CALCULATING THE TOTAL SYSTEM HEAD IN METRIC UNITS: C003
It turns out that 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 depends upon the weight (specific gravity) of the liquid being pumped and 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 Fig #l you should get a clear picture of what is meant by static head. Please note that we always measure from the centerline of the pump 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 head caused by resistance in the piping, fittings and valves called friction head, and an additional head caused by any pressure that might be acting on the liquid in the tanks, including atmospheric pressure. This head is called ” surface pressure head”.
Once we know all of these heads it gets simple. We subtract the suction head from the discharge head and the head 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
hd = total discharge headhsd = discharge static head
hpd = discharge surface pressure head
hfd = discharge friction head
The total suction head also consists of three separate heads
hs = hss + hps – hfs
hs = total suction headhss = suction static head
hps = suction surface pressure head
hfs = suction friction head
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 use the absolute term for these calculations because we are often calculating a vacuum or using negative numbers
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 and these charts:
The next illustration (Figure #2) shows 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:
Since atmospheric pressure at seal level is 1.013 bar we get a maximum siphon distance of 10.2 meters
We will begin with the total suction head calculation
- The suction head is negative because the liquid level in the suction tank is below the centerline of the pump:
- hss = -2 meters
- The suction tank is open so the suction surface pressure equals atmospheric pressure :
- hps = 0 meters gauge
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
- You would look at the charts and add up the K factors for the various fittings and valves in the piping. You would then multiply these K factors by the velocity head that is shown for each of the pipe sizes and capacities. This final number would be added to the friction loss in the piping for the total friction head.
- Or, you can look at a chart that shows the equivalent length of pipe for each of the fittings and add this number to the length of the piping in the system to determine the total friction loss.
For this example, I will tell you the total friction head on the suction side of the pump is:
hfs = 1.5 meters at rated flow
- The total suction head is going to be a gauge value because atmosphere was given as 0,
- hs = hss + hps – hfs = – 2 + 0 – 1.5 = – 3.5 meters of liquid gauge at rated flow
- The total discharge head calculation is similar
- The static discharge head is:
- hsd = 40 meters
- 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 discharge head is:
- hd = hsd + hpd + hfd = 40 + 0 +7 = 47 meters of liquid gauge at rated flow
- The static discharge head is:
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 or ask some one who is good at explaining this type of thing.
Our next example 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 charts:
I will give you the friction numbers for the following examples.
- Transferring 300 m3/hr weak acid from the vacuum receiver to the storage tank
- Specific Gravity = 0.98
- Viscosity = equal to water
- Piping = all 150 mm Schedule 40 steel pipe
- Discharge piping rises 15 meters vertically above the pump centerline and then runs 135 meters horizontally. There is one 90° elbow in this line
- Suction piping has 1.5 meters of pipe, one gate valve, and one 90° elbow, all of which are 150 mm in diameter.
- The minimum level in the vacuum receiver is 2 meters above the pump centerline.
- The pressure on top of the liquid in the vacuum receiver is 500 mm of mercury, vacuum.
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
- The suction side of the system shows a minimum static head of 2 meters above suction centerline. Therefore, the static suction head is
- hss = 2 meters
- Using the first conversion formula, the suction surface pressure is
hps = 500 mm hg x 0.014/ specific gravity = 7.14 meters of vacuum
- The suction friction head hfs equals the sum of all the friction losses in the suction line. If you referenced the metric pipe friction loss table you would learn that the friction loss in 150 mm. pipe at 300 m3/hr is 9 meters per 100 meters of pipe.
In 1.5 meters of pipe, friction loss = 15/100 x 9 = 0.14 meters
In a real life pumping application there would be other valves and fittings that experience friction losses. You might find:
- Check valves
- Foot valves
- Sudden enlargements
- Shut off valves
- Entrance and exit 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
- Static discharge head = hsd = 15 meters
- Discharge surface pressure = hpd = 0 meters gauge
- Discharge friction head = hfd = sum of the following losses :
Friction loss in 150 mm pipe at 300 m3/hr, from the chart is 9 meters per hundred feet of pipe.
- In 150 meters of pipe the friction loss = 150/100 x 9 = 13.5 meters
- Friction loss in 150 mm. Elbow:= 3.4/100 x 9 = 0.31 meters 1
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 static discharge head (hsd) will change from 15 meters to 12 meters since the highest liquid surface in the discharge is now only 12 meters above the pump centerline. This value is based on the assumption that the vertical leg in the discharge tank is full of liquid and that as this liquid falls it will tend to pull the liquid up and over the loop in the pipeline. This arrangement is called a siphon leg.
- The discharge surface pressure is unchanged:
- hpd = 0 meters
- The additional 3 meters of pipe and the additional elbow will increase the friction loss in the discharge pipe.In 3 meters of pipe the friction loss = 3 / 100 x 9 = 0.27 metersThe friction loss in the additional elbow = 3.4 / 100 x 9 = 0.31 meters
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.