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Morison's Equation Subsea Pipeline Stability

Calculate stability of on bottom structures using Morison's equation (Airy Stokes and Cnoidal waves).

For horizontal stability the horizontal wave and current loads must be less than the restraining friction force. For vertical stability the specific gravity should be greater than or equal to 1.1. Wave vertical velocity and acceleration are ignored. For some structures, depending on geometry, tipping should also be considered. Tipping does not generally occur on pipelines.

Refer also to : DNV-RP-F109 On-Bottom Stability Design Of Submarine Pipelines.

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CALCULATOR : Morison's Equation Multi Layer Pipe On Bottom Stability Airy Stokes And Cnoidal Waves [PLUS]   ±

Calculate Morison's equation wave and current loads and lateral stability of cylinders resting on the seabed for Airy, Stokes and cnoidal waves.

Calculate lateral stability and wave loads for circular pipelines and tubulars, or for a user defined cross section. Wave velocity and acceleration can be calculated (Airy, Stokes or Cnoidal wave), or user defined. Wave spreading accounts for wave "choppiness". Vertical wave velocity and acceleration are ignored. Tipping of the structure is not included in the calculation (tipping is dependent on the structure geometry and is not normally a problem for pipelines).

Lateral stability is calculated as the ratio of horizontal force over friction force. The stability ratio should be less than or equal to one. The minimum stabilty ratio is assumed to occur between 0 and 90 degrees phase angle. The phase angle for minimum stability is calculated to the nearest degree. The Keulegan Carpenter number is calculated at the wave phase angle.

Use the Result Plot option to display either the wave profiles versus phase angle, wave velocity versus phase angle, wave loads versus phase angle, or stability factor versus phase angle.

Wave and current heading is measured relative to the structure. A relative heading of zero degrees is parallel to the structure, or ninety degrees is perpendicular to the structure.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Line Pipe Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • wltype : Structure Weight And Dimensions Type
    • Axu : User Defined Section Area
    • OODu : User Defined Outer Diameter
    • wu : User Defined Submerged Weight
    • SGu : User Defined Specific Gravity
  • hwtype : Angle Type
    • Φwu : User Defined Wave Heading
  • sfactype : Shape Type
    • su : User Defined Spreading Factor
  • rdtype : Reduction Factor Type
    • Rwu : User Defined Wave Reduction Factor
    • Rcu : User Defined Current Reduction Factor
  • uctype : Current Velocity Type
  • roughtype : Seabed Roughness Type
    • zou : User Defined Seabed Roughness
  • lttype : Wave Parameter Type
    • Tu : User Defined Wave Period
    • Lu : User Defined Wave Length
  • wavetype : Wave Type
  • phasetype : Wave Phase Type
    • Θu : User Defined Phase Angle
  • WTi : Pipe Liner Wall Thickness
  • ρi : Pipe And Liner Density
  • WTo : Pipe Coating Wall Thickness
  • ρo : Pipe Coating Density
  • C : Load Coefficients
  • Φs : Structure Absolute heading
  • ρc : Contents Fluid Density
  • ρe : Displaced Fluid Density
  • μf : Lateral Friction Factor
  • d : Water Depth
  • H : Wave Height
  • Vr : Reference Velocity
  • zr : Reference Height Above Seabed

Tool Output

  • Θ : Wave Phase Angle
  • Φw : Wave Heading Relative To Structure
  • η : Wave Profile Height Relative To Sea Level
  • Ah : Wave Horizontal Acceleration
  • Ax : Structure Cross Section Area
  • Fd : Drag Load
  • Ff : Maximum Lateral Friction Force
  • Fl : Lift Load
  • Fm : Inertia Load
  • Fr : Residual Lateral Friction Force
  • Fx : Horizontal Wave And Current Load
  • Fx/Ff : Stability Factor (< 1)
  • Fz : Net Vertical Weight Load (Weight Minus Lift)
  • Kc : Keulegan Carpenter Number
  • L : Wave Length
  • OOD : Pipe Outer Diameter Including Coatings
  • Rc : Current Velocity Reduction Factor
  • Rw : Wave Velocity Reduction Factor
  • SG : Pipe Specific Gravity Relative To Displaced Fluid
  • T : Wave Period
  • Vc : Current Velocity
  • Vh : Wave Horizontal Velocity
  • Vx : Total Horizontal Velocity
  • Ws : Pipe Total Weight Per Length Including Contents and Buoyancy
  • cvg : Convergence Check
  • cw : Wave Celerity
  • sf : Wave Spreading Factor
  • w : Wave Trough Height Above Seabed
  • zo : Seabed Roughness

CALCULATOR : Morison's Equation Pipe Submerged Weight (Multi Layer Pipe) [FREE]   ±

Calculate Morison's equation multi layer pipeline submerged weight and outer diameter.

Details for each layer are displayed in the ooutput at the bottom of the page.

Tool Input

  • schdtype : Line Pipe Schedule Type
  • diamtype : Line Pipe Diameter Type
    • ODu : User Defined Outside Diameter
    • IDu : User Defined Inside Diameter
  • wtntype : Line Pipe Wall Thickness Type
    • tnu : User Defined Wall Thickness
  • wltype : Pipe Weight Type
    • OODu : User Defined Outer Diameter Including External Coating
    • wu : User Defined Submerged Weight
    • SGu : User Defined Specific Gravity
  • WTi : Pipe Liner Wall Thickness
  • ρi : Pipe And Liner Density
  • WTo : Pipe Coating Wall Thickness
  • ρo : Pipe Coating Density
  • ρf : Contents Fluid Density
  • ρb : Displaced Fluid Density

Tool Output

  • OOD : Pipe Outer Diameter Including Coatings
  • SG : Pipe Specific Gravity Relative To Displaced Fluid
  • Ws : Pipe Total Weight Per Length Including Contents and Buoyancy

CALCULATOR : Morison's Equation Keulegan Carpenter Number Airy Stokes And Cnoidal Wave [FREE]   ±

Calculate Morison's equation Keulegan Carpenter number and Reynolds number for vertical or horizontal tubulars (Airy Stokes and Cnoidal waves).

The Keulegan Carpenter number and Reynolds number are calculated from the wave horizontal velocity at zero degrees phase angle. For vertical tubulars the wave reduction should be set to 1 (no wave spreading). Wave spreading accounts for multi directional waves.

Tool Input

  • wavetype : Wave Type
  • lttype : Wave Parameter Type
    • Tu : User Defined Wave Period
    • Lu : User Defined Wave Length
  • ztype : Height Above Seabed Type
    • zhu : User Defined Height
  • d : Water Depth
  • H : Wave Height
  • OOD : Pipeline Outer Diameter

Tool Output

  • Kc : Keulegan Carpenter Number
  • L : Wave Length
  • T : Wave Period
  • c : Wave Celerity
  • cvg : Convergence Check
  • w : Wave Trough Height Above Seabed

CALCULATOR : Morison's Equation Sea Water Density From Temperature And Practical Salinity [FREE]   ±

Calculate Morison's equation seawater density at atmospheric pressure from temperature, and practical salinity.

Seawater density is calculated using the TEOS-10 seawater equations. Practical salinity = parts per thousand of dissolved solids (mainly salt). The absolute salinity is taken as 35.16504 / 35 times the practical salinity. The absolute salinity anomaly δSA is ignored.

Use the Result Plot option to plot density versus temperature.

Tool Input

  • T : Seawater Temperature

Tool Output

  • ρ : Seawater Density

CALCULATOR : Morison's Equation Fresh Water Density From Temperature [FREE]   ±

Calculate fresh water density versus temperature at atmospheric pressure (IAPWS R7-97 steam table).

Use the Result Plot option to plot density versus temperature.

Tool Input

  • T : Temperature

Tool Output

  • ρ : Density