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A little help/direction would be very helpful:

The needle of a syringe has a diameter $d=0.6mm$ and its length is $l=2cm$. The water flow forced in the needle is $Q=10^{-7} m^3 s^{-1}$

Assuming laminar flow, calculate:

  1. The average speed of water
  2. What is the pressure drop necessary to have such a flow I think I'm OK with the 1: $Q=S×V$ so:

$$V=Q/S=10^{-7}/( 6×10^{-3} × 6 ×10^{-3}) = 8.84×10^{-4} m s^{-1}$$

2/ For this one I assume I have to use Poiseuille equation:

$$\Delta P = \frac{8\mu LQ}{\pi R^4}$$

but I don't know how to do as I don't have the dynamic viscosity of the water ($\mu$). I don't know if I suppose to know this value (as it depend on temperature I presume?) or if I have to / can express the pressure drop without knowing this value.

Can someone help me/push me a little in the right direction?

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    $\begingroup$ I understand you're not a native English speaker but understand that the word I is ALWAYS capitalised, regardless of its position in a sentence. $\endgroup$
    – Gert
    Dec 4, 2020 at 16:24
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    $\begingroup$ Don't forget the $\pi$ for the cross-sectional area $S$, since capillaries are usually assumed to be circular. Also, you need to halve the diameter to get the radius. $\endgroup$
    – wyphan
    Dec 4, 2020 at 21:18

2 Answers 2

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Less than 5 seconds of googling and I found the dynamic viscosity of water:

$$\mu=8.90\times 10^{-4}\text{ }\mathrm{Pa.s}$$

at $25^{\circ}\mathrm{C}$ of temperature.

A table of dynamic viscosity dependence on temperature is also provided in that link.

or if I have to / can express the pressure drop without knowing this value.

No, of course you can't calculate $\Delta P$ without knowing $\mu$.

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  • $\begingroup$ People doing fluid dynamics courses should know the viscosity of water at room temperature from the top of their head. At 20 degrees it is 0.001 Pa s. $\endgroup$
    – Bernhard
    Dec 4, 2020 at 16:31
  • $\begingroup$ @Bernhard That's silly. I've done a lot of FD in my time and still don't know that value 'of the top of my head'. $\endgroup$
    – Gert
    Dec 4, 2020 at 16:38
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    $\begingroup$ I've known it in my head since 1962 when I had my first course in fluid dynamics: 1 centipoise = 0.01 Poise $\endgroup$
    – Chet Miller
    Dec 4, 2020 at 17:45
  • $\begingroup$ Sure Chet but 'Daphoque' isn't a habitual user of FD, methinks. $\endgroup$
    – Gert
    Dec 4, 2020 at 17:47
  • $\begingroup$ thanks, finally get an answer from our professor indicating we have to use 1x10^-3 $\endgroup$
    – Daphoque
    Dec 6, 2020 at 13:07
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I don't confirm your velocity calculation. The cross sectional area of the capillary is $$\frac{\pi D^2}{4}=2.83\times 10^{-7}\ m^2$$So the velocity is 0.354 m/s.

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  • $\begingroup$ haha yeah thanks stupid mistake ! $\endgroup$
    – Daphoque
    Dec 6, 2020 at 13:05

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