Randy jimenezPrinciples of Hydrostatic PressuresHydraulics is an applied engineering science which treats of water and other fluid in motion.Unit PressureUnit pressure or simply called pressure is the amount of force exerted by a fluid distributed uniformly over a unit area.

If the unit pressure is not uniform over the unit area, it can be expressed as the sum of differential pressure.

Blaise Pascal (1623 1662)Since fluid at rest cannot resist shearing stress, pressure is always at right angle to the area where it is acting. It is also worthy to note that the total hydrostatic forceF = pA, which can be found by cross multiplication.Pascals LawThe French mathematician Blaise Pascal (1623 1662) states that the pressure is the same in all directions at any point in a fluid at rest.From the figure shown below, summation of forces in y-direction:

Since,.

Summation of forces in z-direction:

Since,.Thus, which can be used to conclude Pascal's Law.Summation of forces in x-direction:

Since , .Atmospheric, Gauge, and Absolute PressuresAtmospheric pressureis the weight of all gasses above the surface in which it comes in contact. Under normal conditions, atmospheric pressure at sea level is equal to 101.325 kPa (14.696 psi), usually rounded off to 100 kPa (14.7 psi) by engineers. With increase in altitude, atmospheric pressure decreases.Gauge pressure, measured with the use of pressure gauges, is the pressure above or below atmospheric pressure. Negative gauge pressure indicates a vacuum which cannot go below 101.325 kPa. Positive gauge pressure indicates that the pressure is above atmospheric. Gauge pressure is also calledrelative pressure.Absolute pressureis equal to gauge pressure plus atmospheric pressure. There is no such thing as negative absolute pressure. In the absence of all matter (complete vacuum), the absolute pressure is zero.

Pressure GaugesJust for the purpose of completeness of this page, pressure gauges (or pressure instruments) are listed here. For more detailed discussion about pressure gauges, refer to the links in each type of pressure instrument. Some general types of pressures instruments are as follows.Barometer - used to measure atmospheric pressure.Wikipedia article.Manometer- a U-tube that contains liquid of known specific gravity.Wikipedia article.Bourdon gauge - used to measure large pressure difference.Integrated Publishing article.

Variation of Pressure with Depth in a FluidConsider two points 1 and 2 lie in the ends of fluid prism having a cross-sectional areadAand lengthL. The difference in elevation between these two points is h as shown in Figure 02 below. The fluid is at rest and its surface is free. The prism is therefore in equilibrium and all forces acting on it sums up to zero.

Note: FFS stands for Free Fluid Surface which refers to fluid surface subject to zero gauge pressure.The volume of the prism is equal to the length times the base area of the fluid.

The weight of the fluid prism shown is equal to the product of the unit weight and volume.

Sum up all the forces in x-direction

butL sin = h, thus

Therefore, in any homogeneous fluid at rest, the difference in pressure between any two points is equal to the product of the unit weight of the fluid and the difference in elevation of the points.Ifh = 0so that points 1 and 2 are on the same horizontal plane,p2- p1= 0or

Therefore, in any homogeneous fluid at rest, the pressures at all points along the same horizontal plane are equal.If point 1 lie on the FFS, the gauge pressurep1= 0, makingp2- 0 = hor simply

This means that the pressure at any depth h below a continuous free fluid surface at rest is equal to the product of the unit weight of fluid and the depth h.Transmission of PressureWe can write the equationp2- p1= hinto the form

which means that any change in the pressure at point 1 would cause an equal change of pressure at point 2. In other words, a pressure applied at any point in a liquid at rest is transmitted equally and undiminished to every other point in the liquid.Pressure HeadThe equationp = hmay be written into the form

wherehor its equivalentp/is in hydraulics called the pressure head. Pressure head is the height of column of homogeneous fluid of unit weightthat will produce an intensity of pressurep.To convert pressure head of liquid A to equivalent pressure head of liquid B

To convert pressure head of any liquid to equivalent pressure head of water

where,s= specific gravity= unit weight= densityProperties of Waters = 1.0 = 9.81 kN/m3(or62.4 lb/ft3in English system) = 1000 kg/m3(or1.94 slugs/ft3in English system)