Determining fluid flow velocity from experimental volumetric flow rate data
I would be very grateful if someone helps me with my issue.
I have a pump pumping water into a tube. My goal is to find velocity of the fluid flow in another tube that will be connected to the first one.
To determine the flow rate in the first tube, I used a ~$1000~ml$ container and a stopwatch. I obtained the mean volumetric flow rate, let it be about $100~ml/s$. I use the following relation for laminar flow as a fisrt approximation:
$$ V_1=\frac{Q_1}{S_1}, $$
where $V_1$ is flow velocity ($m/s$), $Q_1$ is volumetric flow rate ($\text{m}^3/s$), and $S_1$ is inner area of the first tube ($\text{m}^2$).
Let the inner radius of the first tube be $4~mm$, so $S_1=\pi \cdot 0.004^2 \approx 5 \cdot 10^{-5}~\text{m}^2$. Thus, we have
$$ V_1=\frac{100~ml/s}{5 \cdot 10^{-5}~\text{m}^2}=\frac{1 \cdot 10^{-4}~\text{m}^3/s}{5 \cdot 10^{-5}~\text{m}^2}=2~m/s. $$
Then I connect the second tube, which has $6~mm$ inner diameter, to the first one ($8~mm$ inner diameter). 453
Outer diameter of the second tube is equal to the inner diameter of the first tube. I use a pump, so I assume flow rates $Q_1$ and $Q_2$ to be equal. From $Q_1=Q_2$ I get $V_1S_1=V_2S_2$, and
$$ V_2=\frac{V_1S_1}{S_2}=\frac{2\cdot0.004^2}{0.003^2}\approx3.6~m/s. $$
The result looks close to what I have seen, but I want to know the Reynolds number to determine if the flow is laminar or turbulent:
$$ \textrm{Re}=\frac{\rho V_2 D_H}{\eta}, $$
where $\rho$ is density of the fluid ($kg/\text{m}^3$), $D_H$ is hydraulic diameter of the second tube ($m$; we let $D_H$ be equal to geometric diameter of the tube $D_2$), and $\eta$ is dynamic viscosity of the fluid ($N\cdot s/\text{m}^2$). In our case, $\rho\approx974~kg/\text{m}^3$ and $\eta\approx 422\cdot10^{-6}~N\cdot s/\text{m}^2$, so
$$ \textrm{Re}\approx\frac{974 \cdot 3.6 \cdot 0.008}{422\cdot10^{-6}}\approx66500, $$
which is way more than $2000$, so the flow is turbulent, and the first approximation of the flow velocity should be corrected.
If I have experimental data of the volumetric flow rate in the first tube, then how can I find the flow velocity in the second tube in the case of turbulent flow? In the literature, they usually use volumetric flow rate in the case of laminar flow only. In some sources, equation $Q_1=Q_2$ ($V_1S_1=V_2S_2$) is used for pumped flows without indication of the flow type (laminar or turbulent). I am a bit confused. 453