Concept of Discharge Fluid Mechanics (GATE Previous Year Question), Mechanical Engineering, GATE Video Lecture

so this is no joke Marcin and the
today's topic is concept of discharge
you are indeed they have asked quotient
related to this topic and you know I
almost everybody knows what is discharge
basically okay suppose that this is a
five a three wood is flowing through
this pipe right and the velocity
velocity per will cross sectional area
is known as discharged it is we also
know by art we need note the it is by Q
their force it will see unit velocity
unit is meter per second unit of area is
meter square so it evens become meter
cube per second now there is a simple
concept that is a concept of PI if you
have a standard flow through pipes in
fluid mechanics then definitely you know
about this concept right that each v 1 v
2 and Phi 3 that there could be any
number of pipes right so if we if will
find out in this simple concept right so
P 1 plus Q 2 is equal to Q 3 I will
discharge from pipe 1 discharged from
pipe 2 is equal to discharge from height
3 if you you know neglected fix a loss
if you consider friction loss hence we
cannot apply because we don't know how
much energy will be I mean how much head
loss will be taking place here and here
and here so we have to neglect that to
to valid this equation Q 1 plus Q 2 is
equal to Q 3 actually based on this
concept concept of discharge there is a
question they have as indeed previous
here and because of that I am creating
this video dot 1 okay so this this is
all about discharge and its unit and its
formula also therefore we know that Q is
lack you will called oh do you want a
one okay if we say q1 is equal to B 1 a
1 Q 2 is equal to Z 2 a 2 and Q 3 is
equal to e 3 E 3 ok this is a simple
formula Q is equal to V a sy there are
many you know maybe you have seen this
a1 v1 is equal to a2 v2 in continuous
continuation if the fluid is
incompressible okay if it is
compressible than Rho 1 a1 v1 is equal
to Rho 2 a 2 V 2 so this this formula so
gravel you have gone through if you are
activating for gate like it summation
right now let's go for us that
chimerical problem with numerical
problem asking get PDF am that's why you
can understand much better I'll come
back to this topic that how to prepare
this topic flow through pipes because
most one time they have as quotient in
gate previous here I have seen and the
it's really simple to solve question
related to this topic okay all talk on
this topic
yes because yeah I have to first airsoft
share with you how to solve the
questions so let's go for it
so in unis question if you can see the
whole whole screen right now with the
question only yeah it will read this
question and probably it will take 2 to
3 minutes ok so let's take the question
first and I will share with you how to
solve it
ok and I have already share with you
formulas we are going to use in this
numerical problem to solve this okay
let's go for it consider steady flow of
water in a situation where two pipelines
v 1 v 2 combined combined into a single
pipeline it is okay but line 3 as shown
below this is below and cross sectional
area of the pipelines are constant okay
flowing data is given so data however
written because of space I do not have
but yeah its area is 1 and coefficient
of discharge is 1 okay
Emel are so yes area is 1 meter
square and this velocity is 1 meter per
second 4x2 it's area is 2 meter square
and velocity be Q meter per second and 4
pi 3 we have given area is 2 point 5
meter square okay
this way not they have given in this
question now what they said is you
assuming water before different
velocities to be me from cross-section
are in from across other section of the
inlet and outlet so exit velocity in 5
degrees that means we have to find out
velocity head
what is the velocity for the fluid
following through heat and then we talk
this again so this is a simple formula
we can implement but and you have gone
through it sir required lot of you know
lot of presence to lead such a lambic
ocean so after seeing this diagram we
can say that what we have to find out ok
I mean the data given in the question
that was that is must to understand
right
so from big guy down what exactly a
harsh a we do the same diagram they have
given in the numerical problem so we
have to use this formula here right so
what is the formula basically Q 1 plus Q
2 is equal to Q 3 okay but miss this
star that pipe 1 discharge at 5 one
disturbs at pi/2 and discharge at PI 3
okay again we know that P 1 is equal to
a 1 e 1 plus Q 2 is equal to a 2 V 2 Q 3
is equal to a 3 DT I have already shared
with you is formula okay now we know a 1
is 1 V 1 V 1 is 1 okay again we know a 2
is equal to 2 and B 2 is equal to 2
again we know a 3 is 225 but we have to
find out weekly at is V 3 we have to
find out right now thing is that most of
the time where exactly we are going to
make me
that is a mistake of you need will not
look at unit so before going to solve
the numerical problem we have to look at
the unit what unique they have given in
the numerical problem then we must go
for solving it right so what are you is
basically given in this question you can
see meter meter per second meter meter
per second meter because the three
things are I mean did this two two four
five things I am using in the situation
so I have to look at these five things
only okay this units are in a single
unit system or not then I will go for
solving the question so this is how a
box is about you know about day if you
are preparing for yet you must
understand all image system if you not
understand all unit system and the unit
you have to be getting Bonnie with
system all unit I think then only we can
get right answer otherwise after knowing
even everything you will make mistake so
don't try to repeat that mistake best
way in my almost all videos I talk about
it and don't make mistake in me need
because you need clear most important
roles that is the thing so here one
multiple one to multiple to four is
equal to two point five multiple V 3
even we don't require calculator okay so
one plus 45 is equal to two point five
15 therefore V 3 is equal to 5 by 2
point 5 is equal to 2 because all units
are in air file and therefore velocity
unit of velocity in SI is meters per
second
okay so on service tube with a per
second now look at the options we have
given in this question so the answer we
caught is matching with optional P okay
so without in doubt it can work the
right answer of this quotient and could
you believe this quotient asking gate p
vs here and the question was up to the
question asked in 2009
and the question was of two bucks okay
as I am sharing with you this quotient
telling you each and everything about
the question the formulas we have used
and of course I am talking about how you
will not make mistake even then I am
taking only a two coming
unfortunately seven two six seven eight
minutes to solve this quotient but value
sitting in the examination you know all
these formulas them I don't think so it
will take more than two minutes or ten
years I mean I will take am only right
to top this part so you don't need to
write in detail in the competition
examination right because you may just
need to find out the right answer so but
one more thing if you are know if your
Boehner or you are not familiar with
formulas then try to write in detail
that's why you will not make mistake
otherwise I have seen most of the times
and when I have seen my students make
mistake because of inherit they are in
earnest and so on so let's go for this
video again it's all things so what we
have instead here it's concept of
discharge all right so in this case what
we have to understand that the discharge
inlet is equal to outlet that is Q 1
plus Q 2 is equal to Q 3 this is the
most important concept to understand in
this or in this case okay now the
formula simple formula for discharge and
the extreme in its system what we also
need to understand okay now most
important we need to also understand
continually patient that is a1 v1 is all
- a - will - but that is valid only for
I am incompressible field ok so this is
all about constructive discharge I hope
you understand a new concept and solve
even solve this type of problem in the
upcoming complete computing examination
thanks for watching see you soon in my
next video ba ba