ES_dPCalc User Manual

1. Introduction

2. Basic Equations

 

2.1 Bernoulli Equation

 

2.2 Darcy Euqation

3. Friction Loss Calculation

 

3.1 Pipe

 

3.2 Nozzle and Orifice

 

3.3 Strainers

 

3.4 Valves and Fittings

4. Major Screens

 

4.1 Input

 

 4.2 Menu

 

4.3 List Output

 

4.4 Graph Output

 

4.5 Text Output


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1.  Introduction

Pressure drop calculation is one of the most frequent calculation in power engineering encompassing the pressure drop calculation of main steam piping having critical effect to power plant performance, through sump pump head calculation having no effect to power plant performance but important for successful operation of sump pump system.

Major fluid of pressure drop calculation in power engineering is water/steam and others include fuel oil, air, etc.

The pressure drop calculation referred herein is for incompressible fluid, which is simple and does not require complicated calculation like compressible fluid.   The pressure drop calculation for incompressible fluid requires only Bernoulli and Darcy equations with friction factors.

Even though the calculation method is simple, the calculation results must be accurate because the equipment such as pumps, piping, etc. is selected based on the calculation results.    For this reason, when calculating by hand, a engineer should pay careful attention to every step of calculation and further the calculation output is checked and reviewed by senior engineers several times.

ES_dPCalc program is the program to perform such an incompressible fluid pressure drop calculation with ease, reliability, repeatability and speed.

The program calculates three fluids, i.e. water/steam, liquid and ideal gas.   Water/steam calculation is performed using built-in steam table program in iso-enthalpy process; liquid calculation is performed using the specific volume(density) input by user; and ideal gas calculation is performed using ideal gas equation in iso-enthalpy process.

 

2. Basic Equations   (TOC)

2.1 Bernoulli Equation

Since the calculation is performed for incompressible fluid flow, the Bernoulli equation as below is used to relate fluid conditions between two locations.   Even though it is negligible, the effect of elevation change is considered for steam and ideal gas as well as water and liquid.

V1^2 / 2 / g + P1 * v1 + z1 = V2^2 / 2 / g + P2 * v2 + z2 + h

where,

V1, V2

: Velocity

 

P1, P2

: Static pressure

 

v1, v2

: Specific volume

 

z1, z2

: Elevation

 

h

: Friction head loww between two locations

 

g

: Gravity acceleration

 

2.2 Darcy Equation

The following Darcy equation is used to calculate the friction head losses of pipes, valves and fittings.

 dP = 0.6376 * K * W ^ 2 / d ^ 4 * v

where,

dP

: Friction head loss in pressure unit, kg/cm2

 

K

: Resistance coefficient = f * L / D

 

W

: Mass flow rate, kg/hr

 

d

: Pipe inside diameter, mm

 

v

: Specific volume of fluid, m3/kg

 

f

: Friction factor

 

L

: Pipe length, m

 

D

: Pipe inside diameter, m

According to Ref. No. 1 Darcy equation may be used for compressible fluid with restrictions as below.

1) If the calculated pressure drop is less than about 10% of the inlet pressure, reasonable accuracy will be obtained if the specific volume used in the Darcy equation is based upon either the upstream or downstream conditions, whichever are known.

2) If the calculated pressure drop is greater than about 10%, but less than about 40% of inlet pressure, the Darcy equation may be used with reasonable accuracy by using a specific volume based upon the average of upstream and downstream conditions; otherwise, the method for compressible fluid analysis may be used.

3) For greater pressure drop, such as are often encountered in long pipe lines, the method for compressible fluid analysis should be used.

ES_dPCalc calculates the pressure drop of each pipe and then, if the pressure drop of steam and ideal gas is higher than 10% of pipe inlet pressure, reiterates the pressure drop calculation using the average specific volume of pipe inlet and outlet calculated previously.  The specific volume of each pipe outlet is calculated based on iso-enthalpy process. 

Furthermore, if the pressure drop re-calculated is higher 40% of pipe inlet pressure, a user alarm is given while the calculation results is provided as they are.

 

3. Friction Loss Calculation   (TOC)

3.1 Pipe

The friction factors of Moody diagram are used for friction loss calculation and calculated as below.

1) Reynolds No.. =< 2000 ( Laminar Flow)

   f = 64 / Re

2) 2000 < Reynolds No. =< 4000 (Transient Flow)

   f = 64 / 2000

3) 4000 < Reynolds No. ( Turbulent Flow)

  1 / Sqr(f) = -2 * Log10(e/3.7 / d + 2.51 / Re / Sqr(f))  : Colebrook Equation

whrer,

f

: Friction factor

 

Re

: Reynolds number

 

e

: Pipe roughness, mm

 

d

: Pipe inside diameter, mm

The program uses a conservative friction factor for transient flow of Reynolds no. 2000.

Reference absolute roughness of various pipes are as below.

-

Drawing Tubing

: 0.0015 mm

-

Commercial Steel

: 0.05 mm

-

Asphalted Cast Iron

: 0.12 mm

-

Galvanized Iron

: 0.15 mm

-

Cast Iron

: 0.26 mm

-

Wood Stave

: 0.18 - 0.91 mm

-

Concrete

: 0.3 - 3 mm

-

Reveted Steel

: 0.91 - 9.1 mm

 

3.2 Nozzle and Orifice   (TOC)

3.2.1 Incompressible Fluid

The program uses the following equation from Ref. No. 1 for incompressible fluid flow at nozzle and orifice.

dP = 0.6376 * W^2 * v / C^2 / ß^4 / d^4

where,

dP

: Pressure drop, kg/cm2

 

W

: Mass flow rate, kg/hr

 

v

: Specific volume, m3/kg

 

C

: Flow coefficient, dimensionless

 

ß

: Ratio of small to large diameter (nozzle throat or orifice edge diameter to pipe diameter) , dimensionless

 

d

: Pipe inside diameter, mm (Not nozzle throat or orifice edge)

Flow coefficients of the program are calculated basically from the experimental equations provided in Ref. No. 2.    Ref. No. 2 provides the experimental equations for flow measurements by measuring the pressure drop between two pressure tabs.   There are two kinds of pressure tabs.   One is close-up tabs and the other is full flow tabs.   

Close-up tabs measure the pressure drop between the locations just upstream of nozzle or orifice and of vena-contracta zone.   Vena-contracta zone is the zone having the least flow area and the lowest local pressure located approximately 0.5 pipe diameter downstream of nozzle throat or orifice edge.   The pressure drop of close-up tabs does not represent the permanent pressure drop by friction of nozzle and orifice, and a pressure recovery factor is required to calculate the permanent pressure drop.

Full flow tabs measures the pressure drop between the locations just upstream of nozzle or orifice and of 8 diameter downstream, where velocity pressure at vena-contracta zone is completely recovered.   Therefore, the pressure drop of full flow tabs represent the permanent pressure drop by friction of nozzle and orifice.

In Ref. No. 2 the experimental equation of full flow tabs is provided for orifice.   However, for nozzle only the experimental equation for close-up tabs is provided.    Therefore, the program uses its own equation to calculate pressure recovery factor of nozzle.

Experimental equations for flow coefficients of nozzle and orifice provided in Ref. No. 2 are as below.

1) Flow Coefficient for Full Flow Tabs of Orifice

 C = 0.58925 + 0.2725 * ß - 0.825 * ß^2 + 1.75 * ß^3

2) Flow Coefficient for Close-up Tabs of Nozzle

 C = 0.98 / Sqr(1 - ß^4)

Having compared the results of experimental equations above with the figures of Page A-20 of Ref. No. 1, the values coincide very well for Reynolds no. 10000 and above, while below 10000 the values do not coincide.   For Reynolds no. 10000 and below the flow is laminar and a correction factor for Reynolds no. is required for flow coefficient calculation.   However, in Ref. No. 2 no experimental equation has not been provided for Reynolds no. correction.   ES_dPCalc uses the flow coefficients without Reynolds no. correction and gives user alarm when Reynolds no. is 10000 or below.

3.2.2 Compressible Fluid

The program uses the following equation from Ref. No. 1 for compressible fluid flow at nozzle and orifice.

dP = 0.6376 * Y * W^2 * v / C^2 / ß^4 / d^4

where,

dP

: Pressure drop, kg/cm2

 

W

: Mass flow rate, kg/hr

 

Y

: Expansion factor

 

v

: Specific volume, m3/kg

 

C

: Flow coefficient, dimensionless

 

ß

: Ratio of small to large diameter (nozzle throat or orifice edge diameter to pipe diameter) , dimensionless

 

d

: Pipe inside diameter, mm (Not nozzle throat or orifice edge)

Equations for compressible fluid from Ref. No. 2 is same with those of incompressible fluid except expansion factor as below.

1) Expansion Factor of Orifice Close-up Tabs

Y = 1 - (0.41 + 0.35 * ß^4) * dP / P1 / k

2) Expansion Factor of Orifice Full Flow Tabs

Y = 1 - (0.333 + 1.145 * (ß^2 + 0.7 * ß^5 + 12 * ß^13 )) * dP / P1 /k

3) Expansion Factor of Nozzle Close-up Tabs

Y = Sqr((1 - ß^4) * k / (k-1) * (P2 / P1)^(2 / k) * (1 - (P2 / P1)^((k-1) / k)) / (1 - ß^4 * (P2 / P1)^(2 / k) / (1 - P2 / P1))

where,

Y

: Expansion factor

 

dP

: Pressure drop

 

P1

: Absolute pressure at upstream tab

 

P2

: Absolute pressure at downstream tab

 

k

: Specific heat ratio (cp/cv)

Expansion factor of nozzle has the maximum value at around pressure ratio(P2/P1) of 0.5 and the pressure ratio is critical pressure ratio.   At the critical pressure the mass flow rate through nozzle reaches the maximum and the mass flow rate does not increase even though the pressure ratio is lowered further.   The flow is called as choked flow.

ES_dPCalc gives user alarm when the mass flow rate input by user exceeds the choked flow rate of a nozzle if exists.

In case of orifice there is no critical pressure or choked flow.    The mass flow rate through orifice increase as the downstream pressure is lowered till absolute zero pressure.    In case of nozzle flow, there is little friction so that when the pressure is lowered flowing through nozzle the specific volume of compressible fluid is increased; eventually the fluid velocity reaches sonic velocity and mass flow rate does not increase further.  However, in case of orifice the frction heat generated at orifice edge by high velocity, is absorbed into flowing fluid and increases fluid temperature so that the mass flow rate per unit area is decreased and choked-flow does not occur.

Even though there is no choked-flow in orifice, the flow increase rate at pressure ration of 0.5 and below is considerably low and flow increase from pressure ratio of 0.5 to 0 is approximately 12 percents only.

The expansion factor equation for orifice close-up tabs above is well in line with the figure of Page A-21, Ref. No. 1 and the shows low flow increase at pressure raio of 0.5 and below.   However, the expansion factor equation for orifice full flow tabs at pressure raio of 0.5 and below strangely shows decrease of flow, while at pressure ratio of 0.5 and above the equation represents.    Therefore, the equation does not represent actual flow at pressure ratio of 0.5 and below.    For this reason, ES_dPCalc uses the expansion factor equation of orifice full flow tabs from pressure ratio of 1 to the pressure ratio representing the maximum expansion factor, while for the pressure ratio below that representing the maximum expansion factor the expansion factor equation for orifice close-up tabs is used in conjunction with pressure recovery factor generally used in engineering field.

Meanwhile, since there must be the maximum mass flow in orifice which corresponds to zero exit pressure, the program provides user alarm when the mass flow input by user exceeds the maximum mass flow of orifice, if exists.

 

3.3 Strainers   (TOC)

For calculation of pressure drop of strainers, the program uses the following equation.

dPc = C * Ct * V^2 / v * Cm * Cv

where,

dPc

: Pressure drop of clean strainer, kg/cm2

 

C

: Conversion factor

 

Ct

: Strainer type coefficient

 

V

: Pipe fluid velocity, m/sec

 

v

: Fluid specific volume, m3/kg

 

Cm

: Mesh correction factor

 

Cv

: Viscosity correction factor

Pressure drop of strainers increases by foreign objects in operation so that strainers are cleaned periodically by measuring differential pressure over strainers.   For this reason, when calculating pressure drop of strainers, a certain amount of clogged condition is assumed.    

The program calculates the pressure drop of clogged strainers by the following equation.

dP = dPc / (1 - %Clogging / 100)^2

 

3.4 Valves and Fittings

The program calculates the pressure drop of valves and fittings by using the resistance coefficients of Ref. No. 1.

 

4. Major Screens   (TOC)

4.1 Input Screen

ES_dPCalc calculates pressure drop of a single piping system with upstream fluid conditions known.

4.1.1 Fluid

Three kinds of fluid can be calculated by the program.   The fluids are steam/water, liquid and ideal gas, and user can select the fluid to be calculated at [Set]-[Calc] menu.   All of these fluids are calculated as incompressible fluids even though steam and ideal gas are actually compressible fluids.    Calculation of steam and ideal gas as incompressible fluids  means that the specific volume of the fluid is considered as constant in pressure drop calculation of a pipe, while the specific volume for calculation of the next pipe is recalculated based on iso-enthalpy process.   The results of iso-enthalpy process calculation for steam and ideal gas actually approach to compressible fluid calculation results when a piping system is divided into many small length of pipes.   Additionally the program has the following distinct functions.

1) Check of water flashing

When the fluid is water and the calculated pressure at each pipe outlet is less than the saturation pressure at local temperature based on iso-enthalpy process, a user alarm is provided.

2) Nozzle/orifice calculation

Nozzle and orifice in steam or ideal gas pipe are calculated as compressible fluid method using expansion factors.   Therefore, nozzle and orifice in steam and ideal gas is calculated actually by compressible fluid method.   The specific heat ratio input is used only for expansion factors calculation of nozzle and orifice.

3) Excess pressure drop warning for each pipe calculation

As explained Clause 2.2 above, the excess pressure drop above 10% and 40% of pipe inlet pressure is checked for each pipe, not for entire piping system.

4.1.2 Upstream Fluid Conditions

Upstream fluid conditions except mass or volume flow rate of steam and water should be entered by using [Steam Table] command button.   Even thought specific heat ratio of steam and water is provided by the built-in steam table, user can edit the value.

Pressure and specific volume are required when use selects [Liquid] fluid, and additionally specific heat ratio is required for [Ideal gas] fluid selection.    Kinematic viscosity of fluid is calculated automatically by the program using the specific volume and absolute viscosity inputs.

4.1.3 Pipe Iso-metric File Open and Edit Buttons

The input of pipe iso-metric information should be performed using the sub-program of ES_PipeIso, of which user manual you may find in ES_PipeIso User Manual web page.   [Pipe Iso-metric File Open] command button is used for opening a existing *.pip file, while [Pipe Iso-metric File Edit] command button is used to open [ES_PipeIso] window for editing a already-opened *.pip file.    A existing *.pip file may be open in [ES_PipeIso}window using its own file open menu.

When *.pip file is open by [Open] command button, the units of the *.pip file keep their original values, while the calculation in the mother program is performed in the mother program's units.    When *.pip file is open in [ES_PipeIso] window, the units of *.pip file are converted into the mother program's units, and then if user saves the *.pip file the units of *.pip file are saved as converted.

Please note that the *.pip file has to be saved before exiting [ES_PipeIso] window in order to apply the changes made in the window to the calculation in  mother program.

The pipe iso-metric screen at the right shows only iso-metric drawing currently opened.

 

4.2 Menu   (TOC)

[File] menu has [New], [Open], [Save], [Save As] and [Exit] items with four file items lately used.

[Run] menu has only [Start] item which uses function key [F5] as a short key.

[Set] menu has [Title], [Unit], [Calc], [Text Output] and [Graph Output] items.

In [Set]-[Title] item, two titles may be input as [Title 1] and [Title 2], which also are shown in Text Output and Graph Output.

In [Set]-[Unit] item, the unit of calculation is set.

In [Set]-[Calc] item, the kinds of fluid and type of flow are selected.

[Set]-[Text Output] has a check box sub-menu of [show calculation details of pipe].

[Set]-[Graph Output] item shows a form to set the parameters of graph output.

 

4.3 List Output   (TOC)

 

 List output is to show the calculation results in a list to provide easy look of results.   Upper list show the information and calculation results of all pipes and lower list shows the information and calculation results of valves and fittings for the pipe selected in the upper list.    

List output is not printed.

 

4.4 Graph Output   (TOC)

Graph output shows the calculation inlet and outlet pressures on iso-metric drawing.    The graph output can be printed.

 

 4.5 Text Output   (TOC)

 

[Text Output Screen] shows the calculation result details and can be printed.

 

References :   (TOC)

1. Crane Technical Paper No. 410, Flow of Fluids, Crane Co., 1977

2. Principles and Practice of Flow Meter Engineering by L. K. Spink, Foxboro

(end)


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