LECTURE NOTES 1 – HYDRAULICS
px = py = p
PRINCIPLES OF HYDROSTATICS
A. INTENSITY OF PRESSURE
p=
C. PRESSURE VARIATION IN A LIQUID
F
A
E. TRANSMISSION OF PRESSURE
• Another law on fluid statics attributed to
Pascal is on the transmission of pressure
which states that “the pressure at any point in
a liquid at rest is transmitted equally and
undiminished to every other point in the
liquid”.
B. LAW OF PASCAL
• The law of Pascal states that “at any point in
a fluid at rest, the pressure is the same in all
directions”.
∑ Fx =0
dF2 - dW sin θ - dF1 = 0
p2 dA - w (L dA) sin θ - p1 dA = 0
Consider the fluid at rest or in equilibrium,
(a)
p2 - p1 = wh
Or
px dy = p (dl cos θ )
Since dy=dl cos θ, then px = p
(b)
D. PRESSURE HEAD
• Pressure head in fluid mechanics is the
pressure exerted by a liquid column on the
base of the container. It is represented as the
height of the liquid column. Pressure head is
also called static head or static pressure.
∑ Fy =0
dFy - dF sin θ = 0
py (dx dz)=p (dl dz) sin θ
Since dx=dl sin θ, then py = p
Therefore
W+ G2 F+G1
=
+ γh
A2
A1
p2 - p1 = γh
∑ Fx =0
dFx - dF cos θ = 0
px (dy dz) = p (dl dz) cos θ
p2 = p1 + γh
h=
p
γ
F. INSTRUMENT FOR MEASURING PRESSURE
a) Bourdon Gauge
• A Bourdon gauge is a mechanical device used
to measure and display pressure. The gauge
can be used for measuring pressure in both
gas and liquid state systems.
b) Barograph
• Barographs are barometers connected to
needles that make marks on a roll of adjacent
graph paper. The barograph records the
number of atmospheres on the vertical axis
and units of time on the horizontal.
c) Aneroid Barometer
• An aneroid barometer has a sealed metal
chamber that expands and contracts,
depending on the atmospheric pressure
around it. Mechanical tools measure how
much the chamber expands or contracts.
These measurements are aligned with
atmospheres or bars.
d) Manometers
• The manometer is so often used to measure
pressure that the difference in column heights
is also a common unit. This is expressed in
inches or centimeters of water or mercury at a
specific temperature, which can be changed to
standard units of pressure with a conversion
table.
e) Piezometers
• A device used to measure liquid pressure in a
system by measuring the height to which a
column of the liquid rises against gravity, or a
device which measures the pressure (more
precisely,
the piezometric
head)
of groundwater[1] at a specific point. A
piezometer is designed to measure static
pressures, and thus differs from a pitot tube by
not being pointed into the fluid flow