** Next:** Pressure Measurements
**Up:** Solids and Fluids
** Previous:** Density and Pressure

One might guess that the deeper you go into a liquid or gas, the greater the pressure on you from the surrounding fluid will be. The reason for the increased pressure is that the deeper into a fluid you go, the more fluid, and thus the more weight, you have over top of you.

We can calculate the variation of pressure with depth by
considering a volume
of fluid of height *h* and cross-sectional area *A* (see Fig. 9.3).

If this volume of fluid is to be in equilibrium, the net force acting on the volume must be zero. There are three external forces acting on this volume of fluid. These forces are:

- 1.
- The force
*P*_{T}*A*due to the pressure on top of the volume of fluid. If the fluid is open to the air,*P*_{T}=*P*_{O}= 1.01`x`10^{5}Pa, which is atmospheric pressure. - 2.
- The weight of the volume of fluid,
*w*=*Mg*. Remembering the definition of density, =*M*/*V*, and that the volume of the fluid may be calculated as*V*=*Ah*, we can write the weight of the fluid as*w*=*ghA*. - 3.
- The force pushing up on the bottom of the volume of fluid,
*P*_{B}*A*, due to the fluid below the volume under consideration.

*P*_{B}*A* - *ghA* - *P*_{T}*A* = 0,

P_{B} = P_{T} + gh.
| (9) |

**Note: **Only the density of the fluid and the difference in depth
affects the
pressure. The shape and size of the container are irrelevant.
Thus the water
pressure 6 inches below the surface of the ocean is the same as it
is 6
inches below the the surface of a glass of salt water.

**Idea: ****Pascal's Principle** states that any pressure applied to
an enclosed fluid is transmitted
undiminished to every point of the fluid. Thus, in Fig.9.4,

a pressure of

F_{2} = P_{2}A_{2} = F_{1}.
| (10) |

10/9/1997