When you’re designing a system to move fluids around – say, a natural gas extraction rig – it’s essential to know how fast the fluid you’re working with is flowing through the pipes. **Superficial flow velocity** (aka *superficial liquid velocity* or *superficial gas velocity*) is a way of estimating the speed at which a **fluid** (i.e. gas or liquid) passes through an object.

Calculating superficial velocity is relatively easy once you know the formula and required measurements. Read on to learn more about the assumptions underpinning superficial velocity and how to calculate it yourself.

## The Superficial Velocity Formula

Superficial gas velocity (aka superficial flow velocity) is an estimate of how quickly a fluid passes through an object (e.g. a pipe) or a porous medium (e.g. gravel). It’s calculated using the following formula:*u__ _{s}* =

*Q*/

*A*

*u__*is the superficial velocity of a given phase in meters/second (m/s)_{s}*Q*is the volume flow rate of the phase, in meters cubed/second (m^{3}/s)*A*is the cross-sectional area of the pipe or porous medium the fluid is flowing through, in meters squared (m^{2}).

## Superficial Velocity is a Convenient Estimation

In the real world, most flows are not uniform – air is made up of multiple gases with tiny solid particles suspended in it. Oil wells typically extract a mix of oil, water, and natural gas all at once. These fluids flowing together, made up of several components, are called *multiphase* *flows*.

Superficial flow velocity ignores the other phases to only estimate the velocity of the phase you’re interested in.

## Fluid Dynamics: Velocity versus Flow

Let’s say you’re a landscaper in a very rainy area. As such, it’s important that any garden beds you might build have excellent drainage to prevent flooding. When you’re building one of these beds, which is more important for you to know: water’s superficial velocity in soil or the flow rate of water through soil? It’s flow rate, as we’ll see below.

The *velocity* (or *superficial velocity*) of a fluid is a measure of the *average speed and direction* the particles of the fluid are moving. It answers the question “how fast?” It’s an important parameter when a fluid is being used to generate force, because force increases with velocity. The air exiting the nozzle needs to be moving fast to blow water off your hands. The total amount of air exiting the machine over time doesn’t actually matter, as far as drying is concerned.*Flow* (aka *flow rate*) is a measurement of the volume of a fluid moving between two places over time. In other words, it answers the question “how much and how quickly?” Flow is what you need to know when you’re interested in how many barrels of oil you’re getting out of your drilling rig each day. Or how much water can fall on your garden and how quickly without flooding it.

## Sample Calculation: Superficial Fluid Velocity

An engineer is designing a hand dryer, and she knows that she needs air to exit the device at a velocity of about 30 meters/second to effectively knock water free from skin. Her current prototype moves 0.4 cubic meters/second of air through a nozzle with a cross-sectional area of about 0.0002 square meters – will the air exit the nozzle at sufficient velocity?*u_{s} = _Q / A* = (15 m

_u_{s}

^{3}/s) / 0.4 m

^{2}

*= 37.5 m/s*

u__

u__

_{s}37.5 meters/second is faster than 30 meters/second, and it’s in the same ballpark – it’s a promising prototype!