Force Per Unit Area
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Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is \"p\" or P.[2]The IUPAC recommendation for pressure is a lower-case p.[3]However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.
Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:
The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.
It is incorrect (although rather usual) to say \"the pressure is directed in such or such direction\". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.[citation needed]
Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.
When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units.[7] One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres (or centimetres) of mercury in most of the world, and lung pressures in centimetres of water are still common.[citation needed]
Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm[citation needed] (1 atm = 101325 Pa / 33.066 = 3064.326 Pa). Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.[citation needed]
Gauge pressure is often given in units with \"g\" appended, e.g. \"kPag\", \"barg\" or \"psig\", and units for measurements of absolute pressure are sometimes given a suffix of \"a\", to avoid confusion, for example \"kPaa\", \"psia\". However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure.[8] For example, \"pg = 100 psi\" rather than \"p = 100 psig\".
As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.[9]
Another example is a knife. If we try to cut with the flat edge, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure[10]
Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as \"kPa (gauge)\" or \"kPa (absolute)\", is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as \"32 psig\", and an absolute pressure as \"32 psia\", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.[8]
In a physical container, the pressure of the gas originates from the molecules colliding with the walls of the container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our \"container\" down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.[citation needed]
Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:
If four interconnected vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference which vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.
Restating this as an energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth.[19] Mathematically, it is described by Bernoulli's equation, where velocity head is zero and comparisons per unit volume in the vessel are
Now, the problem is when I want to find the force due to that pressure I have to multiply that pressure by only half the surface area of the sphere which is the surface area of the hemisphere I'm taking the pressure at
which should be $1/32$ instead of $1/64$ , where have I gone wrong please, Griffiths did it by integrating the force per unit area on every surface element on the northern hemisphere, but I believe I could do it without integration, where have I gone wrong please
Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior. The standard unit for pressure is the Pascal, which is a Newton per square meter.
For an object sitting on a surface, the force pressing on the surface is the weight of the object, but in different orientations it might have a different area in contact with the surface and therefore exert a different pressure.
There are many physical situations where pressure is the most important variable. If you are peeling an apple, then pressure is the key variable: if the knife is sharp, then the area of contact is small and you can peel with less force exerted on the blade. If you must get an injection, then pressure is the most important variable in getting the needle through your skin: it is better to have a sharp needle than a dull one since the smaller area of contact implies that less force is required to push the needle through the skin.
The weight of the air above an object exerts a force per unit area upon that object and this force is called pressure. Variations in pressure lead to the development of winds, which in turn influence our daily weather. The purpose of this module is to introduce pressure, how it changes with height and the importance of high and low pressure systems. In addition, this module introduces the pressure gradient and Coriolis forces and their role in generating wind. Local wind systems such as land breezes and sea breezes will also be introduced. The Forces and Winds module has been organized into the following sections:
Dive down into the ocean even a few feet, though, and a noticeable change occurs. You can feel an increase of pressure on your eardrums. This is due to an increase in hydrostatic pressure, the force per unit area exerted by a liquid on an object. The deeper you go under the sea,