Speed of a Magnetohydrodynamic Propulsion Boat as a Function of Salt Concentration

Speed of a Magnetohydrodynamic Propulsion Boat as a

Function of Salt Concentration

__________________________________________________________

An Investigatory Project Research Study

Presented to the Faculty of the

Science and Mathematics Education Department

College of Education

University of San Carlos

_______________________________________________

_________________________________________________

In Partial Fulfillment of the Requirements for

Research 2

_________________________________________

By:

Moral, Fidelfo Jr. C.

1

Pableo, Niel Wilfred O.

October 2008

2

Chapter 1

PROBLEM AND ITS BACKGROUND

3

Rationale of the Study

Perhaps one of the most abstract areas in Physics is

that of electromagnetism. The reason for this is that many

students have difficulty of understanding the concepts of

electric and magnetic fields, and the behavior of charges

and currents in their presence. Most of the discussions in

this branch of Physics are abstract or intangible. Some are

quite simply beyond the lay person’s common sense. It is

quite hard for students and teachers alike to find familiar

examples or instances where concepts on electromagnetism are

applied. Even those that are available, such as the mere

moving of a bar magnet in and out of a coil of wire, are

rather disengaging and fail to give much motivation for

learning. The more exciting demonstrations, such as a

levitating metal ring, are currently unavailable to

virtually all high schools. All these tend to hamper the

students’ interests and capability to learn the subject.

4

The cinema industry can sometimes prove to be an ally

when searching for material with which to motivate students

to learn physics. Consider, for example, the electromagnetic

force on a current in the presence of a magnetic field. This

phenomenon is the heart of magnetohydrodynamic (MHD)

propulsion systems. A submarine employing this type of

propulsion was immortalized in the movie Hunt for Red

October. While mentioning this to students certainly gets

their attention, it often elicits comments that it is only

fiction and not physically possible. Imagine their surprise

when a working system is demonstrated! It is neither

difficult nor expensive to construct a working system that

can be demonstrated in the front of the classroom. An

article from the October 2004 issue of The Physics Teacher

Volume 42 Number 7 entitled Magnetohydrodynamic Propulsion

for the Classroom presents a detailed methodology in the

construction of such a set-up. It also details how to

optimize the dimensions of the boat.

5

This study however concerns not with the dimensions

of the boat, but rather with the salt concentration of the

water on which the boat can operate. The boat dimensions are

optimized based on the field strength of the available

magnets. The study aims to establish the relationship

between salinity and MHD speed and use the device to

determine the conductivity of a solution.

Theoretical Background

Magnetohydrodynamics

Magnetohydrodynamics (MHD) (magnetofluiddynamics or

hydromagnetics) is the physical-mathematical framework that

concerns the dynamics of magnetic fields in electrically

conducting fluids, e.g. in plasmas and liquid metals. The

word magnetohydrodynamics is comprised of the words magneto-

meaning magnetic, hydro- meaning water (or liquid) and -

dynamics referring to the movement of an object by forces.

One of the most famous scholars associated with MHD was the

6

Swedish physicist Hannes Alfvén (1908-1995), who received

the Nobel Prize in Physics (1970) for fundamental work and

discoveries in magnetohydrodynamics with fruitful

applications in different parts of plasma physics. The

central point of MHD theory is that conductive fluids can

support magnetic fields. The presence of magnetic fields

leads to forces that in turn act on the fluid (typically a

plasma), thereby potentially altering the geometry (or

topology) and strength of the magnetic fields themselves. A

key issue for a particular conducting fluid is the relative

strength of the advecting motions in the fluid, compared to

the diffusive effects caused by the electrical resistivity.

Other topics belonging to the fundamental framework of

magnetohydrodynamics include, e.g. MHD turbulence, MHD waves

(Alfvén waves), magneto-convection, MHD reconnection, and

hydromagnetic dynamo theory. (Biskamp, 1993)

Magnetohydrodynamic Propulsion

7

One of the viable alternatives to the screw propeller

that has gained a relative degree of notoriety is

magnetohydrodynamic (MHD) propulsion. Anyone who has read or

seen The Hunt for Red October has heard of it by its more

popularized name: caterpillar drive. It was the super-silent

propulsion system installed on the fictional Russian

submarine in the Tom Clancy story. MHD offers a propulsion

system that requires no moving parts. It works on a

principle similar to that of an electric motor or generator;

that is, passing an electrical current through a magnetic

field creates a force. In an MHD propulsion system, a

magnetic field is created within the hull, and sea water is

used to conduct the electric current. The underlying

principle is known as Fleming’s Right-Hand Rule as shown in

the Figure 1 below:

8

Figure 1 Fleming’s Right-Hand Rule

which is demonstrated by taking the thumb, index, and middle

finger of the right hand and holding them perpendicular to

each other. If a magnetic field is created in the direction

of the middle finger while electric current passes in the

direction of the index finger, an electromagnetic force

(also known as Lorentz force) will be produced along the

direction of the thumb. This force acts on the conductor (in

this case salt water), so by constraining the sea water

within a tube, the Lorentz force will push it through the

tube, creating a viable propulsive force. (George L. Petrie,

2006)

Lorentz Force on a Current

9

An electrically charged particle moving through a

magnetic field feels a force (see Figure 2 below).

Figure 2 Force on a Moving Charge in a Magnetic Field

The force is given by the equation:

where q and v are the particle charge and velocity,

respectively, and B is the applied magnetic field. (Vector

quantities in the text are represented by bold letters.) The

10

resulting force is perpendicular to both the velocity of the

particle and the magnetic field. Its direction may be

determined with the right-hand rule.

In order to harness this force for propulsion, one

simply passes a stream of charges through a magnetic field

and the charges are accelerated. By Newton's third law, the

propulsive force is exactly equal to the force imparted on

the charges. Since more than one charge will be accelerated,

the equation above may be recast by rewriting the term qv

using:

where n is the number of charges (Na+ and CL- ions) per

volume, A and L are the cross-sectional area (given by the

width w times the height H) and length, respectively, of

the water channel (as shown in Figure 3 below).

11

Figure 3 Boat Channel Dimension

The quantity qnAv is then defined as the current I.

This leads to the statement for the force imparted on a

current in the presence of a magnetic field,

The poles of the magnets used are located on the

sides of the magnet and not on the ends. This creates a

magnetic field across the channel and perpendicular to the

current direction. The magnets are oriented along the sides

of the channel as shown in Figure 4 below:

12

Figure 4 Orientation of Magnets

When NaCl salt dissolves in water, it disassociates

into Na+ and Cl- ions. When the salt solution passes through

the channel in the lack of a magnetic field, the motion of

the ions are random. However, in a magnetic field, the Na+

ions generally move towards the negative electrode of the

channel, while the Cl- ions move to the positive electrode.

Using conventional current, there is now an effective

current flowing from the positive to the negative electrode.

The magnetic field is oriented perpendicular to the current,

and so, by Fleming’s right hand rule, a Lorentz force is

exerted on the ions, and thus the water is pushed outwards

through the channel exit (stern). By Newton’s third law, a

13

reaction force is exerted by the water on the boat, causing

it to move in the direction of the channel entrance (bow).

This is clearly shown in Figure 5:

Figure 5Lorentz Force that Propels the MHD Boat

(Font and Dudley, 2004, pg. 410)

Channel Width Optimization

14

In order to determine the dependence of the current

on the channel dimensions, it is necessary to examine the

transmission characteristics (i.e. resistances) of an

electrical conductor. The current flowing from the top

electrode to the bottom electrode of the channel can be

expressed in terms of the current density:

where J is the current density (A/m2) and A is the cross-

sectional area ( W) and θ is 0° (so cos θ is equal to 1).

The current density can be written in terms of the electric

field E and the conductivity σ, or resistivity ρ of the

water:

Pure water has a resistivity ρ value of 2. 6 × 105

Ωm, while sea (salt) water has a resistivity of about 0.22

Ωm. It is immediately clear that very little current can be

transmitted through pure water. The electric field E can be

15

approximated by the potential difference across the

electrodes divided by the distance between the electrodes:

Therefore, the current in the channel is given by:

Inserting Eq. (7) to Eq. (3), and assuming that the

current and the magnetic field are perpendicular to each

other, gives the force produced,

where θ is 90° so sin θ is 1. Note that the quantity L in

Eq. (3) is the current path and is equivalent to the height

(H) in this geometry because the current path is vertical.

Therefore, to the first order, the force produced does not

depend on the channel height (H) but increases with longer

16

channels ( ) and wider channels (W). This conclusion is

only valid where the magnetic field is constant along entire

the channel. Any part of the channel that is outside of the

influence of the magnets will not add to the force. In order

to optimize the force, the exact behavior of the magnetic

field strength (B) as a function of magnet separation (W)

must be determined. The optimum width is specific to the

magnets chosen. (Font and Dudley, 2004, pp. 410)

Solubility of Sodium Chloride Salt

Solubility is a characteristic physical property

referring to the ability of a given substance, the solute,

to dissolve in a solvent. It is measured in terms of the

maximum amount of solute dissolved in a solvent at

equilibrium. The solubility of salt in water at 25 ºC is 35

grams NaCl in every 100 grams of water. This value will be

used for this study. The solubility of NaCl is somehow

affected by temperature, as shown in the graph below, but

the effect is insignificant to the study and will not be

17

accounted for because the temperature of the water used in

the experiment remains fairly constant. (Wikipedia, the Free

Encyclopedia)

Figure 6 Effect of Temperature on Solubility of NaCl

18

Chapter 2

PROBLEM AND ITS BACKGROUND

19

Statement of the Problem

This investigatory project aims to establish the

relationship between the speed of an MHD propulsion boat and

salt concentration and to construct a prototype conductivity

meter that can be used to determine the conductivity of a

solution.

Specifically, the study aims to:

1. determine the magnetic strength of the magnets used

in the experiment as a function of separation;

2. determine the optimum dimensions of the MHD boat,

given the set of magnets to be used, that would make

it the most efficient;

3. measure the speed of an MHD boat at the following

salt concentrations:

a. 10% of NaCl saturation concentration

b. 30% of NaCl saturation concentration

c. 50% of NaCl saturation concentration

d. 70% of NaCl saturation concentration

20

e. 90% of NaCl saturation concentration;

4. establish the operational equation for the speed of

the boat as a function of salt concentration; and

5. design a prototype conductivity meter design that

can be used to determine the concentration of an

unknown solution within a certain degree of error.

21

Significance of the Study

As was mentioned in the The Physics Teacher article,

the construction of a magnetohydrodynamic boat would be a

good way to motivate the students. Perhaps one of the

reasons why majority of the students have difficulty in

understanding the concepts in electromagnetism is that the

lessons are quite abstract. Showing an operating system that

embodies these concepts would surely make the students

appreciate the study of Physics more. An inexpensive MHD

propulsion boat could be easily constructed as detailed in

this paper. It would be a good demonstration for concepts on

electromagnetic forces on a current and even basic mechanics

such as Newton’s third law. And since this study concerns

itself with the relationship between the speed of the boat

and the salt concentration of the water on which it operates

on, it could also be used as a supplementary demonstration

for lessons in related topics on electrochemistry,

specifically on ionic disassociation kinematics and water

salinity and conductivity.

22

One of the important measuring equipments used in

Chemistry is the conductivity meter, used to measure the

conductivity (or the resistivity) of solutions. It is

commonly used in hydroponics, aquaculture and freshwater

systems to monitor the amount of nutrients, salts or

impurities in the water. This equipment is unavailable to

most schools, since it is commercialized and rather

expensive. It is possible to construct an inexpensive meter

using a simple circuit. This study aims to design a

prototype conductivity meter using the concepts of MHD laws

and processes. The data collected during the experimentation

for the speed function of the MHD boat will be used to

calibrate the MHD system to serve as a conductivity meter.

This study will hopefully serve as a rich resource

for future researchers like us who develop an interest in

pursuing further studies parallel or more intensive than

what we will accomplish. This study may hopefully trigger

23

more interest on contemporary research fields such as

magnetohydrodynamics.

Hypotheses

There is a direct relationship between the speed of

an MHD propulsion boat and the salt concentration of the

water on which it operates on. The boat would attain higher

speeds in higher concentrations than in lower

concentrations. The maximum speed could be attained at

concentrations just short of saturation. The speed of the

boat could be given as a function of salt concentration. The

data collected during the experimentation for the speed

function of the MHD boat could be used to calibrate the MHD

system to serve as a conductivity meter.

Assumptions

There are a few assumptions that were adopted in the

course of this investigatory project. The temperature of the

24

water used in the experiment is assumed to be constant. The

effect of impurities in the salt dissolved in the water is

assumed to be nonexistent. Room conditions would remain

constant and is uniform in the performance of the trials.

Scope and Limitations of the Study

The dimensions of the constructed MHD boat

(specifically the channel width) for this research are

optimum only for the magnetic field strength of the magnets

used. Any other replication of this experiment using a

different pair of magnets should conduct boat dimension

optimization. The magnetic field strength of the magnets

used in this study does not exceed 0.5 tesla because of the

unavailability of stronger magnets. The voltage used to

power the MHD boat does not exceed 90 Volts (from ten 9-volt

batteries) because placing more batteries may weigh the boat

down and significantly decrease the boat speed. The effect

of the formation of bubbles of hydrogen and oxygen being

liberated through electrolysis as the current passes through

25

the water is beyond the scope of this study and is

unaccounted for. The effect of the corrosion of the metal

electrodes due to the highly reactive chlorine ions in the

salt solution is beyond the scope of this study and is

unaccounted for. The research only deals with the effect of

salt concentration. Effects of other factors such as water

temperature, passage turbulence and others are beyond the

scope of this study and are not included in this study.

Definition of Terms

Boat. This refers to the constructed MHD boat used in the

experiments.

Salt. This refers to the sodium chloride (NaCl) used to

change the salt concentration of

the water on which the boat operates.

MHD. MagnetoHydroDynamic propulsion is a means of propelling

a ship without

moving parts like paddlewheels or propellers. Instead,

MHD relies on passing

26

electrical currents through the water, effectively

turning the water itself into part

of an electric motor, where the only thing that moves

is the water.

Laser System. This refers to the pair of a laser source and

a detector that would be used to

activate the time program used in this study.

Magnets. Permanent magnets, whose magnet poles are located

on the sides, are situated

along the channel to provide the external magnetic

field.

Electrodes. Brass scraps that are situated in the top and

bottom of the water channel,

connected to the battery, to provide voltage across the

water current.

Batteries. These are used as the voltage source for the MHD

boat.

27

Chapter 3

RESEARCH METHODOLOGY

28

Magnet Holder Construction

1. Two (2) pieces of Styrofoam® with a length of 17.00 cm

and a width of 2.8 cm were cut. These served as the

holders for the magnet as well as the sides of the

channel.

2. The shape of the magnets was carved on one side of the

Styrofoam®. It was carved in a way that the magnets

were snugly fit.

3. The depth of the carving was as deep as the thickness

of the magnets. This way, when the magnets were put in

place, it doesn’t protrude out of the hole.

4. Two (2) rulers were cut into pieces with a length of

17.00 cm and a width of 2.8 cm.

29

5. The magnets were then placed in their Styrofoam®

holder, with the north pole facing outward on one, and

the south pole facing outward on the other.

6. The ruler was placed over the magnets to secure them in

place. It was secured to the Styrofoam® holder by means

of masking tape wound around them.


1. A teslameter was used to take measurements of the

magnetic field strength between the magnets positioned

side by side.

30

Figure 7 Measuring the Magnetic Field Between Two Magnets

2. The magnets, already secured inside their holders, were

separated using rulers whose individual widths were 1

mm.

3. The first separation distance (W) was 7 mm, and taking

the width of the rulers on the holders, this was

achieved by inserting five rulers between them. The

measurements were done at distance of 2 mm, 4 mm and 6

mm from the north pole of one of the magnets. This was

done by removing the first, third and fifth separator

ruler, respectively, and placing the axial probe of the

teslameter in its place.

31

4. The second separation distance (W) was 11 mm, and

taking the width of the rulers on the holders, this was

achieved by inserting nine rulers between them. The

measurements were done at distance of 2 mm, 4 mm, 6 mm,

8 mm and 10 mm from the north pole of one of the

magnets. This was done by removing the first, third,

fifth, seventh and ninth separator ruler, respectively,

and placing the axial probe of the teslameter in its

place.

5. The third separation distance (W) was 15 mm, and


achieved by inserting 13 rulers between them. The


8 mm, 10 mm, 12 mm and 14 mm from the north pole of one

of the magnets. This was done by removing the first,

third, fifth, seventh, ninth, 11th and 13th separator

ruler, respectively, and placing the axial probe of the

teslameter in its place.

32

6. The fourth separation distance (W) was 19 mm, and


achieved by inserting 17 rulers between them. The


8 mm, 10 mm, 12 mm, 14 mm, 16 mm and 18 mm from the

north pole of one of the magnets. This was done by

removing the first, third, fifth, seventh, ninth, 11th,

13th, 15th and 17th separator ruler, respectively, and

placing the axial probe of the teslameter in its place.

7. The data gathered from the measurements were summarized

into Table 1.

8. Using Microsoft Excel 2003, the magnetic field strength

values were graphically displayed as the magnet

separation is increased.

9. The average magnetic field as a function of the

distance between the magnets was determined by curve-

fitting and integrating the results.

33

10. The magnetic fields were given in teslas and the

separation in meters in order to allow substitution for

the magnetic field strength (B) directly into equation

8 (see Theoretical Background for the derivation):

11. The curvefit for the results of no. 8 were

inserted to the above equation in order to yield an

empirical force function of F that is proportional to a

function of W.

12. The resultant function F versus magnet separation

W was graphed. The value of the Vbattery used is equal to

the resultant voltage output of the nine 9-volt

batteries in series used as the voltage source for the

boat (around 70 volts). Actual Vbattery was measured

using a voltmeter. The resistivity used was the same as

the resistivity of sea (salt) water of 0.22 m. The

value of was the water channel length (17.00 cm).

34

13. From the graph, the optimum separation width

between the magnets was determined.

Construction of the MHD Boat

1. The size of the boat is chosen such that it was large

enough to float the battery stack, composed of nine 9-

volt batteries connected in series. The hull of the

boat was made up of Styrofoam®.

2. The water channel length ( ) was as long as the boat,

approximately equal to the length of the magnets magnet

holders (17.00 cm).

3. The channel height (H) was chosen to match the height

of available magnets plus the thickness of the

electrodes (2.80 cm).

4. The channel width (w) was given by the process of

optimization, as derived in the previous section of

35

this methodology (found to be 1.97 cm, as shown in the

next chapter.

Figure 8 Water Channel Dimensions

5. The water channel was constructed using the dimensions

specified in nos. 2 to 4. Brass strips 17.00 cm long

and 1.76 cm wide were used as electrodes, and were

placed at the top and bottom of the channel. The

electrodes were secured using pieces of rulers.

36

6. Three (3) pieces of Styrofoam® (17.00 cm by 17.00 cm)

was cut and was held together on top of each other by

means of the double-sided tape. This would serve as the

hull of the boat.

7. A gap 17.00 cm long, 5.96 cm wide and 2.80 cm deep was

carved on the underside of the stacked Styrofoam®.

8. The channel was then inserted and secured inside the

gap.

9. The batteries were connected in series and laid on the

hull.

10. Heavy-gauge connecting cables were used to connect

the top electrode to the positive terminal of the

battery stack and the bottom electrode to the negative

terminal.

37

11. A “flag” was placed near the front of the boat. In

this case, a marker pen was used as the flag. Its width

was measured using a Vernier caliper and was then

recorded.

Research Set-up

1. A glass aquarium (with the dimensions 60 cm by 120 cm)

was used for this experiment.

2. The aquarium was filled with 14 liters of distilled

water, sufficient to float the boat. The waster was

measured using a volumetric flask.

3. Using a compass, the direction of the magnetic north

pole was determined. The aquarium was positioned

perpendicular to this direction. This was to align the

magnetic polarity of the boat with the magnetic field

of the earth.

38

4. A laser source was positioned on one side of the

aquarium. A laser sensor/detector was positioned on the

other side. The laser source and sensor were situated

well above the surface of the water, but not over the

height of the boat’s flag.

5. The light sensor was connected to the Phywe digital

counter. The counter was set to the timer function and

at the last trigger. This was so that the timer will

start when the laser is intercepted, and stops when the

laser signal is resumed.

39

Figure 9 Research Set-up

6. Approximately 1.5 kilogram of laboratory-grade sodium

chloride was dissolved in the water. The exact mass was

measured using a weighing scale. It was stirred

thoroughly to ensure that it was completely dissolved.

7. The MHD boat was placed on one end of the aquarium. The

batteries were not yet connected at this point (this is

done by unclipping the connecting cable from the

positive terminal). The boat was allowed to rotate

until it was stable to make sure that it was aligned

with the earth’s magnetic field. It was made sure that

the aquarium was placed on a leveled surface.

8. Once the boat had stabilized, the circuit was closed

allowing the current to flow. The boat is placed with

40

its flag approximately 5cm from the laser beam to allow

it to reach its terminal velocity.

9. After the timer was triggered and stopped, the time

displayed on the digital counter was recorded.

10. Procedures 7 to 9 are repeated twice to get a

total of three trials.

11. The salt solution was then thrown away. The

aquarium was cleaned thoroughly, and 14 liters of

distilled water was added. Approximately two (2)

kilograms of laboratory-grade sodium chloride was

dissolved in the water. The exact mass was measured

using a weighing scale. It was stirred thoroughly to

ensure that it was completely dissolve.



distilled water was added. Approximately 2.5 kilograms

41

of laboratory-grade sodium chloride was dissolved in

the water. The exact mass was measured using a weighing

scale. It was stirred thoroughly to ensure that it was

completely dissolve.



distilled water was added. Approximately three (3)

kilograms of laboratory-grade sodium chloride was

dissolved in the water. The exact mass was measured

using a weighing scale. It was stirred thoroughly to

ensure that it was completely dissolve.



distilled water was added. Approximately 3.5 kilograms

of laboratory-grade sodium chloride was dissolved in

the water. The exact mass was measured using a weighing

scale. It was stirred thoroughly to ensure that it was

completely dissolve.

42

15. The speed of the boat is calculated by dividing

the distance d by the time it took for the boat to

travel across. The average speed of the boat at every

concentration is calculated.

16. All data gathered was summarized in Table 2.

43

Chapter 4

PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA

44

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.005 0.01 0.015 0.02y (m )

B (te

sla) W = 7 mm

W = 11 mmW = 15 mmW = 19 mm


Shown below is the data gathered from the

measurements of the magnetic field strength between the

magnets used in the boat channel. The averages of the field

strengths for every magnet separation (W) are also shown.

Table 1Magnetic Field Strength Between Magnets (T)

MagnetSeparation (W)(mm)

Distance from the North Pole of One Magnet (y) (mm)

2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 Average

7.00 0.1016

0.0941

0.0907 0.095

511.00 0.094

40.0828

0.0713

0.0701

0.0737 0.078

515.00 0.086

90.0680

0.0594

0.0555

0.0536

0.0548

0.0590 0.062

519.00 0.083

30.0612

0.0535

0.0469

0.0452

0.0435

0.0435

0.0461

0.0533

0.0529

The magnetic field strengths (B) are graphed against

the distance from the north pole of one magnet (y) for every

separation (W).

45

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.005 0.01 0.015 0.02W (m )

Averag

e (T)

Figure 10 Magnetic Field Strength between Magnets

As shown in the graph, the magnetic field strength

decreases as the distance from the north pole increases, and

increases back again as it becomes closer to the south pole

of the other magnet. This is due to the square inverted

relationship between magnetic field strength and distance.

The average magnetic field is then graphed against

the magnet separation (W).

46

Figure 11 Average Magnetic Field Strength as a Function of

Magnet Separation

Using Microsoft Excel, the equation of the trend line

of the above graph is found to be:

47

00.0050.010.0150.020.0250.030.0350.040.045

0 0.005 0.01 0.015 0.02 0.025W idth separation (W )

Norm

alized Force

The average magnetic field decreases almost inversely

proportional to distance. Inserting this equation of the

trend line to Eq. 8 (derived in the Theoretical Background)

yields an empirical force function that is proportional to a

cubic function of W:

The function F versus magnet separation W is graphed

below. The value used for Vbattery is 70 volts, value of was

17.00 cm and the value of ρ is that of seawater which is

0.22 Ωm.

48

Figure 12 Normalized Force as a Function of Magnet

Separation

The results show that an optimum does indeed exist.

As the magnet separation increases from zero, the force also

increases. It must increase because the conducting area is

increasing (see Eq. 4). The result is that maximum is

reached between 19 and 20 mm, after which the force

decreases due to the diminishing magnetic field.

The exact value of this maximum point can be

determined by applying the first derivative to the above

graph’s trend line. The equation of the curve fit is:

49

The MHD boat water channel width (W) in the present

study was therefore chosen to be 20 mm. These results are

specific to the magnets chosen, but a similar optimum should

exist for any pair of magnets.

50

Data Presentation and Analysis

Shown below is the data gathered from the research

set-up.

Table 2 Time of Travel of MHD Boat at Different Concentrations

Mass ofNaCl(kg)

Volumeof

Water(L)

CalculatedConcentration (kg/L)

Time of Travel (s) Distance

Travelled(cm)

Calculated Speed(cm/s)

1stTrial

2ndtrial

3rdtrial

Average

1.5001 14 0.1071526.35

25.74

25.96 26.02 1.53 0.0588

1.99949 14 0.1428217.56

17.11

18.12 17.60 1.53 0.0869

2.4987 14 0.1784813.38

14.52

13.54 13.81 1.53 0.1108

3.0059 14 0.2147111.24

11.84

11.69 11.59 1.53 0.1320

3.6165 14 0.2583212.83

13.25

13.66 13.25 1.53 0.1155

The mass of the NaCl dissolved for every solution was

measured by a weighing scale. The volume was measured

accurately using a volumetric flask. The concentration was

determined by dividing the mass of dissolved salt in

kilograms by the volume of water in liters. The data for the

three trials for the time of travel were taken from the

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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.05 0.1 0.15 0.2 0.25 0.3Concentration (kg/L)

Speed (cm/s)

digital counter. The average of the three data for each set

is also determined. The distance traveled during the time

interval measured is equal to the diameter of the “flag” as

measured by a Vernier caliper. The speed is calculated by

dividing the distance traveled in centimeters by the time of

travel in seconds.

The relationship between the speed of the MHD boat

and the concentration of the salt solution on which it runs

on can be easily seen if we look at it graphically, as is

shown below:

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Figure 13 Speed of MHD boat as a Function of Salt

Concentration

As is clearly shown by the trend line (red), there is

a parabolic relationship between the speed of the MHD boat

and salt concentration. As the concentration increases from

zero, the maximum speed the boat could attain rapidly

increases. However, when the concentration reaches a certain

point, the increase in speed stops. If the concentration is

increased further, the maximum speed attainable by the boat

decreases.

The concentration which is the maximum point of the

graph can be determined by applying the first derivative to

the above graph’s trend line. The equation of the trend line

(with a coefficient of variation r2 of 0.9655) is found to

be:

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where S is the speed of the boat in cm/s while C in the salt

concentration in kg/L. Getting the first derivative and

equating it to zero, we have:

The boat is able to attain its maximum speed at a

salt concentration of 0.22395 kg/L. This concentration is

the same as dissolving 3.1353 kilograms of salt in 14 liters

of water. For a point of reference, it requires 4.90

kilograms to completely saturate 14 liters of distilled

water.

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Chapter 5

FINDINGS, CONCLUSIONS AND RECCOMENDATIONS

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FINDINGS

1. The optimum channel width for the magnets used for

this experiment was determined to be 0.19756 meters,

or 1.9756 centimeters.

2. This is wider than the channel width of the MHD boat

in the Physics Teacher article because the magnet

that they had has a stronger magnetic field than

what we used. Since the force produced is

proportional to the current flowing between the

electrodes, and that from Eq. 4 (shown in the

Theoretical Background) we can see that the current

is proportional to the cross-sectional area ( W), a

smaller magnetic field would need a wider separation

for optimum force. As was noted, As the magnet

separation increases from zero, the force also

increases. It must increase because the conducting

area is increasing. The average magnetic field is

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decreasing, but not as fast as the conducting area

is increasing.

3. There is a parabolic relationship between the speed

of the MHD boat and salt concentration. As the

concentration increases from zero, the maximum speed

the boat could attain rapidly increases. However,

when the concentration reaches of 0.22395 kg/L, the

increase in speed stops. If the concentration is

increased further, the maximum speed attainable by

the boat decreases.

4. The relationship between the speed and concentration

could be expressed in the equation S = -5.0246C2 +

2.2505 – 0.1275, where S is the speed of the boat in

cm/s while C in the salt concentration in kg/L.

5. This parabolic relationship could possibly be

explained by the following (it could just be one or

an interplay of the three):

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a. At higher concentrations (beyond the optimum of

0.22395 kg/L), the corrosion of the brass

electrodes with the reactive chloride ions

becomes very rigorous because of increased

electric current. This may cause material from

one brass strip to be electroplated into the

other, decreasing current in the process.

b. There is also a noticeable discoloration of the

solution when the boat operates on solutions of

higher temperature. The introduction of new

solutes (quite certainly from the brass

corrosion) may affect the amount of current,

and thus the speed of the boat.

c. At higher concentrations, a lot more bubbles

are formed by the electrolysis of water into

oxygen and hydrogen gas. The rapid evolution of

gas can cause water turbulence inside the

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channel, hindering the propulsion of the water,

and thus effectively decreasing the speed of

the boat.

d. There is no direct correlation between

conductivity and salt concentration. It doesn’t

follow that if you increase the concentration,

the conductivity of the solution also

increases. We found no literature that shows

correlation between them at concentrations

higher than that of sea water.

CONCLUSION

Constructing an MHD propulsion boat for classroom

demonstration is not as easy and inexpensive as the article

from The Physics Teacher claims it to be. The hardest part

is finding a strong enough magnet, and that magnet should

have the correct orientation for it to work.

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The channel width optimization is a tedious process.

From it, we had learned that although the magnetic field

decreases if the separation between the magnets increase, it

doesn’t follow that a weaker magnet would require you to

have narrower channel. Rather, it is quite the reverse, in

that you’d need a wider channel to increase the conducting

area.

There is also the nature of the MHD boat to align the

polarity of its magnets to the polarity of the Earth’s

magnetic field. For MHD to be a viable alternative means of

propulsion of sea-going vessels, something must be done to

circumvent this tendency to go off course. Also, new

material must be used as the electrodes, since the brass

ones would be corroded by chloride ions. Further, very

strong magnetic fields and electric source are required,

since the concentration of sea water is well blow the

optimum concentration for a MHD propulsion vessel to attain

its maximum velocity.

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Lastly, the boat constructed could not be used to

design a device to determine the concentration of an unknown

solution. This is due to the parabolic relationship between

boat speed and concentration. The device would not be able

to distinguish an increase or decrease of concentration from

0.22395 kg/L.

RECOMMENDATIONS

For further study, the researchers recommend the

following:

Find stronger magnets of the correct orientation,

preferably in bar shape so that there’d be more uniform

magnetic field across the channel, giving you more

accurate results.

For those who want to try something more sophisticated,

you could increase the number of water channels and see

if the speed of the boat would be greater.

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Use another material for the construction of the boat

hull. The Stryrofoam® that we used in this experiment

is advantageous in that it allows the boat to stay

afloat. However, it is highly unstable. You could use

polystyrene plastic or any other material.

You could increase the voltage source of the boat by

adding more batteries to the power source stack.

Instead of using brass as the electrodes, you could

also use other metals that are more resistant to

corrosion.

If you opt to use a power supply as your source, you

can have the MHD device in conjunction with a flow-

meter to have more accurate results.

If you could find a conductivity meter capable of

measuring conductivities of salt solutions with high

concentrations, you could attempt to establish the

relationship between the conductivity and boat speed.

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Speed of a Magnetohydrodynamic Propulsion Boat as a Function of Salt Concentration

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