Question

How do you measure fluid flow?

Answer 1

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(r)=2V_(avg)(1-r^2/R^2)`

where `V_(avg)` 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=0m`, the equation can be simplified to:

`u_(max)=2V_(avg)`

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

`V_(avg)=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_(avg)`, is multiplied by the cross sectional area of the conduit. Mathematically, this looks like:

`Vol_(flowrate)=V_(avg)*A_(cross-section)`
`Vol_(flowrate)=[m/s]*[m^2]=[m^3/s]`