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Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm diameter pipe, what will be the pressure generated by water?

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If the flow is laminar, i.e. not turbulent, then the relationship between flow rate and pressure is given by the Hagen–Poiseuille equation:

$$\text{Flow rate} = \frac{\pi r^4 (P - P_0)}{8 \eta l}$$

where $r$ is the radius of the pipe or tube, $P_0$ is the fluid pressure at one end of the pipe, $P$ is the fluid pressure at the other end of the pipe, $\eta$ is the fluid's viscosity, and $l$ is the length of the pipe or tube.

For turbulent flow there is no simple analytic treatment, but there is an empirical equation called the Darcy–Weisbach equation:

$$ P - P_0 = f_D \frac{l}{2r} \frac{\rho V^2}{2} $$

where $V$ is the flow velocity and $f_D$ is an empirically measured constant called the Darcy friction factor.

There is an online calculator for the Darcy-Weisback equation here.

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    $\begingroup$ I think this answer should at least mention the famous Moody diagram ( en.wikipedia.org/wiki/Moody_diagram ). Which is basically a graphical representation of $f_D$. $\endgroup$
    – Bernhard
    Jul 23, 2014 at 11:40
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The flow rate is proportional to the pipe section and flow velocity, and the relationship between the three is $$Q = 3600 \left(\frac{\pi D^2}{4}\right)v$$ where $Q$ is the flow rate ($\text{m}^3 \text{/h}$), $D$ is the pipe inner diameter ($\text{m}$) and $v$ is the average velocity of the fluid ($\text{m/s}$).

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  • $\begingroup$ Hi, I have formatted your post using MathJax, which is the standard for this site. $\endgroup$ Jul 21, 2021 at 0:39

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