Calculating minor losses for pipe fittings in AioFlo
In order to calculate the minor losses (i.e. pressure drops in fittings and valves) for a pipe it is necessary to give details of the start of the line, the end of the line, and all the fittings and valves in the line. AioFlo therefore breaks up the data input into these categories to make it logical and easy to check that everything has been covered.
Defining the start of the line
In the AioFlo model a pipe can start as the outlet from a tank or vessel, or it can be a continuation from another pipe.
The outlet from a tank can either be flush with the side of the tank, or it can project into the tank (sometimes known as a "Borda" entrance). The radius of the joint between the tank and a flush entrance can vary because a well radiused entrance has a very much lower resistance coefficient than a square outlet.
Because AioFlo is designed for pipes of a single diameter, any change in diameter must occur at either the start or end of the line. The change in diameter can be either an increase or a decrease from the previous section, and it can be implemented as a sudden expansion or contraction, or as a conical reducer, or as a standard pipe reducer. The diameter of the previous section can be keyed in as a numeric value, or it can be selected from the built in pipe dimension tables. The resistance coefficients for the changes in diameter are calculated using the Hooper Method.
Specifying elbows and tees for the calculation of minor losses
A variety of threaded, welded (or flanged) and mitered fittings is included.
The second page covers elbows and tees. The resistance coefficients (K values) for the elbows and tees are calculated using the Darby 3-K Method which allows accurate calculation of pressure drops in the fittings for laminar and turbulent flow. This gives better accuracy than using equivalent lengths or fixed K values.
Where applicable, the details of the fittings are selected from drop down lists, and the number of fittings is keyed in.
Specifying valves and orifices for the calculation of minor losses
A wide variety of generic valves is included, and there is the option of adding specific details for calculating losses in control valves and orifices.
The third page covers valves and orifices. The resistance coefficients for the generic valve types are calculated using the Darby 3-K Method which allows accurate determination of losses for laminar and turbulent flow. These K values are based on average values found in the open literature and catalogs and will be sufficiently accurate in most cases. However, if you have specific data for a valve you can enter that as a separate K value.
The control valve resistance is specified by entering a Cv value in the US, British or European form. Thin, sharp edged orifices as well as thick orifices are included. The permanent pressure loss through the orifices is calculated using the Hooper Method.
Generic resistance coefficient (K value) data is included for gate valves, globe valves, ball valves, plug valves, diaphragm valves, butterfly valves, Y-type strainers and a selection on non-return (check) valves.
Defining the end of the line
In the AioFlo model a pipe can end in the same diameter as the main pipe line, or there can be an increase or decrease in diameter. The kinetic energy change caused by an increase or decrease in velocity between the start and end of the line is converted to a pressure change using the Bernoulli Equation.
If the pipe ends with a free jet of liquid exiting into the atmosphere there is no mixing and therefore no exit loss. But there is also no recovery of the kinetic energy in the jet. On the other hand, if a liquid discharges into a tank below the surface it causes turbulence and mixing and there will be a frictional exit loss. However there is also recovery of the kinetic energy and these two exactly cancel each other. When a gas exits from a pipe it is similar to the liquid exiting below the surface of a tank and again the frictional exit loss and the kinetic energy recovery cancel each other.
These two scenarios where the pipe exit does not feed into another pipe can be treated in the same way because in both cases the exit loss and the kinetic energy recovery are equal to each other (but of different sign). If the fluid continues to another pipe of the same diameter then there is no exit loss and no recovery of kinetic energy. Nevertheless, in all of these scenarios any change in kinetic energy between the start and end of the pipe must be considered using the Bernoulli Equation.
In the same way as a change of diameter is allowed at the start of the line, there can be a change of diameter at the end as well. The change in diameter can be either an increase or a decrease to the downstream section, and it can be implemented as a sudden expansion or contraction, or as a conical reducer, or as a standard pipe reducer. The diameter of the downstream section can be keyed in as a numeric value, or it can be selected from the built in pipe dimension tables. The resistance coefficients for the changes in diameter are calculated using the Hooper Method.
If the end of the line is followed by another pipe of a larger diameter then the frictional loss in the change of diameter will not exactly cancel the pressure recovery due to the deceleration of the fluid and both effects must be considered. If the pipe is followed by another pipe of smaller diameter then the velocity will increase and there are losses due to friction and to the kinetic energy change so they definitely will not cancel each other. As always, any change in kinetic energy between the start and end of the pipe must be considered using the Bernoulli Equation.