Figure 1

Consider water flowing through a pipe from a pump to an outlet at atmospheric pressure. The pipe has a hole in the bottom which initially connects to an empty tank.

  1. The water fills the tank.

  2. Once the tank is filled with water and steady state is reached, a dye is mixed in the water that is pumped in the pipe.

Will this dye be seen inside the tank? Assume that the pump and the outlet are far away from the hole.

  • $\begingroup$ $P_3 > P_2$. So, tracer should not enter the tank. Will that be correct? $\endgroup$ Feb 27, 2022 at 18:04
  • $\begingroup$ Will the entry hole to the tank create a flow disturbance? $\endgroup$
    – Solar Mike
    Feb 27, 2022 at 18:14
  • $\begingroup$ @SolarMike what is your thought if it does not? I am thinking, obviously there will be some flow disturbance near the hole. Maybe, that gets minimized if the velocity is slow enough. $\endgroup$ Feb 27, 2022 at 20:06
  • $\begingroup$ When you say "tracers" are you talking about a dye or something like small plastic pellets? $\endgroup$
    – J. Ari
    Feb 27, 2022 at 20:08
  • 1
    $\begingroup$ still plenty of variables to play with including flow rate, pipe diameter, size of hole in box, and properties of the "dye" - for example if the dye is basically oil, and the flow slow enough, and the pipe diameter large enough, I could see it failing to enter the box. A better approach might be to figure out the results you want and to design the system to meet requirements. That or given an existing system, provide as thorough measurements as possible. $\endgroup$
    – Abel
    Mar 1, 2022 at 13:05

1 Answer 1


There will be turbulent flow at the hole to the tank. This will produce eddy currents in the tank, and there will be a slow exchange of fluid between the tank and the pipe.

  • $\begingroup$ Are you expecting a reynolds' number cutoff for the turbulent flow to happen? $\endgroup$ Mar 1, 2022 at 4:19
  • $\begingroup$ @Brownian_Motion, no, it will be turbulent because it passses a hole. $\endgroup$
    – Tiger Guy
    Mar 2, 2022 at 13:05

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