Having dificulty understanding the meaning of continuity equation

umesh k. · November 6, 2015, 01:40

I am not getting the meaning of continuity equation, mainly the gradient term that is there when flow leaves the control volume, please explain with the example..

kaya · November 6, 2015, 12:11

I can explain it to you but to not to confuse you more, I prefer understanding what exactly confuses you 'in a more clear way' before I give some analogies

umesh k. · November 10, 2015, 08:27

OK,
(Flow rate in=flow rate out+ rate of change of flowrate )#through control volume.
So,what that rate of change of flow rate term is doing at the outlet?

FMDenaro · November 10, 2015, 09:20

Quote:

Originally Posted by umesh k.

OK,
(Flow rate in=flow rate out+ rate of change of flowrate )#through control volume.
So,what that rate of change of flow rate term is doing at the outlet?

I suggest starting from the meaning of the Reynolds theorem, then you can use the Eulerian formulation to say that:

d /dt Int [v] rho dV + Int [BV] n.(v*rho) dS = 0

For steady flow you have the contranint that the surface integral of the mass flux must be zero.

umesh k. · November 10, 2015, 09:34

Yeah that's true.
But how one can physically signify it by considering real life examples related to this particular term and the whole x-direction equation?

FMDenaro · November 10, 2015, 09:47

Quote:

Originally Posted by umesh k.

Yeah that's true.
But how one can physically signify it by considering real life examples related to this particular term and the whole x-direction equation?

along x-direction, quasi 1D flow:

(rho*u*A)inflow -(rho*u*A)outflow = 0

the product (rho*u*A) MUST be the same at any location along the x-axis

umesh k. · November 10, 2015, 10:05

Please find attachment and answer..

FMDenaro · November 10, 2015, 11:08

the answer is in what I already wrote...I strongly suggest to study any basic textbook of fluid dynamics

umesh k. · November 10, 2015, 11:28

Yes. I read. Things got pretty much cleared. Thanks FMDerano

November 6, 2015, 01:40	Having dificulty understanding the meaning of continuity equation	#1
umesh k. New Member UMK Join Date: Sep 2015 Posts: 12 Rep Power: 10	I am not getting the meaning of continuity equation, mainly the gradient term that is there when flow leaves the control volume, please explain with the example..

November 6, 2015, 12:11		#2
kaya Member Kaya Onur Dag Join Date: Apr 2013 Posts: 94 Rep Power: 13	I can explain it to you but to not to confuse you more, I prefer understanding what exactly confuses you 'in a more clear way' before I give some analogies FMDenaro likes this.

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November 10, 2015, 08:27		#3
umesh k. New Member UMK Join Date: Sep 2015 Posts: 12 Rep Power: 10	OK, (Flow rate in=flow rate out+ rate of change of flowrate )#through control volume. So,what that rate of change of flow rate term is doing at the outlet?

November 10, 2015, 09:34		#5
umesh k. New Member UMK Join Date: Sep 2015 Posts: 12 Rep Power: 10	Yeah that's true. But how one can physically signify it by considering real life examples related to this particular term and the whole x-direction equation?

November 10, 2015, 11:08		#8
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,777 Rep Power: 71	the answer is in what I already wrote...I strongly suggest to study any basic textbook of fluid dynamics

November 10, 2015, 11:28		#9
umesh k. New Member UMK Join Date: Sep 2015 Posts: 12 Rep Power: 10	Yes. I read. Things got pretty much cleared. Thanks FMDerano