Morison's Equation Wave And Current Load

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

For vertical structures the load forces are due to the horizontal velocity and acceleration only. For horizontal structures the load forces also include vertical velocity and acceleration. Lateral (lift) forces are due to non symmetric flow around the structure, either because of proximity to the seabed or another structure, or by non symmetric cross section. The Keulegan Carpenter number is a measure of the ratio of wave inertial forces and drag forces.

Change Module :

Airy Stokes Cnoidal Wave Loads Calculators
Morison's Equation Drag Lift And Inertia Coefficient Calculation Module
Morison's Equation Subsea Pipeline Stability Calculation Module
Morison's Equation Wave And Current Amplitude Calculation Module
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More Morison Formula Modules
More Wave Loads Modules

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

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

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. The Keulegan Carpenter number is calculated at maximum horizontal velocity (wave phase angle = 0).

Use the Result Plot option to display either the wave profiles versus phase angle, wave velocity and acceleration 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
ztype : Height Above Seabed Type
- zhu : User Defined Height
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
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 And Current Loads Airy Stokes And Cnoidal Wave [PLUS] ±

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

Wave loads can either be calculated from phase angle, or calculated for the maximum load magnitude. Loads are force per length (unit loads). Wave spreading accounts for wave "choppiness". 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 Keulegan Carpenter number is calculated at maximum horizontal velocity (wave phase angle = 0). Wave and current loads are calculated at the center of the pipe.

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. The current is assumed to be parallel to the waves.

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
ztype : Height Above Seabed Type
- zhu : User Defined Height
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
Fdx : Horizontal Drag Load
Fdz : Vertical Drag Load
Fl : Vertical Lift Load
Fmx : Horizontal Inertia Load
Fmz : Vertical Inertia 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 Cylinder Wave And Current Loads From Horizontal Wave Velocity And Acceleration [FREE] ±

Calculate Morison's equation loads on cylinders from horizontal fluid velocity and acceleration.

Fluid loads are calculated from the horizontal wave velocity and acceleration assuming a first order sinusoidal variation with phase angle (as for the Airy wave). The vertical velocity and acceleration are ignored. 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 Keulegan Carpenter number is calculated from the maximum horizontal velocity.

Use the Result Plot option to plot either the wave velocity and acceleration versus phase angle, or wave loads versus phase angle.

Tool Input

phasetype : Wave Phase Type
- Θu : User Defined Phase Angle
C : Load Coefficients
OOD : Outer Diameter Including Layers
Vc : Current Velocity
Vo : Maximum Horizontal Velocity
Ao : Maximum Horizontal Acceleration
T : Wave Period
ρ : Fluid Density

Tool Output

Θ : Wave Phase Angle
Φ : Force Heading Relative To Horizontal
Ah : Horizontal Acceleration From Phase Angle
Fd : Drag Load
Fl : Lateral Load
Fm : Inertia Load
Ft : Load Magnitude
Fx : Horizontal Load (Drag Load + Inertia Load)
Kc : Keulegan Carpenter Number
Vh : Horizontal Velocity From Phase Angle
Vt : Total Horizontal Velocity (Wave and Current)

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