Problem

What is the "Discharge Coefficient" used in various places such as with the "Discharge Coefficient" and "Valve Characteristics Curve" Valve Type with a TCV node, or when using the Tank throttling inlet valve option?

Solution

The "Discharge coefficient" is also known as a "valve coefficient" or "Cv", which is defined as: Flow / (Pressure Drop) ^ 0.5. The Discharge Coefficient is used to model the relationship between flow and headloss through the valve being modeled (TCV, tank float valve, etc) The value to enter depends on the valve, which may be obtained from the manufacturer.

Note that there are many definitions of the term "discharge coefficient" (example). To learn more about the definition of the one used in WaterCAD, WaterGEMS and HAMMER, see the article "Definition of Discharge Coefficient" under the "See Also" section at the bottom of this article. The definition used in HAMMER, WaterCAD and WaterGEMS is the commonly used valve coefficient Cv, defined as:

Q = Cv (pressuredrop)^0.5.

Another way to express it and consider specific gravity is:

Cv = Q (specific gravity / Pressuredrop)^0.5

A common definition for the valve coefficient Cv is "The volume (in US gallons) of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi". However, you may notice that the units for discharge coefficient in HAMMER, WaterCAD and WaterGEMS are gpm/psi^0.5, not gpm/psi. The reason why this definition can be true while the units can be gpm/psi^0.5 is because that statement is simply the definition, not the units. At a pressure drop of 1psi, this definition holds true, because the square root of 1 is 1. However, for pressure drops other than 1psi, the relationship is exponential, not linear (as seen in the units).

For example, with a discharge coefficient of 3000gpm/psi^0.5 with water at a specific gravity of 1.0, you would expect a flow through the valve of 3000gpm at a pressure drop of 1.0 psi:

Cv = 3000(1/1)^0.5
Cv = 3000

However with the same discharge coefficient, the flow at a 2.0 psi pressure drop would be 4242gpm:

Q = (3000)(2)^0.5
Q = (3000)(1.414)
Q = 4242

Minor Loss Coefficient Conversion

If a discharge coefficient is not available, but you have the minor loss coefficient for the valve (K), then you can use the below equation:

US Units

Cv = ((39.693 * d^4) / K)^0.5

Where:

Cv = discharge coefficient (cfs/ftH20^0.5)
d = diameter (ft)
K = Headloss/Minor Loss coefficient

SI Units

Cv = ((1.22 * D^4)/K)^0.5

Where:

Cv = discharge coefficient (m³/s/Kpa^0.50)
d = diameter (m)
K = Headloss/Minor Loss coefficient

Note: for SI units, WaterCAD, WaterGEMS and HAMMER accept a unit of m³/s/M H2O^0.50 - a unit conversion factor of 3.1316 can be used to multiply the end result in the kpa unit to achieve the unit required by the program.

If you know the discharge coefficient, you can compute the minor loss coefficient with a rearranged version of the equation:

K = 39.693 * D^4/Cv^2 

Where:

Cv = discharge coefficient (cfs/ftH20^0.5)
d = diameter (ft)
K = Headloss/Minor Loss coefficient

Minor Loss Coefficients (K) for common types of valves can be found in places like engineering reference manuals and the included default Minor Loss Library (Components > Engineering Libraries)

Furthermore, if still unsure, you could perform a sensitivity analysis, trying a range of reasonable values and checking the response. If the results that matter to you are not significantly effected, then you may not need to worry about how accurate the discharge coefficient is.

Additional Information

The following document explains the relationships between k (unitless headloss coefficient), H (headloss coefficient referred to flow), Kv (Flowrate Coefficient) and Cd (Discharge Factor).

File Gallery: Valve Characterization Coefficients Comparison

See Also

Valve Type field assumptions and use with a TCV

Modeling Reference - Valves

(Forum) Valve Discharge Coefficient - Kv units