In the practical analysis of piping systems, the quantity of most importance is the **pressure loss due to viscous effects** along the length of the system, as well as **additional pressure losses** arising from other **technological equipments** like valves, elbows, piping entrances, fittings, and tees.

In contrast, to single-phase pressure drops, calculation and prediction of two-phase pressure drops is a much more sophisticated problem, and leading methods differ significantly. Experimental data indicates that the **frictional pressure drop in the two-phase flow** (e.g.,, in a boiling channel) is **substantially higher** than for a single-phase flow with the same length and mass flow rate. Explanations include an increased surface roughness due to bubble formation on the heated surface and increased flow velocities.

## Pressure Drop – Homogeneous Flow Model

The simplest approach to predicting two-phase flows is to treat the entire two-phase flow as if it were **all liquid**, except flowing at the two-phase **mixture velocity**. The two-phase pressure drops for flows inside pipes and channels are the sum of three contributions:

- the static pressure drop
**∆p**(elevation head)_{static} - the momentum pressure drop
**∆p**(fluid acceleration)_{mom} - the frictional pressure drop
**∆p**_{frict}

The total pressure drop of the two-phase flow is then:

**∆p _{total} = ∆p_{static} + ∆p_{mom} + ∆p_{frict}**

The static and momentum pressure drops can be calculated similarly as in the case of single-phase flow and using the homogeneous mixture density:

The most problematic term is the** frictional pressure drop** **∆p _{frict}**, which is based on the single-phase pressure drop multiplied by the

**two-phase correction factor**(

**homogeneous friction multiplier – Φ**). By this approach, the frictional component of the two-phase pressure drop is:

_{lo}^{2}where **(dP/dz) _{2f}** is frictional pressure gradient of two-phase flow and

**(dP/dz)**is frictional pressure gradient if an entire flow (of total mass flow rate G) flows like a liquid in the channel (standard single-phase pressure drop). The term

_{1f}**Φ**is the

_{lo}^{2 }**homogeneous friction multiplier**that can be derived according to various methods. One of the possible multipliers is equal to

**Φ**

_{lo}^{2}= (1+x_{g}(ρ_{l}/ρ_{g}– 1))**and therefore:**As can be seen, this simple model suggests that the **two-phase frictional losses are in any event higher than the single-phase frictional losses.** The homogeneous friction multiplier increases rapidly with **flow quality**.

Typical** flow qualities** in** steam generators** and **BWR cores** are on the order of 10 to 20 %. The corresponding two phase frictional loss would then be** 2 – 4** times that in an equivalent single-phase system.

## Two-phase Minor Loss

Any piping system contains different technological elements in the industry, such as **bends, fittings, valves, or heated channels**. These additional components add to the overall head loss of the system. Such losses are generally termed **minor losses**, although they often account for a major portion of the head loss. For relatively short pipe systems, with a relatively large number of bends and fittings,** minor losses can easily exceed** major losses (especially with a partially closed valve that can cause a greater pressure loss than a long pipe when a valve is closed or nearly closed, the minor loss is infinite).

Single-phase minor losses are commonly measured experimentally. The data, especially for valves, are somewhat dependent upon the particular manufacturer’s design. **The two-phase pressure loss** due to local flow obstructions is treated like** the single-phase frictional losses** – **via local loss multiplier**.

See more: TWO-PHASE FRICTIONAL PRESSURE LOSS IN HORIZONTAL BUBBLY FLOW WITH 90-DEGREE BEND