# How do you measure fluid flow?

Jul 15, 2014

Fluid flow is a very broad term relating to the entirety of fluid mechanics, however, in a practical engineering sense, fluid flow is categorized in two ways:

1) The average velocity of a fluid moving through a conduit.
2) The volumetric flow rate, or simply "flow rate," of a fluid passing through a conduit.

Average velocity of a fluid:

When a fluid passes through a conduit, a phenomenon called the "no-slip condition" causes the velocity profile of the fluid to form a parabolic shape.

At the edges of the conduit, the velocity of the fluid is zero, and at the center of the conduit, the velocity will be at a maximum. The velocity of a fluid with laminar flow in a cylindrical tube is given by:

$u \left(r\right) = 2 {V}_{a v g} \left(1 - {r}^{2} / {R}^{2}\right)$

where ${V}_{a v g}$ is the average velocity of the fluid, $r$ represents the position of the velocity vector perpendicular to a position vector from the central axis of the tube, and $R$ is the maximum inside diameter of the tube.

Since the maximum velocity of a fluid in a cylindrical tube occurs at the center of the tube, or $r = 0 m$, the equation can be simplified to:

${u}_{\max} = 2 {V}_{a v g}$

Using this, the average velocity of the fluid in a cylindrical tube can be simplified to:

${V}_{a v g} = {u}_{\max} / 2$

Volumetric flow rate:

When an engineer is designing a piece of equipment that requires fluid to pass through at a certain rate, a customer will usually specify a volumetric flow rate which the equipment must accommodate. For example, the flow rate through the handle on a gas pump would probably be specified in gallons per minute, which is a volume per unit time. To obtain the volumetric flow rate of a fluid moving through a conduit, the average fluid velocity, ${V}_{a v g}$, is multiplied by the cross sectional area of the conduit. Mathematically, this looks like:

$V o {l}_{f l o w r a t e} = {V}_{a v g} \cdot {A}_{c r o s s - \sec t i o n}$
$V o {l}_{f l o w r a t e} = \left[\frac{m}{s}\right] \cdot \left[{m}^{2}\right] = \left[{m}^{3} / s\right]$