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I am trying to solve for Reynolds number in a problem. However, I do not have the velocity of the water which flows through the pipe. Am I supposed to make up a number for the flow speed of the liquid inside the pipe or is this a mistake in the problem itself?

The pipe dimensions are given to me (its diameter, vertical and horizontal length), I have acquired the K-values ($\zeta$) for the 90° elbow, the inlet, and the outlet of the pipe and for both the gate valves in which the liquid flows through.

To make it easier, the velocity at point 1 is negligible, as small as $c_1 ≈ 0 \frac ms $, $c_1$ being the velocity at the point which is on the free surface (which is on a water tank). Still, I do not know how to get the flow speed of the liquid.

I managed to get the relative pipe roughness, as well, but it's not very handy as I don't have the Reynolds number which is required of me to solve my problem.

If you are wondering, I need the Reynolds number so I can get my friction number and to solve the pressure drop between the two points of 1 & 2, and also the velocity of point 2 which is on the exit of the pipe.

I can provide with image of the system if interested.

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    $\begingroup$ You pretty much know the overall pressure difference and you need to determine the mass flow rate that makes good on this pressure difference. So this is a trial and error calculation. Assume a mass flow rate and see if it matches the overall pressure difference. If it doesn't match, adjust the mass flow rate, and try again. $\endgroup$
    – Chet Miller
    Mar 18, 2021 at 17:46
  • $\begingroup$ Not exactly. In place of the delta p, you need the dissipation term. $\endgroup$
    – Chet Miller
    Mar 18, 2021 at 18:25
  • $\begingroup$ As Chet wrote. Make an assumption, e.g. laminar flow, then calculate flow rate and calculate $\text{Re}$. If this indicates laminar flow you're done. If not, assume turbulent flow and calculate flow velocity and $\text{Re}$. It's a classic problem, very common in Real World. $\endgroup$
    – Gert
    Mar 18, 2021 at 18:27
  • $\begingroup$ Is an assumption of the velocity of the water in the pipe of $ c_{avg} = 3 \frac ms $ good? I think this will be turbulent, by the way. $\endgroup$
    – Qwin
    Mar 18, 2021 at 18:33
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    $\begingroup$ It is only the frictional pressure difference, not the part related to change in gravitational potential energy or kinetic energy. $\endgroup$
    – Chet Miller
    Mar 19, 2021 at 16:25

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