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Morison's Equation Wave Slam

Calculate wave slamming loads on submerged structures using Morison's equation (Airy Stokes and Cnoidal waves).

Wave slamming loads are due to the impact of the wave surface against the structure. The combined wave loading includes wave drag load, inertia load, and lateral load. For horizontal structures buoyancy load is also included. Wave slamming loads occur on the front of the wave only (phase angle ≤ 180 degrees). Wave loads are calulated at the wave surface (wave surface height is calculated from wave phase angle).

theoretical wave slamming load coefficient varies between π and 2 π. The calculated wave slamming load is force per length (unit force). To calculate the total load (force) on a vertical structure the wave curl coefficient can be used

`Lt = λ Hw Fs `

where :

Lt = the total load (force)
λ = the wave curl coefficient
Hw = the wave height
Fs = the slamming load (force per length)

The wave curl coefficient accounts for the variation in time for the wave to contact the whole vertical structure. Typical values of the wave coefficient λ vary from 0.4 to 0.9.

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CALCULATOR : Morison's Equation Vertical Cylinder Wave Slamming Load Airy Stokes And Cnoidal Wave [PLUS]   ±

Calculate Morison's equation combined wave slamming loads and wave loads on vertical cylinders for Airy, Stokes and cnoidal waves.

Wave slamming loads occur on the front side of the wave only, and are due to the impact of the wave surface against the structure. The combined wave loading includes wave drag load, inertia load and lateral load. The wave velocity and acceleration is calculated at the wave surface, hence the height above the seabed varies with wave phase angle. Wave loads can either be calculated from phase angle, or calculated for the maximum load magnitude. Loads are force per length (unit loads). The maximum load is assumed to occur between 0 and 90 degrees phase angle. The phase angle for maximum load is calculated to the nearest degree. The current is assumed to be parallel to the waves. Wave spreading is ignored.

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

Tool Input

  • 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 Angle Type
    • Θu : User Defined Phase Angle
  • C : Load Coefficients
  • OOD : Outer Diameter Including Layers
  • d : Water Depth
  • H : Wave Height
  • Vr : Reference Velocity
  • zr : Reference Height Above Seabed
  • ρ : Fluid Density

Tool Output

  • Θ : Wave Phase Angle
  • Φ : Force Heading Relative To Wave Direction
  • η : Wave Profile Height Relative To Sea Level
  • Ah : Wave Horizontal Acceleration
  • Fd : Drag Force
  • Fl : Lateral or Lift Force
  • Fm : Inertia Force
  • Fs : Wave Slamming Force
  • Ft : Total Force
  • Fx : Inline Force
  • Kc : Keulegan Carpenter Number
  • L : Wave Length
  • T : Wave Period
  • Vc : Current Velocity
  • Vh : Wave Horizontal Velocity
  • Vt : Total Horizontal Velocity
  • c : Wave Celerity
  • cvg : Convergence Check
  • w : Wave Trough Height Above Seabed
  • zh : Height Above Seabed
  • zo : Seabed Roughness

CALCULATOR : Morison's Equation Horizontal Cylinder Wave Slamming Load Airy Stokes And Cnoidal Wave [PLUS]   ±

Calculate Morison's equation combined wave slamming loads and wave loads on horizontal cylinders for Airy, Stokes and cnoidal waves.

Wave slamming loads occur on the front side of the wave only, and are due to the impact of the wave surface against the structure. The combined wave loading includes wave drag load, inertia load, lateral load and buoyancy load. The wave velocity and acceleration is calculated at the wave surface, hence the height above the seabed varies with wave phase angle. Wave loads can either be calculated from phase angle, or calculated for the maximum load magnitude. Loads are force per length (unit loads). Currents are assumed to be parallel to the waves. Wave spreading accounts for multi directional waves. The wave is assumed to contact the diameter of the whole cylinder simultaneously (ie the cylinder diameter is much smaller than the wave height - wave curl is ignored). Wave and current loads are calculated at the center of the pipe.

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

Tool Input

  • hwtype : Wave And Current Heading Type
    • Φwu : User Defined Wave And Current 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 Angle Type
    • Θu : User Defined Phase Angle
  • C : Load Coefficients
  • Φs : Structure Absolute heading
  • OOD : Outer Diameter Including Layers
  • d : Water Depth
  • H : Wave Height
  • Vr : Reference Velocity
  • zr : Reference Height Above Seabed
  • ρ : Fluid Density

Tool Output

  • Θ : Wave Phase Angle
  • Φ : Force Heading Relative To Horizontal
  • Φw : Wave Relative heading
  • η : Wave Profile Height Relative To Sea Level
  • Ah : Wave Horizontal Acceleration
  • Av : Wave Vertical Acceleration
  • Fb : Vertical Buoyancy Load
  • Fdx : Horizontal Drag Load
  • Fdz : Vertical Drag Load
  • Fl : Vertical Lift Load
  • Fmx : Horizontal Inertia Load
  • Fmz : Vertical Inertia Load
  • Fs : Horizontal Slamming Load
  • Ft : Total Force
  • Fx : Horizontal Force
  • Fz : Vertical Load
  • Kc : Keulegan Carpenter Number
  • L : Wave Length
  • Rc : Current Velocity Reduction Factor
  • Rw : Wave Velocity Reduction Factor
  • T : Wave Period
  • Vc : Current Velocity
  • Vh : Wave Horizontal Velocity
  • Vv : Wave Vertical Velocity
  • Vx : Horizontal Velocity
  • c : Wave Celerity
  • cvg : Convergence Check
  • sf : Wave Spreading Factor
  • w : Wave Trough Height Above Seabed
  • zh : Center Of Pipe Height Above Seabed
  • zo : Seabed Roughness
  • zs : Surface Elevation

CALCULATOR : Morison's Equation General Wave Slamming Load Airy Stokes And Cnoidal Wave [FREE]   ±

Calculate Morison's equation wave slamming loads for Airy, Stokes and cnoidal waves.

Wave slamming loads occur on the front side of the wave only, and are due to the impact of the wave surface against the structure.

Tool Input

  • lttype : Wave Parameter Type
    • Tu : User Defined Wave Period
    • Lu : User Defined Wave Length
  • wavetype : Wave Type
  • OOD : Outer Diameter Including Layers
  • d : Water Depth
  • H : Wave Height
  • ρ : Fluid Density
  • Cs : Wave Slam Coeffient

Tool Output

  • Fs : Wave Slam Force
  • L : Wave Length
  • T : Wave Period
  • c : Wave Celerity
  • cvg : Convergence Check
  • w : Wave Trough Height Above Seabed

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