c. bernoullis theorem demonstration

KNC 1101: CHEMICAL ENGINEERING LABORATORY I

LABORATORY MANUAL

EXPERIMENT C

Bernoullis Theorem

Demonstration

Faculty of Engineering

Department of Chemical Engineering & Energy Sustainability

Semester 2_ 2013/2014

KNC 1101: Chemical Engineering Laboratory I 2013/2014

Prepared by Mohamed Afizal Mohamed Amin 2

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:

Constant *hzg

v

g

p

2

2

Where,

p = Fluid static pressure at the cross section

= Density of the flowing fluid

g = Acceleration due to gravity

v = Mean velocity of fluid flow at the cross section

z = 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 Bernoullis 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:

Constant *hg

v

g

p

2

2

This represents the total head at a cross section



Objective of the Experiment

1) To demonstrate Bernoullis Theorem

Prior Knowledge

1) Fluid dynamics (fluid in motion)

2) Bernoullis law : Venturi Meter

Materials and Equipment

1) Bernoullis Theorem Demonstration Unit (Model: FM24)

2) Tap water

Figure 1: Parts Identification Diagram

1. Manometer Tubes

2. Test Section

3. Water Inlet

4. Unions

5. Air Bleed Screw

6. Flow Control Valve

7. Gland Nut

8. Hypodermic Probe

9. Adjustable Feet

5

1

2

3

4

6

7

8

9



Gland Nut

Hypodermic probe

Adjustable feetTest sectionWater inlet

Unions

Manometer tubes

Air bleed screw

Figure 2: Front View of Bernoullis Theorem Demonstration Unit

Additional tapping

Flow control valve

Water outlet

Figure 3: Top View of Bernoullis 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.



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 Bernoullis 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 Bernoullis 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.



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



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 Bernoullis equation where;

)(2 8 ii hhgV

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

Cross Section

Using Bernoulli Equation Using Continuity Equation Difference

h*=hG

(mm)

hi

(mm)

ViB =

[2*g*(h* - hi )]

(m/s)

Ai =

Di2 / 4

(m2)

ViC =

Qav / Ai

(m/s)

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

(kg/m3) = 1000

c. bernoullis theorem demonstration

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