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Almost every piping system has valves, and an accurate solution requires accurate valve losses. For incompressible systems, this is relatively straightforward. What happens when we introduce the complexities of compressible flow?

In liquid flow - like that calculated by AFT Fathom or AFT Impulse - valves are most commonly represented by the flow coefficient **C_{V}**.

It is helpful to modify this equation to be in terms of mass flow.

Defining a conversion factor *N*

And the **pressure drop ratio** *x*

The equation becomes

Where mass flow is in pounds mass per hour. Equation (1) is valid only for **incompressible** flow.

Graphically, this looks something like below.

There are two significant effects we need to account for if we want a similar equation for **compressible** flow.

- Density changes through the valve
- The flow can
**choke**in the valve – the velocity cannot exceed Mach 1 without a converging-diverging nozzle

In gas service, **C_{V}** is still the most readily available value for describing valve loss. However, as an incompressible parameter,

We can account for these effects with the introduction of one more parameter – *x_{T}*.

We can represent this in our previous equation by simply stating that, **for the purposes of the sizing equation, **** is limited to ****.**

Graphically:

Note that this is an example only! The value of **x**_{T} for a real valve depends on the particular valve design.

Applying only this change limits the flow to the sonically choked flowrate but does not address the compressibility of the gas. Without correction, this also introduces a discontinuity in the flow at **x =****x_{T}**.

The solution is to add an expansion coefficient ** Y** to the sizing equation.

This coefficient will vary between 1 at no flow and 2/3 at choked flow. Because density is changing, we must also modify the sizing equation to include inlet density instead of an unchanging density.

Graphically:

There is more loss compared to the incompressible equation as the pressure drop is higher, and a correspondingly lower flow.

Note that Equation 2 above follows the form described by ANSI/ISA 75.01.01. The full standard considers additional effects due to gasses other than air, fittings, and changes in pipe diameters. The full version is implemented in AFT Arrow.

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