What is the formula for pressure 1

Pressure and buoyancy

example

Through the action of a force \ (\ vec F \) on one point of the liquid or gas-filled container, forces occur on all walls of the container, which are directed perpendicular to the respective wall section. It is said that there is pressure in the liquid or in the gas.

Pressure is force on surface

A statement can be made about the magnitudes of these forces with the adjacent arrangement: The arrangement consists of three freely movable punches with the cross-sectional areas \ (A_1 \), \ (A_2 \) and \ (A_3 \). Weights are placed on the stamp so that the arrangement is in "equilibrium".

The sum of the downwardly acting weight forces of the additional bodies and the ram is then exactly as large as the forces \ (\ vec F_1 \), \ (\ vec F_2 \) and \ (\ vec F_2 \) and \ (\ vec F_2 \) and \ (\ vec F_3 \). In this way one can determine the force amounts \ (F_1 \), \ (F_2 \) and \ (F_3 \) emanating from the gas or the liquid via the weight forces.

For the equilibrium case shown, the measurements result in \ [\ frac {{{F_1}}} {{{A_1}}} = \ frac {{{F_2}}} {{{A_2}}} = \ frac {{{F_3} }} {{{A_3}}} \] This quotient, which is the same for all stamps, is called pressure.

example
Let the force \ (F_1 = 15 \, \ rm {N} \) and the cross-sectional area \ (A_1 = 6 \, \ rm {cm} ^ 2 \). Then the pressure on this area is \ (p = \ frac {{{F_1}}} {{{A_1}}} \) so \ (p = \ frac {15 \, \ rm {N}} {6 \, \ rm {cm ^ 2}} = 2 {,} 5 \, \ rm {\ frac {N} {{{cm ^ 2}}}} \).
If the cross-sectional area is now \ (A_2 = 2 \, \ rm {cm} ^ 2 \), you measure a force of \ (F_2 = \ frac {15 \, \ rm {N}} {6 \, \ rm) {cm ^ 2}} \ cdot 2 \, \ rm {cm ^ 2} = 5 \, \ rm {N} \).

Hints

  • \ (F \) is the amount of force through the gas or liquid that acts perpendicular to the area \ (A \).
  • The force \ (F \) (unit N) should not be confused with the mass (unit kg). The force can be calculated from the mass using the location factor.
  • The pressure characterizes a state of the gas or the liquid, it is not a directed quantity (vector) like the force.
  • In the case of solids, the term pressure makes no sense.
  • The weather report uses the pressure unit 1 hPa (1 hPa = 100 Pa).
    This unit is the same size as the unit 1 mbar (1 mbar = 1/1000 bar). Think about why!