Hydrostatics or Fluid Statics: Pressure Variation with Depth

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In Hydrostatics the fluid under consideration is static, that is, the fluid is not flowing and if the fluid is now flowing then there is no question of shear stress coming in to picture. Thus the only physical quantity under consideration for study in Hydrostatics or Fluid Statics is the pressure in the fluid and the variation of the pressure in the fluid body with depth. The interaction of the static fluid with the bodies in contact with it, whether submersed or floating, in the form of force applied, is a major point of study in the Hydrostatics of fluids or Fluid Statics in civil engineering.

Pressure in fluid and its variation

The interaction of the static fluid with its surroundings is in the form of force, which is applied equally on all contact points. This force is the result of the pressure applied on a particular unit area. The pressure in the fluid is not constant throughout. The pressure in any body of fluid varies with depth and it increases with the depth of the fluid. But at the same level relative to the vertical direction the pressure will be same in the fluid. The increase in pressure as we go down the fluid is due to the weight of the fluid column above that level.

The variation of the pressure with depth of the liquid column can be formulated with this simple analysis. Consider a vertical column of a liquid with a constant cross sectional area. The liquid under consideration is at rest so there is no shear forces acting or coming in to picture. The liquid column is in equilibrium so all the forces are balanced in the column. At any point in the column net force is zero. The weight of the column at any particular depth is balanced by the force due to pressure at that point. Thus, the pressure at that point is equal to the weight of the column at that point divided by the area of cross section of the liquid column.

The weight of the column is equal to volume times density multiplied by the acceleration due to gravity. Volume of the liquid column is equal to height of the column times the area of cross section. Thus, the pressure at any particular depth is density of the liquid times acceleration due to gravity times the height of the liquid column above that point. As the density and acceleration due to gravity are constant for the range of problems considered in Civil Engineering Hydraulics, the pressure varies linearly with depth in liquid bodies.

This post is part of the series: Basics of Hydraulics

Hydraulics deals with the study of fluids, their behavior, motion of fluids and the interaction of fluids with other bodies. In this article series on Hydraulics fluids will be analyzed when in motion and as well as the effect of interaction of fluids with different bodies when static.

  1. What is Hydraulics? Civil Engineering and Hydraulics
  2. Basic Properties of Fluids
  3. Hydrostatics or Fluid Statics: Pressure Variation
  4. Measurement of Pressure
  5. Pressure Measurement: Pressure Measurement Devices