Physics Help Forum continuity equation..

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 Nov 22nd 2015, 07:11 AM #1 Junior Member   Join Date: Nov 2015 Posts: 6 continuity equation.. Hello there..my brain is stuck on this equation and I'd like some help.. Continuity equation states that the mass/volume flow through a pipe remains constant at all times. If the pipe size increases, the velocity decreases and vice versa. Q1=Q1=v1xA1=v2xA2...ok I see the logic and I agree.. However, if we have water flowing through the pipe and we have a valve afterwards which we close at 50%...the flow changes afterwards..you'll get less water flowing through...why does this happen? isn't it supposed to be same all the time no matter if you squeeze it through a smaller pipe etc? The question is probably dumb but my brain has short-circuited on this one..please help me out
Nov 22nd 2015, 11:02 AM   #2
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 Continuity equation states that the mass/volume flow through a pipe remains constant at all times.
Not quite.

Chemical engineers like the following version

Input = Output + Accumulation.

So the mass or volume discharge rate is constant so long as there is no accumulation somewhere in the system.
Loss such as a leak is obviously negative accumulation.

Having settled that, let's look at your question.

So you have a pipe feeding a tap which you adjust.
The way to apply the continuity equation is to assume there is no loss or accumulation so the discharge after the tap must be equal to the discharge before the tap which must be equal to the quantity of fluid entering the pipe.

What changes is the velocity as well as the cross section.

So the volumetric discharge is Area Cross Section x Velocity = a Constant

If the area changes at the tap or the pipe gets smaller the velocity increases.

 Nov 22nd 2015, 01:57 PM #3 Senior Member     Join Date: Apr 2008 Location: Bedford, England Posts: 668 The back pressure will also increase, this will affect the amount of water entering the system in the first place... __________________ You have GOT to Laugh !
 Nov 22nd 2015, 03:14 PM #4 Junior Member   Join Date: Nov 2015 Posts: 6 thanks for the reply. I understand that if pipe gets smaller velocity increases. volumetric discharge stays constant. However, as I'm working on water heating/cooling systems I think of an example below which confuses me with the above. When you want to reduce flow of water through a pipe, you use valves which open or close..for example if you have hot water of 80C with a volumetric flow rate of 1m3/h for example, when you put a valve and close it down to 30% for example, the flow rate will be less after the valve and you can even sense it as the temperature of the pipe decreases...so why does this happen? shouldn't volumetric flow rate stay same by just increasing velocity? I mean this valve acts the same as when we're squeezing the water hose on the end, doesnt it? by the way consider this being a closed system with a pump forcing the water one way with steady pressure... and about leak, assume it's not leaking anywhere.so no negative accumulation..and no positive accumulation which I guess would be adding more water into the system?
Nov 22nd 2015, 03:24 PM   #5
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 When you want to reduce flow of water through a pipe, you use valves which open or close..for example if you have hot water of 80C with a volumetric flow rate of 1m3/h for example, when you put a valve and close it down to 30% for example
If the flow rate is 1cum/hr before the valve and 0.3cum.hr after the valve where is the other 0.7cum/hr going?

 Nov 22nd 2015, 03:25 PM #6 Junior Member   Join Date: Nov 2015 Posts: 6 also, about the tap in reality, when you close the tap at the dish, theres less discharge flow compared to when you fully open it..and velocity seems much larger when it's fully opened.. I'm confused..for some reason I think it is different when pipe size changes and different when you just put some resistance infront of it (valve)... sorry if i don't understand the more I think about this the more confused I get.. if you understand what exactly of my thinking is wrong please explain me
Nov 22nd 2015, 03:30 PM   #7
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 Originally Posted by studiot If the flow rate is 1cum/hr before the valve and 0.3cum.hr after the valve where is the other 0.7cum/hr going?
i guess it stays back? hehe I'm not sure. I mean when you fully close the valve it should all stay back..if you open it a bit..some of it flows through...

Nov 22nd 2015, 03:31 PM   #8
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 also, about the tap in reality, when you close the tap at the dish, theres less discharge flow compared to when you fully open it..and velocity seems much larger when it's fully opened.. I'm confused..for some reason I think it is different when pipe size changes and different when you just put some resistance infront of it (valve)... sorry if i don't understand the more I think about this the more confused I get.. if you understand what exactly of my thinking is wrong please explain me
You are confused?

How about telling me what you think about my question in post#5?

 Nov 22nd 2015, 03:38 PM #9 Junior Member   Join Date: Nov 2015 Posts: 6 yap still confused. Sorry for spam. about question #5 , I guess it stays back.. I mean a valve changes the amount of fluid passing through it.. if I'm holding a water baloon filled with 1 liter of water..if I squeeze the end of it to keep it closed (valve closed)..1 liter stays inside the balloon..if i open it just a little..there will be small drops of water flowing through...if I open it more..more volumetric flow...if I fully open it...the water will all flow out of the balloon quickly...
 Nov 22nd 2015, 03:46 PM #10 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 1,035 Keep going, Is the water flowing into the balloon as well as out of it?

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