04/08/2023Faisal Rai ARABTEC

SUMMERY SYSTEM HEAD LOOS CALCULATION DATE : 1/12/2010

PROJECT : xxSYSTEM : xxPrepared ,& Calc. by : Eng. Faisal Rai

Pipe Material

Flow rate ( q ) GPM 500Pipe Diameter ( D ) inch 8Pipe Length ( L ) Ft. 420.00

Mt. -6.40 Z2 Mt. 91.4

Calculated Data

Velocity ft/s (feet/second) Ft./s 3.19The Reynolds Re number is: 175,008.81Friction parameter ( f ) 0.0264Friction Factor Δ HFP / L Ft. / 100 Ft. 0.63The pipe friction loss ∆HFP is: Ft. 2.64

Total head loss in the pipe line (h L) 3.70

HEAD (TDH) = (Hs)+(Hf)+( Hp)+(Hv) Ft. 428.45

PSI 185.48Bar 12.79

PUMP SELECTION AND SIZING

FLOW RATE Q ( GPM) 500TDH H (Ft.) 428.45

Bar 12.79Water Hors Power WHP 54.10Brake Hors Power BHP 72.13

PUMP BRAKE HORSPOWER BHP+10% BHP 79KW 59

PUMPING COST PER YEAR Working hours per year hours / year Electrical cost for operation $KWh 0.17Pumping Cost ( $ / Year) $ USD 0.00

Riser , ELEV. 1 , 2. : Z1

Faisal Rai:

INPUT DATA

PIPE FRICTION CALCULATIONPROJECT : DATE : 1/12/2010xx SYSTEM : xx

INPUT DATA from Summary

Liquid type Waterq = flow rate 500 GPM D = pipe diameter 8 InchL = pipe length 420.00 Feet

Velocity ft/s (feet/second)The average velocity v in the pipe is:

V = 0.4085 Xq / D² = 3.19 Ft / s

1.13

Re = 7745.8 x V *D / μ = 175008.811

ε = pipe roughness ( Ft ) 0.0018

f = friction parameter Non dimensional

0.026422

∆HFP / L friction factor (feet of fluid/100 ft) of pipe

g = acceleration due to gravity (32.17 ft/s2) = 32.17

0.63 Ft./100Ft of pipe

The pipe friction loss ∆HFP is:

∆HFP = ∆HFP / L * ( L/100) = 2.64 Feet

μ = viscosity CSt (centistokes) , WATER at 60 °F

The Reynolds Re number is:

The friction parameter f is:

f = 0.25 / {Log10 (ε /3.7*D + 5.74 / Re^0.9)} ² =

Friction factor ∆HFP / L is calculated with the Darcy-Weisback equation:

∆HFP / L = 1200 f * V² / D * 2g =

ESTIMATING PIPELINE HEAD LOSS AND PUMP SELECTION USING DARCY WEISBACH METHOD

Project : xx Date : 1/12/2010

System : xx Done By: FR

A - PIPE LOSS CALCULATION Page 1 of 4

( Ft. )hL = head loss DATAc1=conversion factor for head loss calculation (table1). 0.0311f = darcy friction factor from pipe friction calculation sheet. 0.02642172L = pipe length (feet) 420.00q = flowrat gal/min 500d = pipe iside diameter ( inch) 8 .

To find the friction factor ( f ) from curve , Re & Rr sould be calculated: Reynolds no. Re = (c2 X q X ρ) / d X µ Relative roughness of the pipe Rr =ε /d

c2 = conversion factor for reynolds No. calculation 50.662.34

µ = fluid absolute viscosity 1.1 ε = Absolute reoughness values for clean pipe : 0.0018

Reynolds No. Re = 175,008.81

R. Roughness Rr = 0.0002

Note:also f ,it can be calculated with these formulas :f =64/Re for laminar flow Re less than 2000

f ={-2log[Rr/3.7 - 5.02/Re log(Rr / 3.7+ 14.5/Re)]}-² for turbulant flow Re greater than 2000

WE CAN USE THIS FORMULA FOR NEW PIPES

f =0.005(1+1/40D) 0.00562

hL Calculation, For flowrate (q) { gal/min} &water @ 60˚F section flowrate pip diam. friction pipe rough. pipe L h L V ( Ft/s )

q d f ε L(Ft) FtL1 500 8 0.026422 0.0018 420.00 2.63 3.19L2 0 1 0 0.0018 0 0.00 0.00L3 0 1 0 0.0018 0 0.00 0.00L4 0 1 0 0.0018 0 0.00 0.00L5 0 1 0 0.0018 0 0.00 0.00L6 0 1 0 0.0018 0 0.00 0.00

L7 0 1 0 0.0018 0 0.00 0.00Pipe Head Loss h L ( Ft ) 420 2.63 V = 0.4085*q/d²

B - VALVES AND FITTINGS HEAD LOSS

hLvf = c3 X K Xq²/d^4 ( Ft. )

c3 = conversion factor for valve head loos calculation

K = valve resistance coefficient

K = f T X (L/d)

f T = turbulant friction factors for a partucular pipe diam.

K FOR FITTINGS AND VALVES TYPE :

TYPE K

Pipe entrance,inward proj. 0.78

Pipe entrance, Flush 0.5Pipe Exit , all 1 OR

K a 1.5 1.78

hL = ( c1 X f X L X q² ) / (d)^5

ρ = fluid weight density

which is : Rr =ε /d

ESTIMATING PIPELINE HEAD LOSS AND PUMP SELECTION USING DARCY WEISBACH METHOD

Project : xx Date : 1/12/2010

System : xx Done By: FR

Page 2 of 4

K1…n =[ f T X (L/d )] x No. of valve or fitting typeTable : 6 f T = turbulant friction factors for a partucular pipe diam.

L/d for valves and fittings PIPE Dia. ( Inch ) =

Fitting L/d from f T fitting Qty K1…nGlobe Valve 340 0.015 0 0Gate Valve 8 0.015 2 0.24Lift Check Valve 600 0.015 0 0Swing Check Valve 50 0.015 1 0.75Ball Valve 6 0.015 0 0Butterfly Valve 35 0.015 1 0.525Tee Through 20 0.015 2 0.6Tee- Branch flow 60 0.015 0 0

Elbow-90 30 0.015 7 3.15Elbow -45 16 0.015 0 0Bend r/D=3 12 0.015 0 0Bend r/D=6 17 0.015 0 0Bend r/D=12 34 0.015 0 0Bend r/D=20 50 0.015 0 0

K b fittings 5.265

kc for EquipmentEquipment kc

Equip. Qty. kc kcCHIL. COIL 0 11 0

AHU COIL 0 0 0

H.Exch. 0 0 0

0

0

0

Equip.kc = 0

K = Ka+(K1 + K2 + K3 …+Kn )+kc for valves + fittings & Equipment =

K = Ka + Kb + Kc = 6.765

Pipe Head Loss h L pipe Ft. 2.63

TOTAL VALVES & FITTINGS H. L. h L fittings Ft. 1.07

Total head loss in the pipe line (h L) = Ft. 3.70

ESTIMATING PIPELINE HEAD LOSS AND PUMP SELECTION USING DARCY WEISBACH METHOD

Project : xx Date : 1/12/2010

System : xx Done By: FR

C TOTAL PRESSURE LOSS Bernoulli theorem H = Z+[144 X P / ρ] + [ V² / (2 X g)] Page 3 of 4 ( pressure head and velocity head )

In Elivation (Z1) -6.40 -20.99

Pipe disch. Elev.(Z2) 91.4 299.792

Z = elevation above a reference level Ft. 320.78p = pressure PSIv = mean velocity of the fluid in the pipeline ft / s 0

g = gravitional constat ft / s² 32.2

Differintial pressure calculation

(Δp) =p1-p2 = ρ /144 { Z2 - Z1 + (v2² - v1² ) / 2g + h L} PSI 140.4756

Ft 324.50Or TDH = Static Head Hf + Friction head Hf+ Velosity head Hv

Hf = K X V² / 2g 1.07Hf = f X L /100 2.63Hv = V² / 2g 0Static Head 320.78

Extra for F.P System 45 PSI *** to be added

>>>>>>>>>>>>>>>>>>>>>>> TDH = Ft. 428.45

1 PSI = 0.068947573 Bar PSI 185.48

1 Bar = 14.503773773 PSI Bar 12.79

Δh Ft fluid = 2.31 p (psi) / SG

F.P.

ESTIMATING PIPELINE HEAD LOSS AND PUMP SELECTION USING DARCY WEISBACH METHOD

Project : xx Date : 1/12/2010

System : xx Done By: FR

D PUMP SELECTION AND SIZING Page 4 of 4

HEAD ( TDH ) = Static head (Hs) + friction head (Hf) + pressure hesd ( Hp) + velocity head(Hv)

Static head ( Hs) = is measured from the surface of the liquid in the section vessel to the surface of the liquid in the vessel where the liquid is being delivered. In closed-loop system , the total static head = 0 .

Fittings & valves Friction head Pipe Friction head ( From friction loss chart ) Velocity head f = friction ft/ 100 ft 0.02642172K = resistance coefficient 6.765

V = Fluid velocity ft/sec. 3.19

g = acceleration due gravity = 32.2 ft./sec² 32.2

Design velocity = ( 4 - 6 ) ft / sec for section = ( 6 - 8 ) ft / sec for discharge

1 PUMP Horsepower and efficiency:water horsepower ( WHP ) = Outpot of the pump handlind a liquid

WHP = (Q X H X sg) / 39602 Brake horsepower ( BHP ) = Actual supplied power from motor

ή = pump efficiency3 Electric current for sizing starters and wire ( I ) [ Amp.]

I = 746 X BHP / 1.73 X E X PF X Eff for 3 phI = 746 X BHP / E X PF X Eff for 1 ph

SG 1E = Voltage ( volts) 380 Q ( GPM) 500

0.85 H (Ft.) 428.45EFF. = Motor efficiency 0.75

1.73 242.25 WHP 54

419.09 BHP 72

I ( AMP.) 128

PUMP BRAKE HORSPOWER BHP+10% = HP 79KW 59

∆Hp = ∆Hf1-2+∆Hequi1-2+ 1/2g * ( V1^2 - V2^2)+ Z2+H2-( Z1 + H1 )

BHP = ( Q X H X sg ) / 3960 X ή = WHP / ή

PF = Power Factor

ESTIMATING PIPELINE HEAD LOSS AND PUMP SELECTION USING DARCY WEISBACH METHOD

Project : xx Date : 1/12/2010

System : xx Done By: FR

Eng. FAISAL RAISYSTEM CURVE

11.2008

System Curve Calculation xxxx

System Curve for Closed Systems

System curve points. The points are calculated as follows:

SYSTEM INPUTS: auto fill from Friction + HL

Friction Head, Ft. DESIGN DESIGN FRICION. Static PRESSURE

1.1 X DF 550 1.21 X DH 4.48 FLOW GPM HEAD Ft. Head (Ft.) PSI

1 X DF 500 1 x DH 3.70248 500 3.70 320.78 45.00

.75 X DF 375 0.56 X DH 2.07339 DF = DESIGN FLOW ( GPM )

.50 X DF 250 0.25 X DH 0.92562 DH = DESIGN HEAD ( Ft. )

.25 X DF 125 0.06 X DH 0.22215 PRESSURE HEAD : 1 PSI = 2.31 Ft.

0 Flow 0 0.00 X DH 0

NOTES :

1. To use this table, one must first have calculated the design flow (DF) and the design head (DH).

2. In closed systems, the friction head is the total head as well, so the values in the right

hand column represent the heads for the system curve.

3. Total System Head = Friction Head

System Curve for Open Systems

Calculating System Curve Points for Open Systems

Flow head head head head( Ft.) calculated static head and pressure head :

550 4.48 320.784 103.95 429.214 Pressure Velocity

500 3.702479 320.784 103.95 428.43648 head ( Ft.) Head

375 2.073388 320.784 103.95 426.80739 103.95 0

250 0.92562 320.784 103.95 425.65962

125 0.222149 320.784 103.95 424.95615

0 0 320.784 103.95 424.734

For open systems:428.44

Total System Head = Friction Head + Static Head + Pressure Head + Velocity Head

Velocity head appears in italics to remind us that velocity head is generally ignored, as it is insignificant

in hydronic applications

Closed System Curve (Friction Head Only)

System Flow Rate, GPM

System Flow Rate, GPM

Friction Head,

Ft.

Static Head, Ft.

Pressure

Head, Ft.

Total Head, Ft.

FR04/08/2023

0 100 200 300 400 500 6000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

CLOSED SYSTEM CURVE

SYSTEM CURVEFLOW (GPM)

HEAD

( Ft

.)

FR04/08/2023

0 100 200 300 400 500 600422

423

424

425

426

427

428

429

430

OPEN SYTEM CURVE

SYSTEM CURVE

FLOW ( GPM )

TH (F

EET)

The Friction Coefficient for Laminar Flow

The flow is laminar when Re < 2300λ= 64 / Re (7) Transient when 2300 < Re < 4000

Turbulent when Re > 4000The Friction Coefficient for Turbulent Flow

Relative roughness for materials are determined by experiments.

Relative roughness for some common materials can be found in the table below :

Surfacefeet

Copper, Lead, Brass, Aluminum (new) 0.001 - 0.002

PVC and Plastic Pipes 0.0015 - 0.007

Epoxy, Vinyl Ester and Isophthalic pipe 0.005

Stainless steel 0.015

Steel commercial pipe 0.045 - 0.09

Stretched steel 0.015

Weld steel 0.045

Galvanized steel 0.15

Rusted steel (corrosion) 0.15 - 4

New cast iron 0.25 - 0.8

Worn cast iron 0.8 - 1.5

Rusty cast iron 1.5 - 2.5

Sheet or asphalted cast iron 0.01 - 0.015

Smoothed cement 0.3

Ordinary concrete 0.3 - 1

Coarse concrete 0.3 - 5

Well planed wood 0.18 - 0.9

Ordinary wood 5

where

The Friction Coefficient - λ

λ = f( Re, k / dh )

k = relative roughness of tube or duct wall (mm, ft)

k / dh = the roughness ratio

Roughness - kx 10-3 m

3.33 - 6.7 10-6

0.5 - 2.33 10-5

1.7 10-5

5 10-5

1.5 - 3 10-4

5 10-5

1.5 10-4

5 10-4

5 - 133 10-4

8 - 27 10-4

2.7 - 5 10-3

5 - 8.3 10-3

3.33 - 5 10-5

1 10-3

1 - 3.33 10-3

1 - 16.7 10-3

6 - 30 10-4

16.7 10-3

The friction coefficient - λ - can be calculated by the Colebrooke Equation:

1 / λ1/2 = -2,0 log10 [ (2,51 / (Re λ1/2)) + (k / dh) / 3,72 ]

Roughness Ratio - k / dh.

λ = D'Arcy-Weisbach  friction coefficient

Re = Reynolds Number

Note that the friction coefficient is involved on both sides of the equation and that the equation must be solved by iteration.The Colebrook equation is generic and can be used to calculate the friction coefficients in different kinds of fluid flows - air ventilation ducts, pipes and tubes with water or oil, compressed air and much more.

k = roughness of duct, pipe or tube surface (m, ft)

dh = hydraulic diameter (m, ft)

The Colebrook equation is only valid at turbulent flow conditions.

The friction coefficient can also be estimated with the Moody diagram:

NPSH (Net Positive Suction Head)

1. Performance deteriorates.

        NPSH is undoubtedly one of the most misunderstood factors in pump selection. The pump NPSH consideration is actually not a difficult concept once you understand two essential concepts:

        1. We tend to think that water boils at 212° F, which is true at atmospheric pressure at sea level. In reality, water boils at different temperatures, depending upon its pressure. The table below shows the relationship. The pressure at which water boils at a given temperature is called its vapor pressure. 

        Under certain operating conditions, as the pump attempts to pull water into the eye of the impeller, it can create a negative pressure (vacuum). If the pressure created drops to the water’s vapor pressure, the water will begin to boil. Obviously, this is more likely to happen if the pump is pumping hot water than if it is pumping cool water.

        2. The second principle is that a pump is designed to handle pure liquid, not boiling liquid, which is a mixture of liquid and vapor. (The vapor is steam in the case of water).

           What happens when water begins to vaporize as it is drawn into the pump?  Vapor bubbles begin to form, just as they do when you boil water on your stove.  As the fluid moves into the vanes of the impeller, it picks up energy from centripetal acceleration ("centrifugal force"). This causes an increase in the pressure of the boiling liquid. This causes the bubble to implode (collapse violently). The process of bubbles forming then collapsing violently is called cavitation. When a pump experiences cavitation:

2. The pump sounds as if it is pumping marbles or gravel (Some people have actually opened up their pumps to find out how the heck the gravel got in!).

3. The impeller and perhaps the casing begin to suffer damage. This happens when the bubbles implode so violently that the water chips away at the metal surfaces. In extreme cases, holes are worn in the impeller, eventually resulting in a "Swiss Cheese" appearance. Figure1  below shows two identical impellers.  The impeller on the left has been subjected to cavitation.  You can see the metal that has worn away at the edge and in the eye of the impeller.  The material at the edge is now extremely thin. Note at the 1:00 O'Clock position, that a hole has actually been worn through the impeller, and at 9:00, a crescent is completely gone.  Soon, this entire impeller would have had the "Swiss Cheese" appearance had it stayed in service.

            Figure 1

                        

Low static height (a suction lift is even worse)

High inlet friction

Large static height

Low inlet friction

Avoiding Cavitation

             Cavitation normally takes place in open systems. Figure 2 below shows the forces that determine the pressure on the water at the lowest pressure point of the system, the entrance to the impeller.

                        Figure 2

                      

Atmospheric pressure: The pressure from the atmosphere is a positive force of 14.7 PSIA. The factor to convert PSI to feet of water is 2.31, so the atmospheric pressure is 14.7 X 2.31 = 33.96 feet.

Static height: This is the height of the water level above the pump inlet. The greater this height, the more positive force is exerted on the water. (Note that if the pump must lift water from a reservoir, that the static height becomes a negative value).

Inlet friction: Strainers, piping, valves and other accessories all cause a pressure drop, contributing to a lower pressure.

NPSHr (NPSH Required) of the pump: The NPSHr is a pressure drop within the pump inlet. The NPSHr for any given pump depends only on the quantity of flow. The NPSHr is shown on the pump curve, either as a separate curve or as a value printed across the top of the curve (Taco uses the latter method).

 We can see from the diagram, that the following factors contribute to low pressure at the inlet:

The following factors that result in higher pressure at the inlet:

        To avoid cavitation, we must select the pump to ensure that the water does not fall below its vapor pressure. From the pressure diagram above, and remembering that the NPSHr of a pump is essentially another pressure loss, we can say:

Atmospheric Pressure + Static Height – Inlet Friction – NPSHr must be greater than the Vapor Pressure of the water at the temperature being pumped.

Equation 3:

Example 1:

1. Per the discussion above, the pump selection must satisfy the following formula:

31.96 + 2’ (static height) – 4’(inlet friction) – 21.5’(vapor pressure) > NPSHr.

        Mathematically, with all values expressed in feet of head, this becomes

Equation 1:  

33.96’ + Static Height-Inlet Friction-NPSHr >Vp           

        This equation is normally rewritten by rearranging terms:

Equation 2: 

 33.96’ + Static Height – Inlet Friction – Vp > NPSHr 

        We need one more modification to the formula to make it practical. We would like to have about a 2’ safety factor. Therefore, we can modify the formula as follows:

31.96’ + Static Height – Inlet Friction – Vp > NPSHr 

        The sum of the terms on the left of the equation is called the NPSH available or NPSHa. If this formula is satisfied, that is if NPSHa > NPSHr, then the selected pump should be a good selection as far as NPSH and cavitation are concerned.

        You wish to use a Taco #VI 1507 to pump 190 ° -F water from a shallow tank having a water level of 2’ above the pump inlet. You estimate that an inlet valve and strainer will have a pressure drop of about 4’. The pump is to handle 100 GPM. Is this pump suitable?

2. From the pump curve below you will note that the NPSHr at 100 GPM is 11 feet. From the vapor pressure curve, you will note that the vapor pressure is about 21.5’. Summing the terms on the left (31.96 + 2 – 4 –21.5) yields an NPSHa of 8.46’. This is not greater than the NPSHr of 11’, so this is not a suitable selection.

         Figure 3: Typical Pump Curve

Example 2:

When a Selection Is Not Suitable

Select a larger pump. Oversized pumps operate on the "left" areas of their curves, where NPSHr is lower.

Select a lower speed pump. Lower speed pumps usually have lower NPSHr requirements.

Reduce the inlet friction. Do away with unnecessary valves, accessories and fittings; oversize inlet piping.

             Figure 4       

        Use the same parameters as in Example 1, except use a water temperature of 85 ° -F. You will find that the NPSHa is over 28’! The NPSHr remains at 11’, so the VI 1507 is definitely suitable for this application. This demonstrates that it is critical to take into account the fluid temperature when considering NPSH.

        If the initial pump selection is not suitable, there are a number of possible solutions:

Lower the temperature, if practical.

Raise the receiver to increase the static height.

Field Considerations

Clarifications

The graph in Figure 4 applies to water only. For other fluids, contact FHI.

Static Height – Inlet Friction – 2’ (safety) > NPSHr

Use a low NPSH pump with a propeller inducer. This is a small propeller installed before the eye of the main impeller. Pumps made specifically for high temperature condensate often have such inducers.

        Sometimes a properly selected pump will cavitate when placed in service. There are usually two conditions that cause this:

1. The flow is not balanced, causing the pump to run out (to operate in the high flow areas of the curve). This is high NPSHr territory. The situation can be resolved by throttling the discharge valve to reduce the flow to the design level.

2. The inlet strainer or filter becomes plugged. This is common in swimming pool applications where the resulting extreme inlet pressure drop causes cavitation, even with 80° water. The solution is to keep the filters and strainers clean.

For most closed heating systems NPSH is not generally a problem. In a closed system, the expansion tank pressure replaces atmospheric pressure (31.96’) in Equation 3. The fill valve setting establishes this pressure to a level high enough to avoid cavitation.

        Note that for closed (non-vented) process systems, such as deaerators and vacuum condensers, the atmospheric pressure is replaced by vapor pressure. This changes the condition to be met to:

        Equation 4:

" Hg Vacuum PSIG

20 -9.8 157

15 -7.3 179

10 -4.9 192

5 -2.45 204

0 0 212

12 244

30 274

Approx. Boiling Temp, Degrees

Fahrenheit

Calculating the 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?

abbreviated to "feet").

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.

Units of Measure: In the U.S. system, head is measured either in PSI or in "feet of head" (usually

Pump Head is the total resistance that a pump must overcome. It consists of the following components:

Static Head: Static head represents the net change in height, in feet, that the pump must overcome.

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 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.

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 V2/2g 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 2-6 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:

1. 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.

2. 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 HeadBasically, 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.

The graphs below are from the ASHRAE Fundamentals Book. Recommended velocities are:

Pipe Sizes of 2" and Under: 2 fps minimum to 4 fps maximum

Friction Head: This is also called pressure drop. When fluid flows through any system component, friction

Pressure Head: When liquid is pumped from a vessel at one pressure to a vessel at another pressure,

Velocity Head: Accelerating water from a standstill or low velocity at the starting point to a higher velocity at

Step 2: Select pipe sizes for each segment, based on proper velocity and pressure drop.

Where P is the head loss (also called friction loss or pressure drop).

Pipe Sizes of over 2": .75 ft. of P/100 equivalent feet minimum to 4 ft. of P/100 equivalent feet maximum

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.

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

Answer: Feet in Head = 8.5 PSI X 2.31ft./PSI = 19.64 ft.

Step 4: Determine the Static Head (Open Systems Only)

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.

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’

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?

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

Long method for determining equivalent length:

The table below lists the number of equivalent feet of piping for various fittings and accessories:

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.).

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.

Shortcut method for determining equivalent length:

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.

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.

Notes

Safety factorsYou may wish to add a safety factor to the calculated head for two reasons:

Pressure Drop Corrections for Glycol.

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.

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

2. 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.

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 corrosion-causing oxygen. This increases friction. Various sources recommend total safety allowances of 15-25% 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!

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.