KNC 1101: CHEMICAL ENGINEERING LABORATORY I
LABORATORY MANUAL
EXPERIMENT C
Bernoulli’s Theorem
Demonstration
Faculty of Engineering
Department of Chemical Engineering & Energy Sustainability
Semester 2_ 2013/2014
KNC 1101: Chemical Engineering Laboratory I
2013/2014
INTRODUCTION
Bernoulli's law states that if a non-viscous fluid is flowing along a pipe of varying
cross section, then the pressure is lower at constrictions where the velocity is
higher, and the pressure is higher where the pipe opens out and the fluid
stagnate. Many people find this situation paradoxical when they first encounter
it (higher velocity, lower pressure). This is expressed with the following equation:
p
v2

 z  h *  Constant
 g 2g
Where,
p
ρ
g
v
z
= Fluid static pressure at the cross section
= Density of the flowing fluid
= Acceleration due to gravity
= Mean velocity of fluid flow at the cross section
= Elevation head of the center at the cross section with respect
to a datum
h* = Total (stagnation) head
The terms on the left-hand-side of the above equation represent the pressure
head (h), velocity head (hv ), and elevation head (z), respectively. The sum of
these terms is known as the total head (h*). According to the Bernoulli’s theorem
of fluid flow through a pipe, the total head h* at any cross section is constant. In
a real flow due to friction and other imperfections, as well as measurement
uncertainties, the results will deviate from the theoretical ones.
In this experimental setup, the centerline of all the cross sections are considering
lie on the same horizontal plane (which we may choose as the datum, z = 0, and
thus, all the ‘z’ values are zeros so that the above equation reduces to:
p
v2

 h *  Constant
 g 2g
This represents the total head at a cross section
Prepared by Mohamed Afizal Mohamed Amin
2
KNC 1101: Chemical Engineering Laboratory I
2013/2014
Objective of the Experiment
1) To demonstrate Bernoulli’s Theorem
Prior Knowledge
1) Fluid dynamics (fluid in motion)
2) Bernoulli’s law : Venturi Meter
Materials and Equipment
1) Bernoulli’s Theorem Demonstration Unit (Model: FM24)
2) Tap water
5
1
6
2
7
3
8
4
9
Figure 1: Parts Identification Diagram
1.
2.
3.
4.
5.
6.
7.
8.
9.
Manometer Tubes
Test Section
Water Inlet
Unions
Air Bleed Screw
Flow Control Valve
Gland Nut
Hypodermic Probe
Adjustable Feet
Prepared by Mohamed Afizal Mohamed Amin
3
KNC 1101: Chemical Engineering Laboratory I
2013/2014
Air bleed screw
Manometer tubes
Unions
Gland Nut
Hypodermic probe
Water inlet
Test section
Adjustable feet
Figure 2: Front View of Bernoulli’s Theorem Demonstration Unit
Water outlet
Flow control valve
Additional tapping
Figure 3: Top View of Bernoulli’s Theorem Demonstration Unit
The unit consists of the followings:
a) Venturi
The venturi meter is made of transparent acrylic with the following
specifications:
Throat diameter
: 16 mm
Upstream Diameter : 26 mm
Designed Flow Rate : 20 LPM
b) Manometer
 There are eight manometer tubes; each length 320 mm, for static
pressure and total head measuring along the venturi meter.
 The manometer tubes are connected to an air bleed screw for air
release as well as tubes pressurization.
Prepared by Mohamed Afizal Mohamed Amin
4
KNC 1101: Chemical Engineering Laboratory I
2013/2014
c) Baseboard
The baseboard is epoxy coated and designed with 4 height adjustable
stands to level the venturi meter.
d) Discharge Valve
One discharge valve is installed at the venturi discharge section for flow
rate control.
e) Connections
Hose Connections are installed at both inlet and outlet.
f) Hydraulic Bench
Sump tank
: 120 litres
Volumetric tank : 100 litres
Centrifugal pump : 0.37 kW, 50 LPM
METHODOLOGY
A. General Start-up Procedures
The Bernoulli’s Theorem Demonstration (Model: FM 24) is supplied ready for
use and only requires connection to the Hydraulic Bench (Model: FM 110) as
follows:
1. Ensure that the clear acrylic test section is installed with the converging
section upstream. Also check that the unions are tighten (hand tight only).
If necessary to dismantle the test section then the total pressure probe
must be withdrawn fully (but not pulled out of its guide in the
downstream coupling) before releasing the couplings.
2. Locate the apparatus on the flat top of the bench.
3. Attach a spirit level to baseboard and level the unit on top of the bench by
adjusting the feet.
4. Fill water into the volumetric tank of the hydraulic bench until
approximately 90% full.
5. Connect the flexible inlet tube using the quick release coupling in the bed
of the channel.
6. Connect a flexible hose to the outlet and make sure that it is directed into
the channel.
7. Partially open the outlet flow control valve at the Bernoulli’s Theorem
Demonstration unit.
8. Fully close the bench flow control valve, V1 then switch on the pump.
9. Gradually open V1 and allow the piping to fill with water until all air has
been expelled from the system.
10. Also check for “Trapped Bubbles” in the glass tube or plastic transfer tube.
You would need to remove them from the system for better accuracy.
Prepared by Mohamed Afizal Mohamed Amin
5
KNC 1101: Chemical Engineering Laboratory I
2013/2014
Note:
To remove air bubbles, you will have to bleed the air out as follow:
a. Get a pen or screw driver to press the air bleed valve at the top right
side of manometer board.
b. Press air bleed valve lightly to allow fluid and trapped air to escape
out. (Take care or you will wet yourself or the premise).
Allow sufficient time for bleeding until all bubbles escape.
11. At this point, you will see water flowing into the venturi and discharge
into the collection tank of hydraulic bench.
12. Proceed to increase the water flowrate. When the flow in the pipe is steady
and there is no trapped bubble, start to close the discharge valve to reduce
the flow to the maximum measurable flow rate.
13. You will see that water level in the manometer tubes will begin to display
different level of water heights. If the water level in the manometer board
is too low where it is out of visible point, open V1 to increase the static
pressure. If the water level is too high, open the outlet control valve to
lower the static pressure.
Note: The water level can be adjusted facilitate by the air bleed valve.
14. Adjust V1 and outlet control valve to obtain a flow through the test section
and observe that the static pressure profile along the converging and
diverging sections is indicated on its respective manometers. The total
head pressure along the venture tube can be measured by traversing the
hypodermic tube.
Note:
The manometer tube connected to the tapping adjacent to the outlet flow
control valve is used as a datum when setting up equivalent conditions for
flow through test section.
15. The actual flow of water can be measured using the volumetric tank with
a stop watch.
B. Experiment
1. Perform the General Start-up Procedures in Section A.
2. Check that all manometer tubings are properly connected to the
corresponding pressure taps and are air-bubble free.
3. Adjust the discharge valve to a high measurable flow rate.
4. After the level stabilizes, measure the water flow rate using volumetric
method.
5. Gently slide the hypodermic tube (total head measuring) connected to
manometer #G, so that its end reaches the cross section of the Venturi
tube at #A. Wait for some time and note down the readings from
manometer #G and #A. The reading shown by manometer #G is the sum of
Prepared by Mohamed Afizal Mohamed Amin
6
KNC 1101: Chemical Engineering Laboratory I
2013/2014
the static head and velocity heads, i.e. the total (or stagnation) head (h*),
because the hypodermic tube is held against the flow of fluid forcing it to a
stop (zero velocity). The reading in manometer #A measures just the
pressure head (hi) because it is connected to the Venturi tube pressure tap,
which does not obstruct the flow, thus measuring the flow static pressure.
6. Repeat step 5 for other cross sections (#B, #C, #D, #E and #F).
7. Repeat step 3 to 6 with three other decreasing flow rates by regulating the
venturi discharge valve.
8. Calculate the velocity, ViB using the Bernoulli’s equation where;
Vi  2  g  (h8  hi )
9. Calculate the velocity, ViC using the continuity equation where
Vi_Con = Qav / Ai
10. Determined the difference between two calculated velocities.
C. General Shut-down Procedures
1. Close water supply valve and venturi discharge valve.
2. Turn off the water supply pump.
3. Drain off water from the unit when not in use.
RESULTS AND DISCUSSION
Using Bernoulli Equation
Cross Section
h*=hG
(mm)
hi
(mm)
ViB =
√[2*g*(h* - hi )]
(m/s)
Using Continuity Equation
Ai =
¶ Di2 / 4
(m2)
ViC =
Qav / Ai
(m/s)
Difference
ViB-ViC
(m/s)
A
B
C
D
E
F
Additional Information:
Throat Diameter, D3 (mm) = 16.0
Inlet Diameter, D3 (mm) = 26.0
Throat Area, At (m2) = 2.011 x 10-4
Inlet Area, Ai (m2) = 5.309 x 10-4
g (m/s2) = 9.81
ρ (kg/m3) = 1000
Prepared by Mohamed Afizal Mohamed Amin
7