The document discusses estimating evaporation loss from onboard tankers using Bernoulli's theorem. It provides background on Srinivasa Ramanujan, the gifted mathematician. It then outlines the problem of estimating fluid volume lost from a vessel when a relief valve opens for a set time. Inputs like pressure, pipe diameter, and time are given. Bernoulli's theorem is applied to calculate flow velocity and discharge, allowing the lost volume to be determined as 435 liters in this example. Limitations in assuming steady flow are noted. The document acknowledges technical inputs and support received.

1. ESTIMATION OF EVAPOURATION
LOSS ON BOARD TANKERS
Application of Bernoulli’s theorem
from Fluid Mechanics

2. ESTIMATION OF EVAPOURATION
LOSS ON BOARD TANKERS
“ AN EQUATION FOR ME HAS NO
MEANING, UNLESS IT
REPRESENTS A THOUGHT OF
GOD”
--GIFTED MATHEMATICIAN OF THIS COUNTRY
MR. SRINIVASA RAMANUJAN (1887-1920)--

3. Few Facts on Srinivasa Ramanujan
• He had no formal qualification prior to going
to UK for higher studies. He passed only F.A
(equivalent to Intermediate or PUC)
• At the age of 12, he mastered Advanced
Trignometry by S.L. Loney
• Poverty stricken Ramanujan, could not afford
to purchase paper but used to work out
problems in slate and write end-results in his
note book.

4. Facts on Srinivasa Ramanujan
• He got employed in a marine related industry.
Yes Madras Port Trust as a Clerk.
• He went to Trinity College, UK for higher
studies in Maths.
• He was the second Indian to have been
elected as Fellow of Royal Society and first
Indian to have been elected as Fellow of
Trinity College, Cambridge.
• Prof. G.H. Hardy- Ramanujan’s Guide, when
asked about his contribution to Mathematics

5. Few Facts on Srinivasa Ramanujan
• Used to say ”Introducing Ramanujan to
western world was his greatest contribution”
• That talks about the fame of this
mathematician.
• His birth day 22 December is declared by
Indian Govt. as National Mathematic Day.
• With these words on that gifted
mathematician and with a thought of God let
me commence my presentation.

6. INTRODUCTION
• THE SPEAKER STARTED OFF HIS CAREER WITH SURVEYING OF
BULK PETROLEUM CRUDE OIL TANKERS.
• AFTER COMPLETION OF SURVEY AND SHORE OUT TURN AND
REASONS FOR PROVIDING MISMATCH BETWEEN SHIP’S QTY
AND SHORE QTY USED TO BE MIND BOGGLING.
• REASONS FOR SHORTAGE NORMALLY ATTRIBUTED IN
GENERAL TO NORAML HANDLING LOSSES LIKE LEAKAGE,
EVAPOURATION, ROB ETC.
• HERE IS AN ATTEMPT TO QUANTIFY EVAPOURATION LOSS, AS
NOW ADAYS TANKERS ARE PROVIDED WITH LOT OF
AUTOMATION/INSTRUMENTATION TO RECORD NECESSARY
DATA.

7. Evaporation loss

8. Problem under study
• Let us assume a vessel containing a certain
fluid at some pressure.
• The vessel contains an automated valve which
opens itself to let out fluid to avoid excess
pressure to build up in the vessel.
• Lets say the valve opens for a certain time
intervals to release pressure.
• The aim of the problem is to estimate the
volume of fluid that came out of the vessel

9. Formulation of Problem
Inputs for the problem:
- Initial Pressure in the vessel
- Cross-sectional area of pipe
- Time duration for which valve is opened
All other material properties and physical
constants are assumed appropriately.

10. Methodology
• With these available inputs, the problem is
solved with the application of Bernoulli’s
theorem.
• Many of you are Engineers and familiar with
Fluid Dynamics and Bernoulli’s theorem. Still
let me give a brief note about the same.

11. Theory
All fluids possess energy (a.k.a. head) in three
forms :-
– Pressure Energy
– Flow Energy
– Gravitational Energy
And the total energy of a fluid is sum of all these
three energy forms.

12. Theory
• According to Bernoulli’s theorem, for a steady,
incompressible fluid flow, the total fluid
energy is constant throughout the flow.
• In other words, the sum of all forms of fluid
energy at one point of flow is equals sum of all
energy forms at another point of fluid flow.

13. Theory

14. Theory
Mathematically, this is written as shown below,
p1/ρ + v1
2/2g + z1= p2/ρ + v2
2/2g + z2
where
p1,p2 = fluid pressure at point 1 & 2
v1,v2 = flow velocity at point 1 & 2
z1,z2 = height/level of fluid at point 1 & 2
ρ is fluid density & g is acceleration due to gravity

15. Theory
• Discharge is defined as the volume of fluid
flow per unit time which is therefore the ratio
of volume to time.
• Mathematically,
• Discharge, Q = V/t ; V-Volume; t-Time
= A x l/t ; V=Area (A) x length (l)
= A x v ; v-flow velocity

16. Applying the theory in current
problem
The above theories may be applied in the
problem under study but subject to following
assumptions.
• The flow is steady i.e. the flow parameters are
constant with time.
• The fluid is incompressible i.e. the fluid has
constant density at a given temperature.
• The temperature of flowing fluid remains
constant.

17. Case study
There is a vessel containing a gas at a pressure of
2bar. The relief valve which is fit on a pipe of
30mm diameter opens for 40seconds. What
volume of gas has escaped? Assume the pipe to
be horizontal or vertical and flow to be steady &
incompressible.
Inputs: p1 = 2bar = 202650 Pa ;
p2 = patm = 1bar = 101325 Pa ; v1 = 0 ; z1 = z2
ρ = 500 kg/m3 ; g = 9.8 m/s2 ; t = 40 s

18. Case study
Applying Bernoulli’s theorem,
p1/ρ + v1
2/2g + z1 = p2/ρ + v2
2/2g + z2
Substituting it in the above theorem and
solving it, we get v2 = 61.58 m/s
Now using the relation, Q = Av (A=πd2/4)
Q = 0.0435 m3/s = Volume / time
But time of flow, t = 10s
Volume, V = Qt = 0.435 m3 = 435 litres

19. Inference
• The above methodology does not describe the
actual volume of gas flowing out because it
assumes steady flow.
• Due to this assumption, the final gas volume
will be increased than the actual.
• However, this can account for the maximum
amount of vapor that has flown out.

20. Limitation
• As Crude oil tankers now a days are fitted with
Crude Oil Washing system using flu gas as
inert gas, it is very difficult to isolate and
estimate how much hydrocarbon contents
lost.

21. Insurer’s point of view.
• As evaporation loss is inherent vice or nature
of any Petroleum product, quantity so
estimated may be excluded as per ICC-A
General Exclusion Clause.
• But in Indian scenario, since Petroleum Crude
and products are invariably insured for TLO
(Total Loss Only), this is only an academic
interest.

22. ACKNOWLEDGEMENT
• SPEAKER COVEYS THANKS TO MR.
T.S.SADAGOAPAN – A RESEARCH SCHOLAR
UNDERGOING M.S IN MECHANICAL
ENGINNERING IN IIT (MADRAS) FOR
TECHNICAL INPUTS.
• SPEAKER ALSO CONVEYS THANKS TO CAPT.
S.P. ANAND AND MR. P.SRIDHARAN OF
HENDERSON INTERNATIONAL FOR THEIR
ENCOURAGEMENT & SUPPORT.