Atmospheric and Gauge Pressure

In another lesson, we defined pressure as the force per unit area, and gave the SI units as Newtons per meter squared, or Pascals. There are actually a couple of different ways to measure pressure based on our frame of reference. We will further define pressure in terms of absolute pressure and gauge pressure.

  • Absolute pressure: The total pressure exerted on a system referenced to zero Pascals, and equal to the gauge pressure plus atmospheric pressure
  • Gauge Pressure: Pressure referenced to one atmosphere, and is the pressure actually shown on the dial of a gauge that registers pressure relative to atmospheric pressure. For example, an ordinary pressure gauge reading of zero does not mean there is no pressure, it means there is no pressure in excess of atmospheric pressure.
  • Atmospheric Pressure: The pressure exerted by the weight of the atmosphere.

Absolute pressure = gauge pressure + atmospheric pressure

Units of pressure - in the SI system: 1 atmosphere = 1.013x105 N /m2 or 101.3 kilopascals

1 Bar = 1.00x105 N/m2 = 100 kilopascals

But where does pressure come from? The pressure of a fluid at any depth depends only upon the density of the fluid (r) and the  distance below the surface of the fluid (h)  and the gravity constant (g). The height of a fluid is sometimes referred to as the pressure head.

Pressure =  density ● gravity ● height

or

P=rgh

A fluid exerts pressure in all directions. The pressure at a given depth on an object is the same in all directions. It is also independent of the volume of the fluid. For example, the pressure in a swimming pool filled with salt water at a depth of 10 meters is the same as the pressure in the ocean at a depth of 10 meters. The pressure on a submerged object is always perpendicular to the surface it is in contact with.  (Picture linked from http://www.workover.co.uk/well%20control1/Well%20control%20online%20training%20manual%20hydrostatic%20pressure.htm)

The pressure of the Earth’s atmosphere changes height, just as the pressure in any fluid changes with the depth of the fluid. Hydrostatic pressure is the pressure at the bottom of a column of fluid caused by the weight of the fluid. Hydrostatic pressure exists at all points below the surface, but it is not constant at all points. The hydrostatic pressure at any point depends on both the fluid density and the depth below the fluid surface. A scuba diver experiences the effects of hydrostatic pressure. As the diver goes deeper beneath the surface, more hydrostatic pressure is exerted on him. The amount of hydrostatic pressure depends on the weight of the water and the diver's distance below the surface. A swimmer diving down in a lake can easily observe an increase in pressure with depth. For each meter increase in depth, the swimmer experiences an increase in pressure of 9,810 N/m2. Since a liquid is nearly incompressible, its density does not change significantly with increasing depth. Therefore, the increase in pressure is caused solely by the increase in depth.  The formula is given by:

Pressure = density gravitydepth

or

P=rg h

 

Sample Problem:

 

Determine the water gauge pressure at a house at the bottom of a hill fed by a tank of water 8.0m deep and connected to a house by a pipe that is 120m long and at an angle of 50° from the horizontal. Assume the tank
is full.

P=rgh            g=9.8m/s2
h=120 m (sin50°) + 8m = 100 m

P= (1000kg/m3)(9.8m/s2)(100 m)

P=9.8 x 105 N/m2

Here is an interesting point to note. In the absence of friction or other net external forces, our behavior of fluids will follow the behaviors of other things that we have modeled in other lessons. For example, in the above problem, should a hole develop in the pipe right before it enters the house and the water is free to spray straight up, it will rise rise to the same height as the level of the water in the tank and remain even with that level as the tank drains and the level drops.

To read what others have to say on the subject, try:

http://hyperphysics.phy-astr.gsu.edu/Hbase/pflu.html

For Practice Problems, Try: Giancoli Multiple Choice PracticeQuestions (It will be a few lessons before all of this is covered)