer is a U-shaed tube in which pressure is measured as the difference in height of the fluid on each side.

A mechanical pressure guage registers fluid pressure by the effects a fluid may have on the size or shape of the container.

A small pressure applied over a large area can produce considerable force. Try the activity as directed in the box below.

 Spread flat on a table top a heavy-duty trash can liner. Use duct tape to seal the open end. Place on the bag a piece of plywood 20 inches square and at least 1/2 in thick. Around the perimeter of the plastic bag in each of six places, cut a small hole large enough to accept a soda straw. You may wish to seal the incision holes with duct tape. Invite a heavy student (say 200 lbs) to sit on the board, legs crossed. Enlist the aid of six students.Ask them to blow on the soda straws. They will levitate their class mate if they can muster a pressure of .5 lbs/in^2 .

Pressure comes to bear around the footwear that you use. Calculate the pressure under your shoe while standing with just one foot on the floor. That pressure is enough to make you sink through the surface of powdered snow. Don snow shoes or crosscountry skis. While you maybe A pound or two heavier with the new apparatus, the larger surface area significantly reduces the pressure under foot. Now you have a chance to make it across a snow field.

A smaller footprint means the pressure underfoot increases dramatically. A woman momentarily balancing on a single spike heel delivers enormous pressure under that heel, enough to damage wooden floors, enough to distract an assailant when driving that heel into his foot.
Ice skates are ground with a concave cross-section, causing the blade to ride on two knife edges. The pressure under those edges is great enough to melt ice. Water expands when it freezes. If you can keep it from expanding, the very cold water will stay in its liquid state and act as a lubricant. It re-freezes as soon as the blade slides along. Avid outdoor skaters will note that on very, very cold nights, relatively little ice liquefies and skating is sluggish because the lubricating cold water is missing.

Fluids exert pressure by virtue of their weight. A cubic foot of water weighs 62.4 lbs and so it delivers to the surface on which it rests a pressure of 62.4 lbs/ft^2. Add another box o' water on top of the first and you have doubled the pressure. From this simple reasoning we conclude that the pressure at any depth of fluid is simply a function of the depth of the fluid. In the equation that follows, h = fluid depth, g = acceleration due to gravity, and rho is the mass density of the fluid.

This equation works for most purposes even at great ocean depths because water is for the most part incompressible.

Other useful facts about fluid pressure are:

1. Fluids at any given depth exert the same pressure in all directons.

2. Fluid pressure is independent of the shape of the container holding it.