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CALCULATOR MODULE : Hot Pipeline Temperature Decay Curve   ±
CALCULATOR MODULE : Pump Delta Pressure Versus Flowrate Curve   ±

Calculate pump curve (pressure versus flowrate) for viscous and non viscous flow. Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt.

The pump curve is calculated using a three term quadratic curve (ΔP = ΔPo - A Q - B Q^2) calculated from the shut-in delta pressure (zero flow), the maximum flowrate, and the best efficiency point (BEP).

Note : The delta stagnation pressure is required for the calculation. Some pump curves show delta static pressure (the pressure equals zero at maximum flow) instead of delta stagnation pressure (the pressure equals the dynamic pressure at maximum flow). Use the pump pressure and head conversion calculator to convert delta static pressure to delta stagnation pressure.

The pump flowrate, delta pressure, inside diameter and efficiency can be scaled for a geometrically similar pump using the affinity or similarity laws. For geometric similarity the pump inside diameter should be proportional to the impeller diameter. In practice the pump inside diameter is usually limited to pipe sizes (eg 10 inch, 12 inch etc). The impeller diameter is also normally limited to fixed sizes. It is often more practical to select an available pump inside diameter and impeller diameter, and vary the pump speed. Pump efficiency scaling is based on an empirical formula. Pump efficiency scaling should be combined with flowrate scaling. Pump efficiency varies with flowrate. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Specific Speed   ±

Calculate pump specific speed from pump rotational speed, flowrate and delta pressure.

The pump specific speed is calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency.

`Ns = n Q^(1/2) (ρ/(ΔP))^(3/4) = n (Q^(1/2)) / (g.ΔH)^(3/4) `

where :

Ns = pump specific speed
n = pump rotational speed
Q = flow rate at BEP
ρ = fluid density
ΔP = delta pressure at BEP
ΔH = delta head at BEP
g = gravity constant
BEP = best efficiency point

The pump specific speed can be used to determine the type of pump which should be used (multi stage, centrifugal, mixed flow or axial). The pump size and speed can then be determined from the pump coefficients using the affinity or similarity laws. Usually, a known pump is scaled to operate at the BEP with the required design flow rate and delta pressure.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Affinity Or Similarity Law Scaling   ±

Calculate pump scaling from pump speed and impeller diameter using the affinity or similarity laws for pumps and combined pump and piping systems.

If the operating parameters of a pump are known (pump 1), the operating parameters for a geometrically similar pump (pump 2) which is operating with the same pump coefficients can be calculated from the pump speed and impeller diameter ratios using the affinity or similarity laws .

`(P2)/(P1) = (ρ2)/(ρ1) ((n2)/(n1))^2 ((d2)/(d1))^2 `
`(Q2)/(Q1) = (n2)/(n1) ((d2)/(d1))^3 `
`(1-E2)/(1-E1) = ((d1)/(d2))^(1/4) `

where :

P1 and P2 = the delta pressure (ΔP) for pump 1 and 2
Q1 and Q2 = the flowrate for pump 1 and 2
n1 and n2 = the rotation speed for pump 1 and 2
d1 and d2 = the impeller diameter for pump 1 and 2
ρ1 and ρ2 = the fluid density for pump 1 and 2
E1 and E2 = the pump efficiency at BEP for pump 1 and 2
BEP = Best Efficiency Point

For geometric similarity the pump inside diameter should be proportional to the impeller diameter. In practice the pump inside diameter is usually limited to standard pipe sizes (eg 10 inch, 12 inch etc). The impeller diameter is also normally limited to fixed sizes. It is therefore often more practical to select an appropriate pump inside diameter and impeller diameter, and vary the pump speed. Pump efficiency scaling is based on an empirical formula. Pump efficiency scaling should be combined with flowrate scaling. Pump efficiency varies with flowrate. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3).

For cases where the impeller size is varied (impeller trim) and the pump ID is constant, the flowrate can be calculated by:

`(Q2)/(Q1) = (n2)/(n1) (d2)/(d1) `

For cases where both the impeller diameter and the pump ID vary, but not in proportion, the flowrate can be calculated by:

`(Q2)/(Q1) = (n2)/(n1) (d2)/(d1) ( (ID2)/(ID1))^2 `

where :

ID1 and ID2 = the pump ID for pump 1 and 2

A known pump can be scaled to operate at the best efficiency point (BEP) with a required design flow rate and delta pressure using the affinity laws. The pump curve is calculated using a three term quadratic equation

`ΔP = ΔPo - A Q - B Q^2`

.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Cavitation And NPSH   ±

Calculate pump cavitation number (Ca), nett positive suction pressure (NPSP), and suction specific speed (Nss).

`Nss = n* Q*^1/2 (ρ/NPSP*)^3/4 `
`NPSP* = Ps + 1/2 ρ V^2 - Pv = Ps + Pd - Pv = Pg - Pv `
`Ca = (Ps - Pv) / Pd `

where :

Nss = pump suction specific speed at BEP `
`NPSP* = nett positive suction pressure at BEP `
`Ca = cavitation number `
`n* = pump rotational speed at BEP `
`Q* = flowrate at BEP `
`Ps = static pressure at inlet `
`Pg = stagnation pressure at inlet `
`Pd = dynamic pressure at inlet `
`Pv = vapour pressure `
`V = fluid velocity at inlet `
`ρ = fluid density

The pump suction specific speed and nett positive suction pressure are calculated at the best efficiency point (BEP), the point on the pump curve with the greatest efficiency. The pump suction specific speed, nett positive suction pressure and cavitation number can be used to determine the onset of cavitation. The minimum recommended values are dependent on the pump geometry and operating conditions, and should be obtained from the manufacturer.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Best Efficiency Point (BEP) Scaling   ±

Calculate pump speed, impeller diameter and inside diameter to operate a known pump at the design delta pressure and flowrate, and at the best efficiency point (BEP).

The reference pump specific speed can be calculated by:

`Ns = nr.Qr^(1/2) ((ρr)/(ΔPr))^(3/4) `

where :

Ns = reference pump specific speed at BEP
nr = reference pump rotational speed at BEP
Qr = reference flow rate at BEP
ρr = reference fluid density
ΔPr = reference delta pressure at BEP

The flowrate and delta pressure can be calculated from the pump specific speed, and design flowrate and delta pressure using the affinity or similarity laws. For geometric similarity the pump inside diameter should be proportional to the impeller diameter.

`np = (Ns) / (Qd^(1/2)) ((ΔPd) / (ρd))^(3/4) `
`dp = dr √((ΔPd) / (ΔPr) (ρr) / (ρd)) (nr) / (np) `
`Dp = ((dp) / (dr)) Dr `

where :

np = scaled pump rotational speed
dp = scaled impeller diameter
dr = reference impeller diameter
ρd = design fluid density
Qd = design flow rate
ΔPd = design delta pressure
ΔPr = reference delta pressure at BEP
Dp = scaled pump inside diameter
Dr = reference pump inside diameter

For this case the scaled pump matches the design delta pressure and flowrate at BEP. In practice the pump inside diameter is usually limited to pipe sizes (eg 10 inch, 12 inch etc). Similarly, the impeller diameter is also normally limited to fixed sizes. It is therefore often more practical to select an available pump inside diameter and impeller diameter, and vary the pump speed. This means that it is possible to match either the design delta pressure or the design flowrate, but not both. For example to calculate the pump speed to match the design flowrate at BEP:

`np = nr ((Qd) / (Qr)) ((dr) / (dp)) ((Dr) / (Dp))^2 `

To calculate the pump speed to match the design delta pressure at BEP:

`np = nr √( (ΔPd) / (ΔPr) (ρr) / (ρd) ((dr) / (dp))^2 ) `

Usually a pump speed is selected so that the scaled delta pressure and flowrate are greater than or equal to the design delta pressure and flowrate. Check that ΔPp-ΔPd and Qp-Qd are both greater than or equal to zero.

The design pump specific speed can be calculated from the design pump speed, delta pressure and flowrate, and can be used to determine the type of pump which should be used (multi stage, centrifugal, mixed flow or axial).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Hydraulic And Input Power   ±

Calculate pump hydraulic power and input power or motive power from flowrate and delta pressure.

`Wh = Q ΔP `
`Wi = (Wh) / E `

where :

Wh = hydraulic power
Wi = input power or motive power
Q = volume flowrate
ΔP = delta stagnation pressure
E = efficiency factor

The pump efficiency accounts for energy losses in the pump such as friction etc. The input power is the motive power required to drive the pump (the size of motor). To calculate the energy required (eg electrical energy) the efficiency factor should equal the pump efficiency times the motor efficiency.

`E = Ep.Ee `

where :

Ep = pump efficiency factor
Ee = electric motor efficiency factor

Pump efficiency varies with flowrate. The flowrate with maximum efficiency is referred to as the best efficiency point (BEP).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

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CALCULATOR MODULE : Pump Viscosity Correction   ±
CALCULATOR MODULE : Pump Variable Frequency Drive (VFD) Design Speed   ±

Calculate pump variable frequency drive (VFD) speed to match pump design pressure and design flowrate for viscous and non viscous fluids.

The design pump speed is calculated using the affinity or similarity laws.

`(ΔP2)/(ΔP1) = (ρ2)/(ρ1) (n2)/(n1)^2 `
`(Q2)/(Q1) = (n2)/(n1) `

where :

ΔP1 and ΔP2 = the delta pressure for pump 1 and 2
Q1 and Q2 = the flowrate for pump 1 and 2
n1 and n2 = the rotation speed for pump 1 and 2
ρ1 and ρ2 = the fluid density for pump 1 and 2

The pump curve is calculated using a three term quadratic curve:

`ΔP = ΔPo (1 - A Q - B Q^2 ) `

where :

ΔPo = the shut in delta pressure
A and B are constants

The design pump speed can be calculated by solving the quadratic equation for the design delta pressure and flowrate. For fluids with a kinematic viscosity ν > 20 cSt, the viscous calculation is recommended.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump And Piping System Curve   ±

Calculate pump and piping combined system curve (pressure versus flowrate) for viscous and non viscous flow.

For a combined pump and piping system, the flowrate reaches an equilibrium so that the pump delta pressure equals the piping delta pressure. If the pump shutin delta pressure is less than or equal to the piping shutin delta pressure, the flowrate is zero.

The piping delta pressure is calculated from the change in elevation, and piping friction losses calculated from the Moody diagram. The inlet conditions can be calculated for either the liquid depth at the inlet in a tank or reservoir, or the stagnation pressure at the inlet. The outlet conditins can be calculated for either an exit to atmosphere, the liquid depth at the outlet in a tank or reservoir, or the stagnation pressure at the outlet.

Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt. Pump performance is normally measured using water (density is assumed to be 1000 kg/m^3).

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Pump Efficiency Curve   ±

Calculate pump efficiency curves for viscous and non viscous flow. Viscous flow is recommended if the kinematic viscosity is greater than 20 cSt.

The efficiency curve is calculated using a three term cubic equation calculated from the best efficiency point, and the maximum flowrate:

`E = A Q + B Q^2 + C Q^3 `

where :

Q = the flowrate
A, B and C are constants

The efficiency is assumed to be zero at shut-in. The maximum efficiency occurs at the best efficiency point.

PLEASE NOTE : The pump calculators are currently being updated. Apologies for any inconvenience.

Change Module :

CALCULATOR MODULE : Maths Polynomial   ±

Calculate polynomial coefficients, roots or zeros, maximum and minimum, points of inflection, and interpolate polynomial value, slope and curvature.

Polynomials can be calculated for linear (first order), quadratic (second order), cubic (third order), quartic (fourth order), quintic (fifth order), sextic (sixth order), septic (seventh order), octic (eighth order) or nth degree. For polynomials with all real roots, all roots can sometimes be solved simultaneously using the Durand Kerner method. In other cases solve for individual roots. The maximum or minimum points (slope equals zero) and the inflection points (curvature equals zero) can also be calculated. Use a plot page to plot the polynomial and identify the approximate root values if any.

Lagrange's method is used to interpolate between data points. This method is useful for interpolating between data points, but can give poor results when extrapolating outside the data range. Evenly spaced data points can result in cyclic behaviour.

Polynomial coefficients can be calculated from the real roots, and the nth coefficient. There are an infinite number of polynomials with the same roots. The nth coefficient is required in order to calculate unique coefficients. This method only applies if all of the roots are real. Polynomial coefficients can also be calculated from XZ data points.

Change Module :

CALCULATOR MODULE : Maths Polynomial Interpolation   ±

Calculate polynomial value, slope and curvature by interpolating between data points.

Lagrange polynomial interpolation is calculated by breaking up the data into sections and using a linear, quadratic, cubic, quartic, or quintic polynomial for each section. The cubic interpolation is recommended for most situations. The nth degree polynomial option uses all of the data points in a single section. The Lagrange method calculates the polynommial value only (not the slope or curvature), and does not calculate the polynomial coefficients, roots, maximum and minimum, or points of inflection.

Polynomial coefficients can be calculated from XZ data points using matrix factorisation using all of the data points. The polynomial value, slope and curvature are then calculated from the coefficients.

Cubic splines are used to fit a cubic polynomial between each set of XZ data points. The cubic spline method calculates the polynommial value only (not the slope or curvature), and does not calculate the polynomial coefficients, roots, maximum and minimum, or points of inflection.

Note : Using high order polynomials may cause harmonics on the interpolation line, particularly if the data points are evenly spaced. Extrapolated results calculated from outside the range of data points should be used very carefully, particularly for high order polynomials. Use the plot options to check the behaviour of the polynomial outside the data range.

Multiple roots, maximum and minimum or points of inflection are calculated using the Durand Kerner method. This method is only valid if all roots, maximum and minimum or points of inflection are real.

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CALCULATOR MODULE : Maths Linear Regression   ±

Calculate the best fit line for scatter data points using the least squares linear regression method. The curve does not have to pass through each data point.

For straight line or linear curves (Z = A x + B) the regression is performed directly on the X and Z data values. For power curves (Z = A x^B) the regression is performed on the ln(X) and ln(Z) values. For logarithmic curves (Z = ln(X)) the regression is performed on the ln(X) and Z values. For exponential curves (Z = A e^B) the regression is performed on the X and ln(Z) values. For the user defined transform (Z = A f(X) + B) the regression is performed on f(X) and Z where f(X) is the user defined transform.

The X and Z offsets can be used to change the origin for log values (ln(X - Xo) and ln(Z - Zo)) and user defined transform (f(X - Xo)). The offsets are not used for the X and Z values.

The Z unit value is applied for the log of negative Z values. The Z unit value is not applied for X and Z values, or for user defined transforms (user defined transforms should account for the sign of the data points).

The regression data and regression parameters are displayed in the output view at the bottom of the page. The correlation coefficient r is a measure of how well the curve fits the data points (close to one is better). Extrapolated values should be used carefully.

Enter vector data as X,Z pairs separated by a comma or tab, with each pair on a new line. Or copy and paste the data points from a spreadsheet. Enter array data X and Z values as separate comma or tab separated lists. Store file data to a text file as comma or tab separated pairs (X,Z), with each pair on a new line (or copy and past cells from a spreadsheet). Refer to the example text file in resources.

Use the data plot option on the plot bar to display the data points and the best fit line.

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CALCULATOR MODULE : Maths Lagrange Polynomial Interpolation   ±

Calculate a Lagrange polynomial to fit the data points. The polynomial passes through all the data points.

Higher order polynomials may be cyclic (lower order polynomials are preferred). The slope and curvature are not continuous. Extrapolated values should be used carefully.

For vector data calculators enter the data as X,Z pairs separated by a comma or tab, with each pair on a new line. Or copy and paste the data points from a spreadsheet. For array data calculators, enter the X and Z values as separate comma or tab separated lists. Use the data plot option on the plot bar to display the data points and the Lagrange polynomial.

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CALCULATOR MODULE : Maths Cubic Spline   ±

Calculate a cubic spline to fit the data points.

The cubic spline is calculated so that the slope and curvature match at each data point. The end points are assumed to have zero curvature. Extrapolated values should be used carefully.

For vector data calculators enter the data as X,Z pairs separated by a comma or tab, with each pair on a new line. Or copy and paste the data points from a spreadsheet. For array data calculators, enter the X and Z values as separate comma or tab separated lists. Use the data plot option on the plot b(u, m)ar to display the data points and the cubic spline.

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CALCULATOR MODULE : Maths Curve Data Check   ±

Calculate smoothed data values from raw input data.

The calculator is intended for checking and smoothing digitised plot data. Use the Result Plot option to display the data value, slope and curvature. The value, slope and curvature curves should be smooth. Sudden changes in slope and or curvature indicate possible faulty values.

Options include data order (ascending or descending data), plot axies (Z versus X or X versus Z), smoothing type, and whether to smooth the maximum and minimum values. Smoothing uses a simple weighted mean value.

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CALCULATOR MODULE : Weibull Gumbel And Frechet Extreme Event Probability   ±

Calculate extreme event amplitude and return period from return period data using the Weibull, Gumbel and Frechet probability distributions.

A best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for X versus Z instead of Z versus X (the X and Z values are swapped). The three parameter distribution amplitude offset is a minimum amplitude. The regression data points and regression parameters are displayed in the output view at the bottom of the page. Use the Data Plot option on the plot bar to display the data points and the best fit line.

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CALCULATOR MODULE : DNVGL RP C203 Fatigue   ±

Calculate DNVGL-RP-C203 fatigue allowable number of cyles from stress amplitude, or allowable stress amplitude from number of cycles.

The calculated SN curves include reduction factors for temperature, thickness, and system effects. The stress concentration factor is in addition to the embedded SCF factors. A user defined SCf is often used with a base curve with embedded SCF = 1, such as curve D. The design fatigue factor (DFF) can be used to account for accessibility and other risk factors. The DFF is applied to the number of cycles, and shifts the apparent SN curve to the left. Use the Result Plot option to display the selected SN curve.

Reference : DNVGL-RP-C203 Fatigue Design Of Offshore Steel Structures (Download from the DNVGL website)

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Related Modules :

CALCULATOR MODULE : DNVGL RP C203 Pipeline Fatigue Stress   ±
CALCULATOR MODULE : DNVGL RP C203 Simplified Fatigue Damage   ±
CALCULATOR MODULE : DNVGL RP C203 Fatigue Stress Limit   ±
CALCULATOR MODULE : DNVGL RP C203 Accumulated Fatigue Damage Miner's Law   ±
CALCULATOR MODULE : DNVGL RP C203 Fatigue Stress Concentration Factor   ±
CALCULATOR MODULE : DNVGL RP C203 Fatigue Stress Amplitude   ±
CALCULATOR MODULE : DNVGL RP C203 Fatigue System Effect   ±
CALCULATOR MODULE : DNVGL RP C203 Mean Stress Factor   ±
CALCULATOR MODULE : DNVGL RP C203 Tubular Fatigue Stress   ±
CALCULATOR MODULE : DNVGL RP C203 Flat Plate Fatigue Stress   ±
CALCULATOR MODULE : DNVGL RP C203 Bolt Fatigue Stress   ±
CALCULATOR MODULE : Ocean Wave Probability And Return Period   ±

Calculate ocean wave height and period from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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CALCULATOR MODULE : Ocean Current Probability And Return Period   ±

Calculate ocean current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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CALCULATOR MODULE : Ocean Wave And Current Probability And Return Period   ±

Calculate ocean wave height, wave period and current velocity from return period data using the Weibull, Gumbel or Frechet probability distributions.

The three parameter distribution and Z offset is used to account for a minimum value, the smallest event which can occur in any sample period. The best fit line is calculated for the data points using the least squares linear regression method. The regression is calculated for return period versus amplitude (the X and Z values are swapped). Use the Data Plot option on the plot bar to display the data points and the calculated best fit. The regression data points and regression parameters are displayed in the output view at the bottom of the page.

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