Fluid mechanics - Question Poiseuille exercise

Question

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:

The average speed of water
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:
$$Delta P = frac{8mu LQ}{pi R^4}$$
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?

Gert · Answer

Less than 5 seconds of googling and I found the dynamic viscosity of water:
$$mu=8.90times 10^{-4}text{ }mathrm{Pa.s}$$
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 $mu$.

Chet Miller · Answer

I don't confirm your velocity calculation.  The cross sectional area of the capillary is $$frac{pi D^2}{4}=2.83times 10^{-7} m^2$$So the velocity is 0.354 m/s.

Fluid mechanics - Question Poiseuille exercise

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