Fluid Statics

Fluid Statics

Fluid statics is concerned with the balance of forces which stabilise fluids at rest. In the case of a liquid, as the pressure largely changes according to its height, it is necessary to take its depth into account. Furthermore, even in the case of relative rest (e.g. the case where the fluid is stable relative to its vessel even when the vessel is rotating at high speed), the fluid can be regarded as being at rest if the fluid movement is observed in terms of coordinates fixed upon the vessel.

Pressure- 

                   When a uniform pressure acts on a flat plate of area A and a force P pushes the plate, then 

                                                               p = P/A

Units of pressure- 

                                      The unit of pressure is the pascal (Pa), but it is also expressed in bars or metres of water column (mH,O).In addition, in some cases atmospheric pressure is used: 1 atm = 760mmHg(at273.15K,g = 9.80665m/s2) = 101 325Palatm is standard 1 atmospheric pressure in meteorology and is called the standard atmospheric pressure. 

Absolute pressure and gauge pressure-

                                                                             There are two methods used to express the pressure: one is based on the perfect vacuum and the other on the atmospheric pressure. The former is called the absolute pressure and the latter is called the gauge pressure. Then, gauge pressure = absolute pressure - atmospheric pressure In gauge pressure, a pressure under 1 atmospheric pressure is expressed as a negative pressure. This relation is shown in Fig.. Most gauges are constructed to indicate the gauge pressure.

                                                     

Characteristics of pressure -

                                                         The pressure has the following three characteristics.

1. The pressure of a fluid always acts perpendicular to the wall in contact with the fluid.

2. The values of the pressure acting at any point in a fluid at rest are equal regardless of its direction. Imagine a minute triangular prism of unit width in a fluid at rest. Let the pressure acting on the small surfaces dA,, dA, and dA be p,, p2 and p respectively. The following equations are obtained from the balance of forces in the horizontal and vertical directions:

                                                       

                                                         pldA, = pdAsin0

                                                         p2dA2 = pdAcos0  + idA,dA,pg

The weight of the triangle pillar is doubly infinitesimal, so it is omitted. From geometry, the following equations are obtained:

                                                           dA sin@ = dA,

                                                        dA COS 0 = dA,

Therefore, the following relation is obtained:

                                                         PI =P2=P 

Since angle 8 can be given any value, values of the pressure acting at one point in a fluid at rest are equal regardless of its direction.

3. The fluid pressure applied to a fluid in a closed vessel is transmitted to all parts at the same pressure value as that applied (Pascal’s law).

   when the small piston of area A, is acted upon by the force F,, the liquid pressure p = FI/A, is produced and the large piston is acted upon by the force F, = PA,.