Fluid Mechanics Help Please

[donburke]

I'm trying to correctly design a cooling coil to be used as an immersion chiller,

I have seen these pre fabricated stainless steel coils http://www.kegking.com.au/chillerbox_inlinechiller.html

can someone please tell me what sort of flow rate i can expect if connecting 16 metres of 6mm ID tubing to normal water tap pressure ? water currently flows at around 20 litres per minute out of the tap now, and i know that running the water through this coil would slow it down, but how much would it slow it ???

is there a simple formula i can use to play around with pipe length and diameter to compute what the flow rate will be with mains water pressure ?

thanks in advance

 

[Acasta]

I can't find my fluids notes from last year, ill see if the net will help.
The equations im thinking of would be friction in pipe, and one for heads.

------------Alright, i found this on head pressures, the bernouilli equation.

http://www.engineeringtoolbox.com/bernouil...tion-d_183.html

Looking at equation (3)
v = velocity
g = gravity (9.8 or 10)
p= pressure
p = density of the liquid (1000)
h = height

So basically, the equation equal to itself will be equal (in balence), so you need quite a few known values.
You said you have the tap water rate, so convert that so m/s, water pressure may be difficult, and height is vertical only, not the length of tube.

--------------Here is a bit on losses inside the pipe, theres a calculator you will see there that could be handy.
http://www.engineeringtoolbox.com/hazen-wi...ater-d_797.html

Sorry if its not much help, like i said i can't find my notes and this is the best i can do.

--------------
To calc your velocity from flow rate out of tap (discharge) use this formula q=(crossectional area of pipe)(velocity of fluid), where q is the discharge rate.

 

[donburke]

I can't find my fluids notes from last year, ill see if the net will help.
The equations im thinking of would be friction in pipe, and one for heads.

thanks, thats would be great because its all over my head

 

[Acasta]

Im not too sure if this is helping much? Do you have much background in fluid or maths or anything?

 

[donburke]

Im not too sure if this is helping much? Do you have much background in fluid or maths or anything?

its way over my head, i read somewhere that tap pressure is approx 40 psi if that helps

any chance of giving it a stab for me as i have no engineering background ?

thanks

 

[Acasta]

Ill have a quick stab.
16 metres of 6mm ID tubing, 20 litres per minute out of the tap.
Whats the height difference between tap and exit point?

q = 0.333 L/s
v = q/d = 0.333/6 = .055m/s

 

[donburke]

Ill have a quick stab.
16 metres of 6mm ID tubing, 20 litres per minute out of the tap.
Whats the height difference between tap and exit point?

i suppose exit point can be 30cm below the tap

 

[Acasta]

Ill have a quick stab.
16 metres of 6mm ID tubing, 20 litres per minute out of the tap.
Whats the height difference between tap and exit point?

q = 0.333 L/s
v = q/d = 0.333/6 = .055m/s

i suppose exit point can be 30cm below the tap

Alright,
h = .3m
q = 0.333 L/s
v = q/d = 0.333/6 = .055m/s

all we need now is to figure out a water pressure, which is something not easily done... Im thinking we could possibly assume pressure is equal, but thats just being hopeful.


Just found this: http://www.engineeringtoolbox.com/static-p...head-d_610.html

h = (p2 - p1) / γ

γ = 9.789 kN/m3
40psi = 275.79kpa

sooo...

.3 = (p2 - 275.8) / 9.79 ... p2 =278.7kpa

This change is pretty neglectable.

 

[donburke]

Alright,
h = 300mm
q = 0.333 L/s
v = q/d = 0.333/6 = .055m/s

all we need now is to figure out a water pressure, which is something not easily done...

try 40 psi, i remember reading that somewhere, thanks for running these calcs

 

[flavo]

try 40 psi, i remember reading that somewhere, thanks for running these calcs

40psi is around 30m of head. Which could be about right depending on where you are. In Brisbane, they have a minimum standard of 21m.

First time in a long time I wish I remembered stuff from uni.

 

[Acasta]

v^2 / 2g + p / γ + h = v^2 / 2g + p / γ + h

.55^2 / 2(9.8) + 278.7 / 9.79 + .3 = v^2 / 2(9.8) + 275.8 / 9.79 + 0

You know what, **** this head ache...

What don't you use a smaller/bigger pipe? These formulas are for water system on a big scale, ie, 30cm diameter over 100m down slopes... Crunching these small numbers isn't going to help really.

Probably don't need to look at head at all..

The best way to modify flow rate on a small scale is that formula i said before: discharge (flow rate) = crossectional area of pipe x velocity of fluid, easiest thing is this to modify is diameter of your tubing. The height wont really do much, the length (depending on the internal frictions) probably wont effect much either.
Another this is adjusting pressure at the tap, is that possible?

 

[donburke]

v^2 / 2g + p / γ + h = v^2 / 2g + p / γ + h

.55^2 / 2(9.8) + 278.7 / 9.79 + .3 = v^2 / 2(9.8) + 275.8 / 9.79 + 0

???

 

[michael_aussie]

???

lol......
I was hoping to learn (relearn actually) something too....

 

[Acasta]

???

lol......
I was hoping to learn (relearn actually) something too....

lol, i can finish it off for you, but like i said, its pointless. Thats why i recommended techniques for a smaller scale system.

don, are you able to shorten your length, or is it just the diameter that can change or neither?

Anyway, im off. PM me if u want a hand or anything.

 

[mesuite77]

v^2 / 2g + p / γ + h = v^2 / 2g + p / γ + h

.55^2 / 2(9.8) + 278.7 / 9.79 + .3 = v^2 / 2(9.8) + 275.8 / 9.79 + 0

You know what, **** this head ache...

What don't you use a smaller/bigger pipe? These formulas are for water system on a big scale, ie, 30cm diameter over 100m down slopes... Crunching these small numbers isn't going to help really.

Probably don't need to look at head at all..

The best way to modify flow rate on a small scale is that formula i said before: discharge (flow rate) = crossectional area of pipe x velocity of fluid, easiest thing is this to modify is diameter of your tubing. The height wont really do much, the length (depending on the internal frictions) probably wont effect much either.
Another this is adjusting pressure at the tap, is that possible?

Actually this is the correct formula no matter what size pipe you use the problem is accounting for the pressure loss. For this problem the pressure loss in question is going to be the frictional loss in the pipe. In a 6mm ID pipe I would imagine there will be some fairly large pressure loss particularly over 16m.

Having said that you can't make the assumption that the flow rate of the open tap will be the same as that once 16m of 6mm ID pipe is attached to it. The increase in static pressure from the pipe will reduce the flow rate.

 

[unrealeous]

v = q/d = 0.333/6 = .055m/s

I have one of these tubes - and I can assure you it comes out a lot faster than .055m/s (a dribble).

One of the troubles with theory and reality is that in theory, theory and reality give the same result, but in reality they don't.

 

[dr K]

First, Acasta is spot, you are wasting your time trying to calculate (there are too many unknowns in your scaled down model)
Second stainless is a crap conductor and thus a crap heat exchanger
Third a slower water flow will actually be more efficient than a faster one (rough rule of thumb, if the water coming out of your imersion chiller is almost as warm as the remaing wort you are efficient)
Get some copper pipe

K

 

[michael_aussie]

One of the troubles with theory and reality is that in theory, theory and reality give the same result, but in reality they don't.

That's not entirely true.

The equations behind fluid mechanics have been fine tuned for hundreds of years.
Applied correctly they yeild very good approximations to reality.
The black art is the application.
There are some parameters that you need to input to make it work.
Among other things, they relate to the roughness of whatever you are transmitting the fluid in, and how your fluid performs at whatever temperature you are moving it. In your case the temperature will be changing, so to get this "right" you would also need to involve some thermodynamics (heat-transfer) in conjunction with your fluid mechanics. You will also need to know the flow vs pressure performance of your water supply .. just inputting 40psi could be wide of the mark.

Experts make an assumtpion, take some measurements, to confirm or fine-tune these assumptions, and then can apply these "fine-tuned" parameters to similiar systems.

You are going to need to make an assumtion about the roughness of your tubing, to yeild a result. The accuracy of this assumption will have a huge bearing on how accurate the calculated values approximate to what you actually get.

This doesn't help you, 'cause you don't even have the coil in your hand to test your calculated values.

In saying all that, I'm sure someone here who have been down this path before will be able to give you a pretty good approximation.

 

[malt_shovel]

As K says, get some copper and don't try to blast the water through it as fast as possible. The idea being, the quicker it goes through, the less contact time the water has with your hot copper/SS making it less efficient. Heat transfer has a time component.

So relax, put the maths book down, have a homebrew and go to your favorite hardware store and ask for some 3/8" or 1/4" copper pipe.

Or go no chill? h34r:

 

[Smashin]

+1 +1 etc....

But just to jump on the band wagon,

a few points:

-system supply pressure will be a function of flow (as someone mentioned), easily measured.
-the heat flux calculation from the tubing to the cooling water inside the pipe is the easy one and is a function of dT, reynods number and surface roughness (the inputs to the moody diagram.
- conductive flux through the tubing is easy calculated, a function of dT, t & k and area
-flux from the wort to the tubing, here is where you need to be very specific re: what you intend to model, i.e forced or natural convention??
-at anyone with an immersion chill can tell you if you stop moving the chiller around the outlet temperature drops dramatically, once stirring the temperature goes up significantly. Here enters many years of experimental data compiled into volumes of table of unit less measures to enable estimates to be scaled from.
-Dr K mentioned efficiency and using a lower flow and he is right but what is the objective here... to get the temp down asap not with the least water usage, (depends which side of the chain saw you stand)
-the faster the water flow the great the greater the dT along the pipe and hence the greater flux,
-use copper over stainless as it thermal conductivity is a magnitude higher.

all in all this is home scale brewing, use plenty of pipe and crank the tap and if using an imersion chiller keep it moving or stir your wort....

thats my 2c, anyway back important thinks like stepping up my witbier mash to 68, its going to take forever for this one to sparge so I may have to find some more places to waffle on, to fill inn the day..

Smashin