Lesson 7

Calculating a design scheme

A real network has pipes, and pipes cost pressure. Here the open pipe of lesson 1 gets a neighbour, both hang on a main line through a tee, and the compressor has to make up for every metre of pipe in between. You will see where the pressure goes and check the calculation by hand.

The scheme you will build:

1. Start from lesson 1 and make room

   Open the file of lesson 1 and save it at once as lesson7.gf9: it already holds the Input parameters of lesson 1, which this lesson keeps. The Units tab belongs to your installation, not to the file, so it still shows the units of lesson 1 — check that it does.

   Right-click the red outlet of the compressor — the connection to the pipe is released. Drag the open pipe well to the right; the network needs about two hand widths between them. Rename the items (F2, lesson 5): the compressor COMP, the open pipe B1.

2. Place the pipes and the tee

   Type pipe in the catalog filter and place pipe from # Generic elements # three times: one after the compressor, two side by side before the open pipes. Its card is called generic pipe and, like the open pipe, it is described by your own numbers. Then type tee, open Connectors → Equal Tee and place d-1 in_Equal Tee after the first pipe. This one is a catalog item — a 1 in aluminium tee with a 23 mm bore — so its pressure loss comes from its card. Rename the items as in the picture above: P1, T1, P2, P3.

   The second open pipe is a copy of the first: select B1, Ctrl+C, Ctrl+V, drag the copy below and rename it B2. A copy keeps the green values of its original.

   A connection point holds one line, so a line cannot fork by itself: every branch starts at a tee. The tee has one inlet and two outlets.

3. Join them

   From each red outlet to the next green inlet: COMP → P1 → T1; one outlet of T1 → P2 → B1, the other → P3 → B2. Six connections.

   About the screenshots of lessons 7–9. They were taken on a file in which the items kept the IDs the program gave them, and the names on the sheet are plain captions (Text tab, lesson 5). So the windows show the old IDs where yours show the names: ID7 is COMP, ID13 is P1, ID1 is B1 and ID2 is B2 — in the Source list, the ID box, the Problems panel, the pressure profile. In that file Qn and Q also had units of their own (an orange frame round NL/min and L/min) and the Weight list was on g, so CO₂ is in grams there. The figures themselves are those of this lesson.

4. Fill in the green rows

   Pipe lengths run to tens of metres, and 50000 mm is easy to mistype. Click a pipe, click the unit cell of its Length row and choose m (lesson 6): every Length row of the scheme is now in metres, while Diameter stays in millimetres. A unit cell with a unit of its own is framed in orange.

   Now click each pipe and fill its rows in the Item tab:

   Item	Diameter	Length
   P1	25 mm	50 m	the main
   P2	16 mm	5 m	branch to B1
   P3	16 mm	5 m	branch to B2

   Diameter is the inner diameter, the bore the air sees. The Material row is green too and reads Aluminum: leave it — it sets the roughness of the wall.

   Then the open pipes. Their Length now reads 0.1 m — the same 100 mm in the new unit:

   Item	Diameter	Length	Pin
   B1	4 mm	0.1 m	6 bar
   B2	3 mm	0.1 m	6 bar

   Pin of a consumer in design mode is its design point: the pressure it must get. The calculation works out what has to happen upstream for it to get exactly that.

5. Calculate

   Press Calculate. In design mode EasyCAS works from the consumers back to the compressor:

   1. each consumer takes the flow it needs at its design pressure;
   2. each pipe carries the flow of everything behind it and adds its pressure loss, so the pressure grows on the way upstream;
   3. at the tee two branches meet; the one that needs more pressure decides, and the flows add up;
   4. the compressor gets the total flow and the highest pressure any branch needs.

   If a green row is empty, the calculation stops and asks for it in a dialog. The status bar shows the progress of a longer calculation and, for a few seconds after it, how long it took.

6. Read the consumers

   Row	B1	B2	Unit
   m	0.0208	0.0117	kg/s
   Qn	1048.25	589.64	NL/min	B2 has (3/4)² = 0.5625 of the area
   Q	149.75	84.23	L/min

   B1 gives exactly what it gave in lesson 1: a consumer in design mode always gets its design pressure, so the pipes in front of it do not change its flow. They change what the compressor has to do.

7. Read the pipes

   Click P2. Under your green rows it now has blue ones: the mass flow m, Pin and Pout, the pressure loss delta P, the velocity v and E, the power the air loses in the pipe. A pipe has no Qn or Q row: its flow is given as mass. All three pipes also show Min. possible diameter — the smallest bore at which the loss of that one pipe still stays under Allowable pressure drop of the Optimization tab and its velocity under the limit of step 9. It is a hint that the pipe could be smaller, not an error: about 23.4, 14.6 and 10.9 mm for P1, P2 and P3 here.

   Row	P1	P2	P3	Unit
   m	0.0324	0.0208	0.0117	kg/s
   v	7.87	12.41	6.98	m/s
   delta P	0.1034	0.0466	0.016	bar

   Check by hand: the velocity

   Velocity is the volume of air passing the bore each second, taken at the outlet of the pipe, where the pressure is lowest. For P2: Pout is 6 bar gauge, 7 bar absolute, so at 20 °C a cubic metre of air weighs 700 000 / (287 × 293.15) = 8.32 kg (287 is the gas constant of air, 293.15 the ambient temperature in kelvin). The 16 mm bore has π × 0.016² / 4 = 0.000201 m². Then v = m / (density × area) = 0.0208 / (8.32 × 0.000201) = 12.4 m/s. The main has more air but a bore 2.4 times larger, so it runs slower.

   Check by hand: the flows

   m of P1 is the sum of the two branches, 0.0208 + 0.0117 = 0.0324 kg/s — the last digit is rounding. Mass is conserved through every pipe and tee; actual flow is not, because the air expands as it loses pressure. Click T1: a tee shows its flow as Qn too, 1048.25 + 589.64 = 1637.89 NL/min.

8. Read the compressor

   Row	Expected	Unit
   Pout	6.1656	bar	6 bar at B1 plus the losses of P2, T1 and P1
   Qn	1637.89	NL/min	both consumers
   New unit cost	0.02439732	€/Nm³	a little above 0.024: Pout is above Pressure of air
   Cs	4603.41	€	a year

   Check by hand: the pressure

   Follow the path that needs the most pressure, from B1 back: Pout of the compressor equals 6 bar + delta P of P2 + delta P of T1 + delta P of P1. Add the three rows — the sum matches Pout to the last digit shown. Do the same along P3 and the sum falls short: the B2 branch needs less pressure than the tee gives it. A design calculation always sizes for the worst branch; what the surplus does at B2 is part of lesson 8.

   Every 0.1 bar more at the compressor costs roughly 0.7 % more energy. On this scheme the pipes and the tee cost 0.1656 bar, well under the 0.3 bar advisory threshold, and the 50 m main takes most of it — a well-sized network. Lesson 8 breaks it on purpose.

9. See it on the scheme

   View → Pipe display → Velocity colours each pipe by its velocity against its limit — green below 70 %, yellow from 70 to 100 %, orange above. The limit is 9 m/s for a pipe that feeds more than one consumer (the main) and 15 m/s for the others.

   Pipe	v	Limit	Share	Colour
   P1	7.9	9	87 %	yellow
   P2	12.4	15	83 %	yellow
   P3	7.0	15	47 %	green

   The line from the compressor to P1 has no pipe at one end and takes the colour of P1; a line with no pipe at either end is grey. Rest the mouse on a pipe to read the figures behind its colour. Pressure drop colours by the loss from the compressor instead, and Flow animation runs a dash along every line in the direction of the air.

10. Decide when to calculate

    Preferences → Autocalc recalculates after every change. On a scheme like this it is instant and pleasant; on a plant of several hundred items switch it off and press Calculate when the data is complete. Clear wipes the results and keeps your input — handy when you want to be sure you are reading fresh numbers.

    Save the file. Lesson 8 starts from it.

When it does not work

Try this next

• Shorten P1 to 20 m. Its loss falls with the length and Pout falls with it, by about 0.06 bar; nothing changes at the consumers.
• Set Pin of B2 to 5. The compressor does not move — B1 still needs more — but B2 now gets a whole bar more than it needs. Lesson 8 shows how the program tells you.

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