Calculating the total system head in metric units 14-10
"Head" is a very convenient term in the pumping business. Pressure is not as convenient a term because the amount of pressure that the pump will deliver is dependent upon the weight (specific gravity) of the liquid being pumped and as you know, the specific gravity changes with the fluid temperature and concentration.
Each liter of liquid has weight so we can easily calculate the kilograms per minute being pumped. Head or height is measure in meters so if we multiply these two together we get kilogram meters per minute which converts directly to work at the rate of 610 kgM/min = 1 kilowatt.
If you are more comfortable with metric horsepower units you should know that 735.5 watts makes one metric horsepower
If you will refer to the above drawing (Fig #l ) you should get a clear picture of what is meant by static discharge head. Please note that we always measure from the center-line of the pump impeller to the highest liquid level
To calculate head accurately we must calculate the total head on both the suction and discharge sides of the pump. In addition to the static head we will learn that there is a second head caused by resistance in the piping, fittings and valves called friction head and a third head caused by any pressure that might be acting on the liquid in the suction or discharge tanks including atmospheric pressure. This third head is called " surface pressure head".
Once we know all of these heads it becomes simple.We subtract the suction head from the discharge head and the head that is remaining will be the amount of head that the pump must be able to generate at its rated flow. Here is how it looks in a formula:
System head = total discharge head - total suction head or H = hd - hs
The total discharge head is made from three separate heads:
hd = hsd + hpd + hfd
The total suction head also consists of three separate heads
hs = hss + hps - hfs
As we make these calculations you must be sure that all your calculations are made in either "meters of liquid, gauge" or "meters of liquid, absolute". In case you have forgotten "absolute" means that you have added atmospheric pressure (head) to the gauge reading. Normally head readings are made in gauge readings and we switch to the absolute readings only when we want to calculate the net positive suction head available (NPSHA) to find out if our pump is going to cavitate.
We will begin by making some actual calculations. You will not have to look up the friction numbers because I am going to give them to you, but you can find them in a number of publications including my web site, my Pump and Seal Manual, or my CD. . Please note that the Pump annd Seal Manual is only available in the U.S. and Canada. My CD is available Internationally and domestically.
Figure #2 demonstrates that the discharge head is still measured to the liquid level, but you will note that it is now below the maximum height of the piping.
Although the pump must deliver enough head to get up to the maximum piping height it will not have to continue to deliver this head when the pump is running because of the "siphon effect". There is of course a maximum siphon effect. It is derived from the formula to convert pressure to head:
Head(meters) = pressure x 10.2/ specific gravity
Since atmospheric pressure at seal level is 1.013 bar we get a maximum siphon distance of about 10 meters if we ignore friction in the piping
We will begin with the total suction head calculation
In these examples you will not be calculating the suction friction head. When you learn how you will find that there are two ways to do it
For this example, I will tell you the total friction head on the suction side of the pump is:
The total suction head is going to be a gauge value because atmosphere was given as 0,
The total discharge head calculation is similar
The discharge tank is also open to atmospheric pressure, so: hpd = 0 feet, gauge
I will give you the discharge friction head as: hfd =7 meters at rated flow
The total system head calculation becomes:
Head = hd - hs = 47 - (-3.5) = 50.5 meters of liquid at rated flow
Note: Did you notice that when we subtracted a minus number (-10) from a positive number (150) we ended up with a positive 160 because whenever you subtract minus numbers it is the same as adding them? If you have trouble with this concept you can learn more about it from a mathematics book.
Our next example (figure #3) involves a few more calculations, but you should be able to handle them without any trouble.
If we were pumping from a vented suction tank to an open tank at the end of the discharge piping we would not have to consider vacuum and absolute pressures. In this example we will be pumping from a vacuum receiver that is very similar to the hotwell we find in many condenser applications
Again, to make the calculations you will need some pipe friction numbers that are available from my book, CD or web site. I will give you the friction numbers for the following examples.
To calculate suction surface pressure use the following formula:
Now that you have all of the necessary information we will begin by dividing the system into two different sections using the pump as the dividing line.
Total suction head calculation
150 mm normal bend elbow
150 mm Gate valve
In a real life pumping application there would be other valves and fittings that experience friction losses:
The loss in the suction fittings becomes:
in 5.5 meters of pipe friction loss = 5.5/100 x 9 = 0.50 meters
The total friction loss on the suction side is:
hfs = 0.14 + 0.50 = 0.64 meters at 300 m3/hr
The total suction head then becomes:
hs = hss + hps - hfs = 2 - 7.14 - 0.64 = - 5.78 meters gauge at 300 m3/hr
Now we will look at the total discharge head calculation
Friction loss in 150 mm pipe at 300 m3/hr, from the charts is 9 meters per hundred feet of pipe.
The discharge friction head is the sum of the above losses, that is:
hfd = 13.5 + .31 = 13.81 meters at 300 m3/hr
The total discharge head then becomes:
hd = hsd + hpd + hfd = 15 + 0 + 13.81 = 28.81 meters at 300 m3/hr.
Total system head calculation:
H = hd - hs = 28.81 - (-5.78) = 34.59 meters at 300 m3/hr
Our next example will be the same as the one we just finished except that there is an additional 3 meters of pipe and another 90° flanged elbow in the vertical leg. The total suction head will be the same as in the previous example. Take a look at figure # 4
Nothing has changed on the suction side of the pump so the total suction head will remain the same:
hs = - 5.78 meters at 300 m3/hr
Total discharge head calculation
The friction head will then increase as follows:
hfd = 0.27 + 0.31 = 0.58 at 300 m3/hr.
The total discharge head becomes:
hd = hsd + hpd + hfd
= 12 + 13.81+ 0 + 0.58
= 26.39 meters at 300 m3/hr
Total system head calculation
Head = hd - hs
= 26.39 - (-5.78)
= 32.17 meters at 300 m3/hr.
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