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)