# Calculation of pressure from flow rate of water

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?

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.

• 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 $f_D$. Jul 23, 2014 at 11:40

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 ($$\text{m/s}$$).

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