Pressure

Pressur

What is it?

Pressure is stress which is exerted uniformly (or the same way) in all directions. Pressure is measured in units of force applied per unit of area.

Give me an example!

Have you ever pumped up the tires on your bicycle? The pump increases the pressure of the air inside the tire against the tire. You stop pumping when the air gauge tells you that the pressure inside the tires has reached the desired level. In America, tire pressure is normally measured in units of pounds per square inch, or psi.

Pressure

• Pressure (the symbol: P) is the force per unit area applied in a direction perpendicular to the surface of an object.

Pressure is an effect which occurs when a force is applied on a surface. Pressure is the amount of force acting on a unit area. The symbol of pressure is P.

Formula

    Mathematically:

where:

P is the pressure,

F is the normal force,

A is the area.

Pressure is a scalar quantity. It relates the vector surface 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 fact that the force is considered towards the surface element, while the normal vector points outwards.

The SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N/m² or kg·m⁻¹·s⁻²). 

This special name for the unit was added in 1971; before that, pressure in SI was expressed simply as N/m²

• Although pressure itself is a scalar, we can define a pressure force to be equal to the pressure (force/area) times the surface area in a direction perpendicular to the surface. The pressure force is a vector quantity.
• Pressure forces have some unique qualities as compared to gravitational or mechanical forces. In the figure shown above on the right, we have a red gas that is confined in a box. 
• A mechanical force is applied to the top of the box. The pressure force within the box opposes the applied force according to Newton's third law of motion. The scalar pressure equals the external force divided by the area of the top of the box. Inside the gas, the pressure acts in all directions. So the pressure pushes on the bottom of the box and on the sides. 
• This is different from simple solid mechanics. If the red gas were a solid, there would be no forces applied to the sides of the box; the applied force would be simply transmitted to the bottom. But in a gas, because the molecules are free to move about and collide with one another, a force applied in the vertical direction causes forces in the horizontal direction.

• Fluid pressure

Fluid pressure is the pressure at some point within a fluid, such as water or air.

Fluid pressure occurs in one of two situations:

1. an open condition, such as the ocean, a swimming pool, or the atmosphere; or
2. a closed condition, such as a water line or a gas line.

• Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. 
• The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either "static," when the fluid is not moving, or "dynamic," when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

Liquid pressure or pressure at depth

Used with liquid columns of constant density or at a depth within a substance (ex. pressure at 20km depth in the earth).

P = gdh

Where:

P is Pressure

g is gravity at the surface of overlaying material

d is density of liquid or overlaying material

h is height of liquid or depth within material

Fluids Pressure & Depth

A fluid is a substance that flows easily. Gases and liquids are fluids, although sometimes the dividing line between liquids and solids is not always clear. Because of their ability to flow, fluids can exert buoyant forces, multiply forces in a hydraulic systems, allow aircraft to fly and ships to float.

The topic that this page will explore will be pressure and depth. If a fluid is within a container then the depth of an object placed in that fluid can be measured. The deeper the object is placed in the fluid, the more pressure it experiences. This is because is the weight of the fluid above it. The more dense the fluid above it, the more pressure is exerted on the object that is submerged, due to the weight of the fluid.

The formula that gives the P pressure on an object submerged in a fluid is:

P = r * g * h

where

• r (rho) is the density of the fluid, ( Density= mass/volume)
• g is the acceleration of gravity
• h is the height of the fluid above the object

If the container is open to the atmosphere above, the added pressure must be included if one is to find the total pressure on an object. 


The total pressure is the same as absolute pressure on pressure gauges(measure) readings, while the gauge(measure)  pressure is the same as the fluid pressure alone, not including atmospheric pressure.

P_total = P_atmosphere + P_fluid

P_total = P_atmosphere + ( r * g * h )

A Pascal is the unit of pressure in the metric system. It represents 1 newton/m²

Example: 
Find the pressure on a scuba diver when she is 12 meters below the surface of the ocean. Assume standard atmospheric conditions.
Solution:
The density of sea water is 1.03 X 10 ³ kg/m³ and the atmospheric pressure is 1.01 x 10⁵ N/m².

P_fluid = r g h = (1.03 x10 ³ kg/m³) (9.8 m/s²) (12 m)

= 1.21 x 10⁵ Newtons/m²
P_total = P_atmosphere + P_fluid                           = (1.01 x 10⁵) + (1.21 x 10⁵ ) Pa 

                            = 2.22 x 10 ² kPa (kilo Pascals)

Exercises :

1. What is the pressure experienced at a point on the bottom of a swimming pool 9 meters in depth? The density of water is 1.00 x 10³ kg/m³. (Answer=189kp)
2. The interior of a submarine located at a depth of 45 meters is maintained at normal atmospheric conditions. Find the total force exerted on a 20 cm by 20 cm square window. Use the density of sea water given above.
   (Answer=1.81 x 10.4 newtons)
   
3. How many atmospheres is a depth of 100 meters of ocean water?
   (Answer= 11 atm)
   
   
4. If the weight density of pure water is 62 pounds/ft³, find the weight of water in a swimming pool whose dimensions are 20 ft by 10 ft by 6 feet.
   (Answer=74,400 pounds)  
5. An airplane in level flight whose mass is 20,000 kg has a wing area of 60 m². What is the pressure difference between the upper and lower surfaces of its wing? Express your answer in atmospheres.
   (Answer=.032 atm)