Overview
The study of fluid characteristics and behavior in Civil Engineering applications
is of the greatest importance to Hydraulic/Environmental Engineers. The engineers must
take into account many factors when designing a special system (wastewater treatment
facility, sewer pipe system, potable water distribution system, etc.), such as:





Flow
Temperature
Specific Gravity
Viscosity
Pressure
Out of all these factors, the pressure of the fluid is by far the most significant. For
example, when designing the stability of a pipe in a dynamic fluid system, the pressure
largely affects the support forces needed to keep the pipe in a static equilibrium:
Momentum Equation (x-direction):
 p1 A1 x   p2 A2 x  Fx  QV2  V1 x
Equation 1
(P.194, Finnemore-Franzini)
Determining these pressure forces becomes a concern for the engineer, and must be found
using special fluid static/dynamic studies.
The main study used for the pressure within a pipe is the application of a simple
device called a manometer. Manometers appear in many shapes and sizes (simple
manometer, differential manometer, U-shape manometer, barometer, etc.) and serve
different purposes (single pipe pressure, difference in pipe pressures, atmospheric
pressure). The different manometer devices measure gage pressures; however, through a
simple calculation knowing the atmospheric pressure, the absolute pressure of the desired
point of points can be determined:
p abs  p atm  p gage
Equation 2
(P. 53, Finnemore-Franzini)
Also, the pressure head or absolute pressure head of the system can be determined in
length units of a certain fluid by dividing the calculated pressure by the specific weight of
that fluid. The next section will go into greater detail of the theory of the different types
of manometers and the process of calculating the desired pressures.
Piezometer columns are used for measuring moderate pressures of liquids. The
piezometer tube has a small opening and is generally very tall making it inconvenient for
us with high pressures. In the case of higher pressures, it is ideal to use a manometer. A
manometer is a double-leg column gage that is used to measure the difference in pressure
between two fluids.
The various types of manometers have many similar characteristics: hollow tube,
liquid partially filling the tube and a scale. The U-tube manometer consists of a hollow
tube connecting two pressures sources. A differential manometer involves two enclosed
pressure sources that are connected with the tube. On the other hand, a simple
manometer involves a pressure source connected to atmospheric pressure through the
tube.
General Equations
Simple Manometer
The idea in solving for a simple manometer is to begin at the point of atmospheric
pressure, then continue through the different fluids by calculating the pressure changes
till the point of interest is reached. In Figure 1, a pipe with a steady flowing fluid, F, is
connected with simple open-end manometer. The manometer fluid is indicated by M and
is different from the pipe fluid. Also, the dimension, Rm, is the manometer reading,
which is simply the height difference between the two surfaces of the manometer fluid.
The dimension, h, is the difference in height of the pipe fluid/manometer fluid interface
and the desired location in the pipe. The pressure is calculated using the specific weight
and height dimension as shown below:
Pressure:
p  h
Pressure Head:
h
p

Equation 3
(P. 50, Finnemore-Franzini)
Equation 4
(P. 51, Finnemore-Franzini)
The pressure difference is determined by the direction of calculation. For instance, the
pressure increases when moving in the negative elevation direction and decrease when
moving in the positive elevation direction. In the example of Figure 1, the calculations
would start at the free surface (atmospheric pressure), travel through the fluid M and
finally travel through fluid F to point A. The equation of the gage pressure would be as
follows:
0  s M  W Rm  s F  W h  PA
Equation 5
The pressure at A in this equation is the gage pressure. This pressure can be converted to
either a pressure head in length units of a fluid (Equation 4) or an absolute pressure
(Equation 2).
Differential Manometer
The same concepts of fluid statics are used in solving a differential manometer; however,
the difference between the two types is that in a differential manometer the pressures are
not always known. Therefore, the result will sometimes come out as a difference in pipe
pressure. In Figure 2, the same concepts as used in the simple open-end manometer. The
dimension, Rm, is the manometer reading, which is the height difference between the two
surfaces of the manometer fluid, M. The dimensions, hA and hB, are the height
differences between the pipe fluid/manometer fluid interface and respective pipe location
(A or B). The equation for the difference in the pressure of A and B for this manometer is
as follows:
p A  s F  W hA  s M  W Rm  s F  W hB  p B
Equation 6
p A  p B  s F  W hA  s M  W Rm  s F  W hB
Equation 7
This equation can also be written as:
pA


 s
 z B  z A)   1  M

sF

pB

 Rm

Equation 8
(P. 62, Finnemore-Franzini)
p
  s
  z   1  M
sF

 

 Rm

Equation 9
(P. 62, Finnemore-Franzini)
As in simple manometers, the pressure or pressure difference can be determined as a gage
pressure (or pressure head), or as an absolute pressure (or pressure head).
Sample Manometer Problems
Simple Manometer
Find the gage and absolute pressure at point A of the system.
p atm  14.7 psia
p gage A  ?
h  1.5 ft
Rm  8in
 w  62.4lbs / ft
pabs A  ?
3
p  gage A  s M Rm  s F h  w


8
p  gage A  13.6   (.83)(1.5)(62.4)
 12 


p  gage A  488.1lbs / ft 2  3.39 psi
pabs A  patm  p gage A
pabs A  14.7  3.39  18.09 psi
Differential Manometer
Find pressure at B, and pressure head at B in length units of water.
Rm  2 ft
h  2.5 ft
z  1 ft
 w  62.4lbs / ft 3
p A  7.21 psi
pB  ?
p head , B  ?
p B  p A  s F ( Rm  h  1) w  s M Rm w  s F h w
p B  (7.21)(144)  (1)( 2  2.5  1)(62.4)  (13.6)( 2)(62.4)  (1)( 2.5)(62.4)
p B  2548.32lbs / ft 2  17.7 psi
p head , B 
pB
w
 40.8 ft