Determining Flowrates Through Pump and System CurvesFor complete documentation click here

Parameters Legend

1000 Parameters specified by userLiquid viscosity (Pa s) 0.001 Intermediate calculations

9.81 Cells used in Goal SeekPipe diameter (m) 0.1Pipe length (m) 10Pipe roughness (m) 0.0001

0.007854

Pump Curve CoefficientsHpump = 0.1 -0.001 Q 0 Q^2

CalculationsGuess value for liquid velocity 0.943791 Set to an initial guess valueReynolds number 94379.13 With Goal Seek, vary this number…Friction factor (Haaland) 0.022083Pump curve 0.100254System curve 0.099993Pump curve - System curve 0.000262 …so that this number is zero

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Liquid density (kg m-3)

Gravity (m s-2)

Pipe cross-sectional area (m2)

Determining Flowrates Through Pump and System Curves

Balancing a Pump Curve against a System Curve

IntroductionThis article will demonstrate how you can balance a pump curve against a system curve to calculate liquid velocity with Excel.

First, we'll develop the equations that determine the liquid velocity in a simple pump and pipe system. Then we'll discuss how these equations be solved using Excel's Goal Seek feature. Finally, we'll show Visual Basic code that can be used to automate Goal Seek so that any parameter change will automatically calculate the new liquid velocity.

Pump and Pipe SystemConsider a centrifugal pump receiving liquid from a reservoir and forcing liquid through a pipe to a reservoir.

First consider the pump. Its flowrate-head curve is can be described by a polynomial derived from empirical data, where a, b and c are best-fit coefficients, and Q is the volumetric flowrate

Equation 1

But the volumetric flowrate is

Equation 2

where A is the cross-sectional area of the pipe and V is the liquid velocity through the pipe. Substituting Equation 2 into Equation 1 to eliminate Q gives

Equation 3

This equation now describes the head produced by the pump as a function of the liquid velocity through the pipe.

Now consider the pipe. Frictional head loss through the pipe can be described by the Bernoulli equation and written as

Equation 4

Equation 5

where Re is the Reynolds Number.

The spreadsheet can be downloaded here, but read the rest of this article if you'd like to understand the theory.

We'll call Equation 4 the System Curve. f is the friction factor, given by the Haaland Equation.

Equation 6

The Haaland equation is only valid in turbulent flow, i.e. if the Reynolds Number is over 2500.

For our pump and pipe system, the pump head is equal to the head loss in the pipe. Hence

Equation 7

We can now use Excel to find the liquid velocity that satisfies Equation 7 (effectively determining the intersection between the pump curve and the system curve).

Excel ImplementationThe Excel spreadsheet uses this cell coloring convention.

You should now have the correct value of the liquid velocity.

Step 1. First define the parameters and calculate the cross-sectional area of the pipe.

Step 2. Now define the coefficients of the pump curve

Step 3. Set up the calculations required by Goal Seek

Step 4. Go to Data > What-If Analysis > Goal Seek. Make the changes such that we find the liquid velocity that makes difference between pump curve and the system curve equal to zero.

Ensure that the Reynolds number is greater than 2500 so that our assumption of turbulent flow (and hence the use of the Haaland equation) is verified.

Visual Basic Macro to Automate Goal SeekIf you're really keen, you can use Visual Basic to automate Goal Seek.

Private Sub Worksheet_Change(ByVal Target As Range)

Dim bSuccess As Boolean

On Error Resume Next

bSuccess = Range("C23").GoalSeek(0, Range("c18"))

On Error GoTo 0

If Not bSuccess Then

MsgBox "Goal Seek Failed"

End If

End Sub

Whenever any value in the worksheet is changed, the Worksheet_Change() event is initiated . The VB code then asks GoalSeek() to find the liquid velocity ("C18") that makes the difference between the pump and system curve ("C23") equal to zero.

Balancing a Pump Curve against a System Curve

This article will demonstrate how you can balance a pump curve against a system curve to calculate liquid velocity with Excel.

First, we'll develop the equations that determine the liquid velocity in a simple pump and pipe system. Then we'll discuss how these equations be solved using Excel's Goal Seek feature. Finally, we'll show Visual Basic code that can be used to automate Goal Seek so that any parameter change will automatically calculate the new liquid velocity.

Consider a centrifugal pump receiving liquid from a reservoir and forcing liquid through a pipe to a reservoir.

First consider the pump. Its flowrate-head curve is can be described by a polynomial derived from empirical data, where a, b and c are best-fit coefficients, and Q is the volumetric flowrate

where A is the cross-sectional area of the pipe and V is the liquid velocity through the pipe. Substituting Equation 2 into Equation 1 to eliminate Q gives

This equation now describes the head produced by the pump as a function of the liquid velocity through the pipe.

Now consider the pipe. Frictional head loss through the pipe can be described by the Bernoulli equation and written as

The spreadsheet can be downloaded here, but read the rest of this article if you'd like to understand the theory.

We'll call Equation 4 the System Curve. f is the friction factor, given by the Haaland Equation.

The Haaland equation is only valid in turbulent flow, i.e. if the Reynolds Number is over 2500.

For our pump and pipe system, the pump head is equal to the head loss in the pipe. Hence

We can now use Excel to find the liquid velocity that satisfies Equation 7 (effectively determining the intersection between the pump curve and the system curve).

You should now have the correct value of the liquid velocity.

. First define the parameters and calculate the cross-sectional area of the pipe.

. Make the changes such that we find the liquid velocity that makes difference between pump curve and the system curve equal to zero.

Ensure that the Reynolds number is greater than 2500 so that our assumption of turbulent flow (and hence the use of the Haaland equation) is verified.

Visual Basic Macro to Automate Goal SeekIf you're really keen, you can use Visual Basic to automate Goal Seek.

Whenever any value in the worksheet is changed, the Worksheet_Change() event is initiated . The VB code then asks GoalSeek() to find the liquid velocity ("C18") that makes the difference between the pump and system curve ("C23") equal to zero.

First, we'll develop the equations that determine the liquid velocity in a simple pump and pipe system. Then we'll discuss how these equations be solved using Excel's Goal Seek feature. Finally, we'll show Visual Basic code that can be used to automate Goal Seek so that any parameter change will automatically calculate the new liquid velocity.

First consider the pump. Its flowrate-head curve is can be described by a polynomial derived from empirical data, where a, b and c are best-fit coefficients, and Q is the volumetric flowrate

We can now use Excel to find the liquid velocity that satisfies Equation 7 (effectively determining the intersection between the pump curve and the system curve).

. Make the changes such that we find the liquid velocity that makes difference between pump curve and the system curve equal to zero.

Whenever any value in the worksheet is changed, the Worksheet_Change() event is initiated . The VB code then asks GoalSeek() to find the liquid velocity ("C18") that makes the difference between the pump and system curve ("C23") equal to zero.

First, we'll develop the equations that determine the liquid velocity in a simple pump and pipe system. Then we'll discuss how these equations be solved using Excel's Goal Seek feature. Finally, we'll show Visual Basic code that can be used to automate Goal Seek so that any parameter change will automatically calculate the new liquid velocity.