Calculating Flow Rate

[physics337]

I am trying to find a first principle model in order to calculate the flow rate of the following setup. A bottle with water (density = 1000 kg/m^3) is on a lab stand, and has rubber tubing at the end of the bottle coming down to the benchtop. The top of the water is 17 inches above the benchtop. You insert a needle (with Inner diameter of 0.015 inches) into the tubing to start collecting water in a beaker for 30 seconds. The needle length is 0.75 inches but then is attached to a plastic tubing with a length of 12inches and a Inner diameter of 0.02 inches. What is the Flow Rate of the water that is being collected?

I have used this to calculate the flow rate:
Velocity = √(2gh) =√(2*(386)*(17))=115 in/s
Q=Area* Velocity = ∏ (0.015/2)^2 * 115 = .02 in^3 / s = .33 cm^3/s = .33 g/s
Q for 30 seconds = .33* 30 = 9.9 grams.

When I actually do the testing I am collecting about 1.8 grams of water over 30 seconds.

I know I am losing some water due to frictional losses and have looked up equations for head loss and friction factor. However I am unsure how to apply this to get a more accurate model or if my way of calculating theoretical flow is completely off.

Any help will be appreciated! Thanks!

 

[LittleInch]

Perhaps you could explain your theory a bit, but to me looks very odd. Calculating velocity as being proportional to the square root of the head??

These flows and sizes are very very small and I'm really not sure if the equations will work for something this small without some normally inconsequential effect becoming significant.

If the majority of the head drop is taken with your big tubing then you can probably ignore the friction losses in that tube. You then start with the head available of 17 inches or thereabouts at your needle.

Looking at this I think virtually all your friction losses will occur in the minute 0.02", (500 micron) diam tubing, so find an equation for flow in tubing and you know the ID, you know the length, you know the pressure drop (17 ins of water) so should be able to solve for flow. Far better to do what you're doing and do some practical tests....

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[physics337]

After some thinking I tried the Laminar Flow Rate equation (pi*d^4*P)/(128*u*l). However I am still not getting the correct results. I have attached a sketch of the setup I had in mind. I am trying to figure out the flow rate through the needle device. I know from actual experiments that the tubing length does not play a big part in the amount of water flowing through (Experiment was done on 12 inches and 6 inch tubing) as both yielded similar results. Any help figuring out the theoretical model to match the real world results will be greatly appreciated.

 

[hahor]

Hello Physics,

you may want to try the "Engineer's Approach":

v = k * SQRT(delta p / density)

Q = A * v

Measure your flow rate at 5 different heights of the bottle, calculate "k", that's it.

Kind Regards,
hahor