


Calculating Pump Head
Before we can discuss pump head, we
must understand the difference between an open hydronic system and
a closed hydronic system. It is important to know whether the pump
serves an open or a closed
system, because the pump head calculation depends on the type of
system that the pump serves.
In a closed system, the fluid is not
exposed to a break in the piping system that interrupts forced flow
at any point. In an open system, it is. In a closed system, the
fluid travels through a continuous closed piping system that starts
and ends in the same place there is no break in the piping loop.
The vast majority of hydronic piping systems are closed. The most
common open system is the cooling tower portion of a chilled water
system, as depicted below. A break in the piping system occurs where
the water exits the spray nozzles, and is exposed to air in the
fill section of the tower. The water collects in the cooling tower
sump before being pumped around the loop again. Note that the chilled
water side of this diagram (the right side) is closed. Because it
is closed, an expansion tank absorbs any thermal expansion of the
fluid. Open systems don’t require expansion tanks, as the fluid
is naturally free to undergo thermal expansion.
Figure 1: Closed and Open Hydronic
Systems
What is Pump Head?

Static Head: Static head represents the net change in height, in feet, that
the pump must overcome. It applies only in open systems. Note
that in a closed loop system, the static head is zero because
the fluid on one side of the system pushes the fluid up the
other side of the system, so the pump does not need to overcome
any elevation.

Friction Head: This is also called pressure drop. When fluid flows through
any system component, friction results. This causes a loss in
pressure. Components causing friction include boilers, chillers,
piping, heat exchangers, coils, valves, and fittings. The pump
must overcome this friction. Friction head is usually expressed
in units called "feet of head." A foot of friction
head is equal to lifting the fluid one foot of static height.

Pressure Head: When
liquid is pumped from a vessel at one pressure to a vessel at
another pressure, pressure head exists. Common applications
include condensate pumps and boiler feed pumps. Condensate pumps
often deliver water from an atmospheric receiver to a deaerator
operating at 5 PSIG, meaning that in addition to the other heads,
the pump must overcome a pressure head of 5 PSIG. One
PSIG equals 2.31 feet, so the differential head in this application
is 5 X 2.31 = 11.6.’ Pressure head is a consideration only in
some open systems.

Velocity Head: Accelerating water from a standstill or low velocity at the
starting point to a higher velocity at an ending point requires
energy. In closed systems the starting point is the same as
the ending point. Therefore the beginning velocity equals the
final velocity, so velocity head is not a consideration. In
an open system, the velocity head is theoretically a
consideration, but the pipeline velocities used in hydronics
are so low that this head is negligible, and is ignored. (Note that the velocity head is defined by the formula V^{2}/2g
where V is the fluid velocity in feet per second and g is the
gravitational constant 32 feet/second ^{2}. Therefore
at typical velocities of 26 fps, the velocity head is a fraction
of a foot. Since head loss calculations are really estimates,
this small figure becomes insignificant).
So, for hydronic applications, we can
say that:

For closed systems: Pump head =
the sum of all friction pressure drops
Where:
Friction pressure drop = piping
pressure drop + terminal unit pressure drop + source unit pressure
drop* + valve pressure drop + accessories pressure drop.

For open systems: Pump head = the
sum of all friction losses plus the static lift of the fluid plus
the pressure head.
* The "source unit" is
defined as the boiler, chiller, or heat exchanger, which creates
the hot or chilled water.
Steps in Calculating the Pump Head
Basically, we need to plug values into
the proper formula above.
Step 1: Lay out the piping system using
logical routing as determined by the building requirements. Note
each terminal unit and its GPM.
Step 2: Select pipe sizes for
each segment, based on proper velocity and pressure drop.
The graphs below are from the ASHRAE Fundamentals Book. Recommended
velocities are:
Where P is the head loss (also
called friction loss or pressure drop).
The recommended ranges ensure that
the piping system will be quiet, consume reasonable pump horsepower,
and be reasonably economical to install. Note that the minimum velocities
are recommended based on the fact that lower velocities will allow
air to collect at high points, with the possible result of air binding.
Once the layout and pipe size for each
section has been determined follow these steps:
Step 3: Determine Friction Due to Source,
Terminal and Accessory Equipment Including:

Source and terminal Equipment:
Consult manufacturer’s catalogs or computer selections.

Accessory items include filters,
strainers, check valves or multi purpose valves that could have
a significant pressure drop that would not be covered under
the equivalent feet of piping rule of thumb.

To determine valve D P refer to
curves or Cv ratings. A Cv is defined as the flow at which the
valve will have a resistance of 1 PSIG (2.31 feet). Since the
pressure drop is proportional to the square of the flow rate,
use the following formula to calculate the pressure drop through
the valve for any flow rate:
PD In Feet = (Flow Rate/ Rated
Cv)^{2 }X 2.31
Example: A valve has a Cv of 10. Flow through the valve is 21 GPM. What is
the valve D P in feet of head?
PD in Feet = (21/10)^{2} X 2.31= 10.2’
Special Consideration: Pressure Drops
In PSI and Converting PSI to Head
Sometimes pressure drops will be given
in PSI units instead of feet of head. To convert PSI units to feet
of head:
PD in feet = PD in PSI X 2.31
Example:
A plate and frame heat exchanger printout shows a pressure drop
of 8.5 PSI. What P in feet must be added to the pump for this
item?
Answer: Feet in Head = 8.5 PSI X 2.31ft./PSI
= 19.64 ft.
Step 4: Determine the Static Head (Open
Systems Only)
The static head is simply the total
height that the pump must lift the fluid. It applies only in open
systems. Remember that the static head is the difference in height that the pump will be required to provide.
In the drawing below, showing a cooling
tower, the static height might appear to be 40’. However, the water
level in the tower sump is 28’ above the pump, so the pump must
only provide a net lift of 12’. Therefore, the static head is 12’.
Figure 2, Static Height Example
Step 5: Determine the Pressure Head
(Some Open Systems Only)
If the system is open, determine the
pressure differential required, if any. Don’t forget to multiply
pressure differentials in PSI X 2.31’/PSI.
Step 6: Determine the "Worst Pressure
Drop Loop" and Estimate the Friction Loss for that Loop by
Using ‘Equivalent Feet"
Because fittings result in more pressure
drop than plain pipe, we account for them by using "equivalent
length." The equivalent length of a piping circuit is the actual
measured length plus an allowance for all the fittings (elbows,
tees, valves, etc.).
The table below lists the number of
equivalent feet of piping for various fittings and accessories:
To use this method, add the equivalent
length of each item in the fluid’s path to the actual length of piping to get the total equivalent feet of piping.
Designers often skip the above method
and simply multiply the actual piping length times 1.5 to 1.75
to get the equivalent length. This provides speed and a reasonably
accurate estimation for "typical" hydronic piping systems.
As with any rule of thumb, however, watch out for oddball situations
(the boiler room is 2 blocks away from the building, a piping system
with an extreme number of fittings, etc). In such situations, the
long method provides better accuracy.
Now multiply the friction loss
per 100’ of piping from the ASHRAE charts times the equivalent length
in the "worst" loop to get the total piping friction loss.
Select the worst loop by inspection, if possible. Calculate several
branches if there is a doubt. The
friction in the worst loop is used as the friction head.
Figure 3, Worst Pressure
Drop Circuit
Note that the worst loop is simply
that the loop that results in the largest total pressure drop.
Do not add pressure drops from other parallel loops. In the
drawing above, assume that the pressure drop through Coil 3 and
its valve are higher than the pressure drop through Coils 1 and
2. Assuming that the branch piping for all three circuits is similar,
the "worst case" total friction loss loop is shown in
light blue. It would be erroneous to add the pressure drops of the
piping shown in black.
Notes

Those circuits with less pressure
drop than the "worst" circuit will be balanced in the field
by partially closing balancing valves (not shown above).

If there are different pipe sizes on
the circuit, the circuit may have to be analyzed in sections, because
the pressure drop/foot may vary by section. This is one good reason
for selecting all piping at the same pressure drop per 100.’ It
simplifies the calculations considerably.
Safety factors
You may wish to add a safety factor
to the calculated head for two reasons:

Jobsite conditions may not allow direct
routing of piping as shown on the plan. Extra length and extra elbows
result in added friction.

The interior pipe walls become rough
over time due to corrosion, especially in open systems, where fresh
water makeup brings in a steady supply of corrosioncausing oxygen.
This increases friction. Various sources recommend total safety
allowances of 1525% for friction calculations. Note that the friction
tables assume cold water, which results in more friction than hot
water. Therefore, if you are designing a hot water system,
you already have a safety margin of around 12%. Be careful
of excessive safety factors. They result in oversized pump impellers
that cause wasted energy!
Pressure Drop Corrections for Glycol.
Some systems utilize either ethylene
or propylene glycol mixtures in lieu of water. These fluids result
in higher pump heads than does water. For discussions of the effects
of glycol, see the Newsletter section of this WEB site. The Summer
2000 newsletter discusses the correction required to calculate
the amount of glycol to be circulated to meet a given heat transfer
load. The Winter 2001 newsletter provides correction factors
for pump applications, including factors for correcting head calculations. 
