## Basic Parameters of Two‐phase Fluid Flow

In this section we will consider the simultaneous flow of** gas (or vapor) and liquid water** (as encountered in steam generators and condensers) in concurrent flow through a duct with cross-sectional area A. The subscripts **“v”** and** “ℓ”** indicate the **vapor** and **liquid** phase, respectively. Fundamental parameters that characterize this flow are:

## Superficial Velocity

**Superficial velocity** is a hypothetical flow velocity calculated as if the given phase or fluid were the **only one flowing** or present in a given cross-sectional area. The velocity of the given phase is calculated as if the second phase was ignored.

In the engineering of multiphase flows and flows in porous media, **superficial velocity (V _{phase} or j_{phase})** is commonly used because it is the value that is unambiguous. In contrast, real velocity is often spatially dependent and subject to many assumptions.

Superficial velocity can be expressed as:

For better understanding, let us consider a pipe with a 0.1 m^{2} cross-section of flow area. Assume that the flow rate is 1 m^{3}/s. For** single-phase fluid flow,** the **superficial velocity will be equal to real fluid** **velocity,** which will be 10 m/s.

For t**wo-phase fluid flow** (e.g.,, vapor-liquid flow), the situation will be different. Assuming the slip ratio is unity, both phases have taken separately, will have superficial velocities of **5 m/s**. The resulting real velocity will then be equal to **10 m/s**. If the two phases have different velocities (with slip), the situation will be more complicated.