Question

I have a large syringe ; Diameter = 4cm, Length = 20cm, filled with a liquid which is a mix of water, soap and another detergent. This mix has a viscosity of 0.4 Poise.
The exit of the syringe is a 7mm diameter tube, about 3m long, filling another container.
I need to figure what Force (in N) need to be applied on the pusher to inject the liquid in 5 sec.
Thanks !!!

Answer 1

Poiseuille’s formula seems to be/could be what’s needed here. (You quote viscosity in Poise, after the Frenchman - ? – who derived the formula ...)

According to this calculation, a 4kg mass would have the weight (40N) to push the plunger/pusher enough to create a pressure that would produce the volume flow rate through the 3m tubing. I don’t know very much about syringes, but 4kg seems high.
If you want to discuss it further, let me know.

http://perendis.webs.com

Answer 2

Hello "Osprey",
Thanks for your answer. While waiting I got it figured out...

The flow rate is a volume of liquid which flows for a period of time.
1 . Flow= V/dt … expressed in m3/sec.


It is also proportional to the velocity of the liquid in the area of the passage where it flows
2. Flow=Av
A = area of a cross section of the tube in m2
v = velocity of the liquid in m/sec


When a liquid flows through a pipe, the pressure decreases when moving in the same direction as flow: it creates a force in the direction of flow, offsetting the friction force caused by the fluid viscosity. The decrease of pressure through a portion of pipe is…
3. ΔP=R.Flow
R is the hydraulic resistance in the portion of the pipe
P is the pressure, expressed in Pa (Pascal - 1Pascal = 1N/m2)


When a liquid flows at a constant speed and without turbulences, the flow is considered laminar and the formula for the hydraulic resistance is…
4. R= 8ηL/(πr^4 )
L is the length of the portion of the pipe
r is the radius of the pipe
η (greek letter eta) is the liquid viscosity, expressed in Pa.s


Combining equation 3 with equation 4, we get the Poiseille’s law…
5. ΔP= 8ηL/(πr^4 ) .Flow

With this fomula we can figure out the differential of pressure created by the flow, in the main syringe and in the 7mm x 3m tube. Adding both you get the whole pressure you need to create in the syringe to start the flow.

We need to overcome this pressure by a force applied on the pusher of the syringe…
6. F=PA Force equals the Pressure times the Area
The pressure time the area of the pusher will give me the required force I need.

And voilà...
It gives me 126.8N to inject this amount of liquid (which has a viscosity of 0.4 Poise) in 5 sec.

btw, for the viscosity units...
1 Pa.s = 10 Poise = 1000 centipoise

1 Pa.s = 1 N.s/m2
1 Poise = dyne.sec/cm2