✖The Reynolds Number for Mooring Forces refers to the number for mooring forces involved in understanding the flow conditions around mooring lines or structures.ⓘ Reynolds Number for Mooring Forces [Re_m]			+10% -10%
✖Kinematic Viscosity in Stokes is defined as the ratio between the dynamic viscosity μ and the density ρ of the fluid.ⓘ Kinematic Viscosity in Stokes [ν^']			+10% -10%
✖Average Current Speed for propeller drag refers to calculating propeller drag in water depending on factors, including the type of vessel, size and shape of propeller, and operating conditions.ⓘ Average Current Speed [V_c]			+10% -10%
✖Waterline Length of a Vessel is the length of a ship or boat at the level where it sits in the water.ⓘ Waterline Length of a Vessel [l_wl]			+10% -10%

✖Angle of the Current refers to the direction at which ocean currents or tidal flows approach a coastline or a coastal structure, relative to a defined reference direction.ⓘ Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number [θ_c]

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Formula

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Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number

Formula

`"θ"_{"c"} = acos(("Re"_{"m"}*"ν"^{"'"})/("V"_{"c"}*"l"_{"wl"}))`

Example

`"1.472717"=acos(("200"*"7.25St")/("728.2461m/h"*"7.32m"))`

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Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel))
θ_c = acos((Re_m*ν^')/(V_c*l_wl))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Angle of the Current - Angle of the Current refers to the direction at which ocean currents or tidal flows approach a coastline or a coastal structure, relative to a defined reference direction.
Reynolds Number for Mooring Forces - The Reynolds Number for Mooring Forces refers to the number for mooring forces involved in understanding the flow conditions around mooring lines or structures.
Kinematic Viscosity in Stokes - (Measured in Square Meter per Second) - Kinematic Viscosity in Stokes is defined as the ratio between the dynamic viscosity μ and the density ρ of the fluid.
Average Current Speed - (Measured in Meter per Second) - Average Current Speed for propeller drag refers to calculating propeller drag in water depending on factors, including the type of vessel, size and shape of propeller, and operating conditions.
Waterline Length of a Vessel - (Measured in Meter) - Waterline Length of a Vessel is the length of a ship or boat at the level where it sits in the water.

STEP 1: Convert Input(s) to Base Unit

Reynolds Number for Mooring Forces: 200 --> No Conversion Required
Kinematic Viscosity in Stokes: 7.25 Stokes --> 0.000725 Square Meter per Second (Check conversion here)
Average Current Speed: 728.2461 Meter per Hour --> 0.202290583333333 Meter per Second (Check conversion here)
Waterline Length of a Vessel: 7.32 Meter --> 7.32 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_c = acos((Re_m*ν^')/(V_c*l_wl)) --> acos((200*0.000725)/(0.202290583333333*7.32))

Evaluating ... ...

θ_c = 1.47271693471467

STEP 3: Convert Result to Output's Unit

1.47271693471467 --> No Conversion Required

FINAL ANSWER

1.47271693471467 ≈ 1.472717 <-- Angle of the Current

(Calculation completed in 00.020 seconds)

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< 25 Mooring Forces Calculators

Latitude given Velocity at Surface

Go Latitude of the Line = asin((pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Water Density*Angular Speed of the Earth))

Angular Velocity of Earth for Velocity at Surface

Go Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Water Density*sin(Latitude of the Line))

Density of Water given Velocity at Surface

Go Water Density = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Angular Speed of the Earth*sin(Latitude of the Line))

Depth given Velocity at Surface

Go Depth of Frictional Influence = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Water Density*Angular Speed of the Earth*sin(Latitude of the Line))

Velocity at Surface given Shear Stress at Water Surface

Go Velocity at the Surface = pi*Shear Stress at the Water Surface/(2*Depth of Frictional Influence*Water Density*Angular Speed of the Earth*sin(Latitude of the Line))

Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number

Go Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel))

Kinematic Viscosity of Water given Reynolds Number

Go Kinematic Viscosity in Stokes = (Average Current Speed*Waterline Length of a Vessel*cos(Angle of the Current))/Reynolds Number

Waterline Length of Vessel given Reynolds Number

Go Waterline Length of a Vessel = (Reynolds Number*Kinematic Viscosity in Stokes)/Average Current Speed*cos(Angle of the Current)

Average Current Speed given Reynolds Number

Go Average Current Speed = (Reynolds Number*Kinematic Viscosity in Stokes)/Waterline Length of a Vessel*cos(Angle of the Current)

Wind Speed at Standard Elevation of 10 m above Water's Surface using Drag Force due to Wind

Go Wind Speed at Height of 10 m = sqrt(Drag Force/(0.5*Air Density*Coefficient of Drag*Projected Area of the Vessel))

Waterline Length of Vessel for Wetted Surface Area of Vessel

Go Waterline Length of a Vessel = (Wetted Surface Area of Vessel-(35*Displacement of a Vessel/Draft in Vessel))/1.7*Draft in Vessel

Displacement of Vessel for Wetted Surface Area of Vessel

Go Displacement of a Vessel = (Vessel Draft*(Wetted Surface Area of Vessel-(1.7*Vessel Draft*Waterline Length of a Vessel)))/35

Wetted Surface Area of Vessel

Go Wetted Surface Area of Vessel = (1.7*Vessel Draft*Waterline Length of a Vessel)+((35*Displacement of a Vessel)/Vessel Draft)

Coefficient of Drag for Winds Measured at 10 m given Drag Force due to Wind

Go Coefficient of Drag = Drag Force/(0.5*Air Density*Projected Area of the Vessel*Wind Speed at Height of 10 m^2)

Projected Area of Vessel above Waterline given Drag Force due to Wind

Go Projected Area of the Vessel = Drag Force/(0.5*Air Density*Coefficient of Drag*Wind Speed at Height of 10 m^2)

Mass Density of Air given Drag Force due to Wind

Go Air Density = Drag Force/(0.5*Coefficient of Drag*Projected Area of the Vessel*Wind Speed at Height of 10 m^2)

Drag Force due to Wind

Go Drag Force = 0.5*Air Density*Coefficient of Drag*Projected Area of the Vessel*Wind Speed at Height of 10 m^2

Total Longitudinal Current Load on Vessel

Go Total Longitudinal Current Load on a Vessel = Form Drag of a Vessel+Skin Friction of a Vessel+Vessel Propeller Drag

Waterline Length of Vessel given Expanded or Developed Blade Area

Go Waterline Length of a Vessel = (Expanded or Developed Blade Area of a Propeller*0.838*Area Ratio)/Vessel Beam

Vessel Beam given Expanded or Developed Blade Area of Propeller

Go Vessel Beam = (Expanded or Developed Blade Area of a Propeller*0.838*Area Ratio)/Waterline Length of a Vessel

Area Ratio given Expanded or Developed Blade Area of Propeller

Go Area Ratio = Waterline Length of a Vessel*Vessel Beam/(Expanded or Developed Blade Area of a Propeller*0.838)

Expanded or Developed Blade Area of Propeller

Go Expanded or Developed Blade Area of a Propeller = (Waterline Length of a Vessel*Vessel Beam)/0.838*Area Ratio

Elevation given Velocity at Desired Elevation

Go Desired Elevation = 10*(Velocity at the Desired Elevation z/Wind Speed at Height of 10 m)^1/0.11

Wind Speed at Standard Elevation of 10 m given Velocity at Desired Elevation

Go Wind Speed at Height of 10 m = Velocity at the Desired Elevation z/(Desired Elevation/10)^0.11

Velocity at Desired Elevation

Go Velocity at the Desired Elevation z = Wind Speed at Height of 10 m*(Desired Elevation/10)^0.11

< 25 Important Formulas of Mooring Forces Calculators

Average Current Speed for Form Drag of Vessel

Go Longshore Current Speed = sqrt(Form Drag of a Vessel/0.5*Water Density*Form Drag Coefficient*Vessel Beam*Vessel Draft*cos(Angle of the Current))

Form Drag Coefficient given Form Drag of Vessel

Go Form Drag Coefficient = Form Drag of a Vessel/(0.5*Water Density*Vessel Beam*Vessel Draft*Average Current Speed^2*cos(Angle of the Current))

Vessel Draft given Form Drag of Vessel

Go Vessel Draft = Form Drag of a Vessel/(0.5*Water Density*Form Drag Coefficient*Vessel Beam*Average Current Speed^2*cos(Angle of the Current))

Propeller Drag Coefficient given Propeller Drag

Go Propeller Drag Coefficient = Vessel Propeller Drag/(0.5*Water Density*Expanded or Developed Blade Area of a Propeller*Average Current Speed^2*cos(Angle of the Current))

Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number

Go Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel))

Waterline Length of Vessel given Reynolds Number

Go Waterline Length of a Vessel = (Reynolds Number*Kinematic Viscosity in Stokes)/Average Current Speed*cos(Angle of the Current)

Average Current Speed given Reynolds Number

Go Average Current Speed = (Reynolds Number*Kinematic Viscosity in Stokes)/Waterline Length of a Vessel*cos(Angle of the Current)

Waterline Length of Vessel for Wetted Surface Area of Vessel

Go Waterline Length of a Vessel = (Wetted Surface Area of Vessel-(35*Displacement of a Vessel/Draft in Vessel))/1.7*Draft in Vessel

Displacement of Vessel for Wetted Surface Area of Vessel

Go Displacement of a Vessel = (Vessel Draft*(Wetted Surface Area of Vessel-(1.7*Vessel Draft*Waterline Length of a Vessel)))/35

Wetted Surface Area of Vessel

Go Wetted Surface Area of Vessel = (1.7*Vessel Draft*Waterline Length of a Vessel)+((35*Displacement of a Vessel)/Vessel Draft)

Coefficient of Drag for Winds Measured at 10 m given Drag Force due to Wind

Go Coefficient of Drag = Drag Force/(0.5*Air Density*Projected Area of the Vessel*Wind Speed at Height of 10 m^2)

Projected Area of Vessel above Waterline given Drag Force due to Wind

Go Projected Area of the Vessel = Drag Force/(0.5*Air Density*Coefficient of Drag*Wind Speed at Height of 10 m^2)

Drag Force due to Wind

Go Drag Force = 0.5*Air Density*Coefficient of Drag*Projected Area of the Vessel*Wind Speed at Height of 10 m^2

Undamped Natural Period of Vessel

Go Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant))

Waterline Length of Vessel given Expanded or Developed Blade Area

Go Waterline Length of a Vessel = (Expanded or Developed Blade Area of a Propeller*0.838*Area Ratio)/Vessel Beam

Area Ratio given Expanded or Developed Blade Area of Propeller

Go Area Ratio = Waterline Length of a Vessel*Vessel Beam/(Expanded or Developed Blade Area of a Propeller*0.838)

Expanded or Developed Blade Area of Propeller

Go Expanded or Developed Blade Area of a Propeller = (Waterline Length of a Vessel*Vessel Beam)/0.838*Area Ratio

Individual Stiffness of Mooring Line

Go Individual Mooring Line Stiffness = Axial Tension or Load on a Mooring Line/Elongation in the Mooring Line

Elongation in Mooring Line given Individual Stiffness of Mooring Line

Go Mooring Line Elongation = Axial Tension or Load on a Mooring Line/Individual Stiffness of a Mooring Line

Axial Tension or Load given Individual Stiffness of Mooring Line

Go Axial Tension or Load on a Mooring Line = Mooring Line Elongation*Individual Stiffness of a Mooring Line

Elongation in Mooring Line given Percent Elongation in Mooring Line

Go Elongation in the Mooring Line = Length of Mooring Line*(Percent Elongation in a Mooring Line/100)

Wind Speed at Standard Elevation of 10 m given Velocity at Desired Elevation

Go Wind Speed at Height of 10 m = Velocity at the Desired Elevation z/(Desired Elevation/10)^0.11

Velocity at Desired Elevation

Go Velocity at the Desired Elevation z = Wind Speed at Height of 10 m*(Desired Elevation/10)^0.11

Mass of Vessel given Virtual Mass of Vessel

Go Mass of a Vessel = Virtual Mass of the Ship-Mass of Vessel due to Inertial Effects

Virtual Mass of Vessel

Go Virtual Mass of the Ship = Mass of a Vessel+Mass of Vessel due to Inertial Effects

Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number Formula

Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel))
θ_c = acos((Re_m*ν^')/(V_c*l_wl))

What causes Skin Friction?

The Skin friction drag is caused by the viscosity of fluids and is developed from laminar drag to turbulent drag as a fluid moves on the surface of an object. Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force.

How to Calculate Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number?

Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number calculator uses Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel)) to calculate the Angle of the Current, The Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number formula is defined as a parameter influencing the skin friction coefficient as a function of Reynolds number. Angle of the Current is denoted by θ_c symbol.

How to calculate Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number using this online calculator? To use this online calculator for Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number, enter Reynolds Number for Mooring Forces (Re_m), Kinematic Viscosity in Stokes (ν^'), Average Current Speed (V_c) & Waterline Length of a Vessel (l_wl) and hit the calculate button. Here is how the Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number calculation can be explained with given input values -> 1.472717 = acos((200*0.000725)/(0.202290583333333*7.32)).

FAQ

What is Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number?

The Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number formula is defined as a parameter influencing the skin friction coefficient as a function of Reynolds number and is represented as θ_c = acos((Re_m*ν^')/(V_c*l_wl)) or Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel)). The Reynolds Number for Mooring Forces refers to the number for mooring forces involved in understanding the flow conditions around mooring lines or structures, Kinematic Viscosity in Stokes is defined as the ratio between the dynamic viscosity μ and the density ρ of the fluid, Average Current Speed for propeller drag refers to calculating propeller drag in water depending on factors, including the type of vessel, size and shape of propeller, and operating conditions & Waterline Length of a Vessel is the length of a ship or boat at the level where it sits in the water.

How to calculate Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number?

The Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number formula is defined as a parameter influencing the skin friction coefficient as a function of Reynolds number is calculated using Angle of the Current = acos((Reynolds Number for Mooring Forces*Kinematic Viscosity in Stokes)/(Average Current Speed*Waterline Length of a Vessel)). To calculate Angle of Current Relative to Longitudinal Axis of Vessel given Reynolds Number, you need Reynolds Number for Mooring Forces (Re_m), Kinematic Viscosity in Stokes (ν^'), Average Current Speed (V_c) & Waterline Length of a Vessel (l_wl). With our tool, you need to enter the respective value for Reynolds Number for Mooring Forces, Kinematic Viscosity in Stokes, Average Current Speed & Waterline Length of a Vessel and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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