Angular velocity of Earth for velocity at surface Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Density of Water*sin(Latitude of the line))
ΩE = (pi*τ/Vs)^2/(2*D*ρ*sin(L))
This formula uses 1 Constants, 1 Functions, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
Variables Used
Angular Speed of the Earth - (Measured in Radian per Second) - Angular Speed of the Earth is the measure of how fast the central angle of a rotating body changes with respect to time.
Shear Stress at the Water Surface - (Measured in Pascal) - Shear Stress at the Water Surface, shear stress describes the force of water that is trying to drag the channel surface downstream with it.
Velocity at the Surface - (Measured in Meter per Second) - Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium.
Depth of Frictional Influence - (Measured in Meter) - Depth of Frictional Influence called by Eckman is the depth over which the turbulent eddy viscosity is important. At this depth velocity is 1/23 of its value at surface.
Density of Water - (Measured in Kilogram per Cubic Meter) - The Density of Water is mass per unit of water.
Latitude of the line - (Measured in Meter) - Latitude of the line is the projection of the specific line in north-south direction.
STEP 1: Convert Input(s) to Base Unit
Shear Stress at the Water Surface: 0.6 Newton per Square Meter --> 0.6 Pascal (Check conversion here)
Velocity at the Surface: 0.5 Meter per Second --> 0.5 Meter per Second No Conversion Required
Depth of Frictional Influence: 6 Meter --> 6 Meter No Conversion Required
Density of Water: 1000 Kilogram per Cubic Meter --> 1000 Kilogram per Cubic Meter No Conversion Required
Latitude of the line: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΩE = (pi*τ/Vs)^2/(2*D*ρ*sin(L)) --> (pi*0.6/0.5)^2/(2*6*1000*sin(20))
Evaluating ... ...
ΩE = 0.00129728757248781
STEP 3: Convert Result to Output's Unit
0.00129728757248781 Radian per Second --> No Conversion Required
FINAL ANSWER
0.00129728757248781 0.001297 Radian per Second <-- Angular Speed of the Earth
(Calculation completed in 00.004 seconds)

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Coorg Institute of Technology (CIT), Coorg
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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*Density of Water*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*Density of Water*sin(Latitude of the line))
Density of Water given Velocity at Surface
Go Density of Water = (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*Density of Water*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(pb)*Kinematic Viscosity)/(Average Current Speed*Waterline Length of a Vessel))
Kinematic Viscosity of Water given Reynolds Number
Go Kinematic Viscosity = (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)/Average Current Speed*cos(Angle of the Current)
Average Current Speed given Reynolds number
Go Average Current Speed = (Reynolds Number*Kinematic Viscosity)/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*Drag Coefficient*Projected Area of the 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)
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/Vessel Draft))/1.7*Vessel Draft
Mass Density of Air given Drag Force due to Wind
Go Density of Air = Drag Force/(0.5*Drag Coefficient*Projected Area of the Vessel*Wind Speed at Height of 10 m^2)
Coefficient of Drag for Winds Measured at 10 m given Drag Force due to Wind
Go Drag Coefficient = 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*Drag Coefficient*Wind Speed at Height of 10 m^2)
Drag Force due to Wind
Go Drag Force = 0.5*Air Density*Drag Coefficient*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 Z
Go Velocity at the desired elevation z = Wind Speed at Height of 10 m*(Desired Elevation/10)^0.11

Angular velocity of Earth for velocity at surface Formula

Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Density of Water*sin(Latitude of the line))
ΩE = (pi*τ/Vs)^2/(2*D*ρ*sin(L))

What is Ocean Dynamics?

The Ocean Dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamics has traditionally been investigated by sampling from instruments in situ.

How to Calculate Angular velocity of Earth for velocity at surface?

Angular velocity of Earth for velocity at surface calculator uses Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Density of Water*sin(Latitude of the line)) to calculate the Angular Speed of the Earth, Angular velocity of Earth for velocity at surface also known as angular frequency vector, is vector measure of rotation rate, that refers to how fast object rotates or revolves relative to another point. Angular Speed of the Earth is denoted by ΩE symbol.

How to calculate Angular velocity of Earth for velocity at surface using this online calculator? To use this online calculator for Angular velocity of Earth for velocity at surface, enter Shear Stress at the Water Surface (τ), Velocity at the Surface (Vs), Depth of Frictional Influence (D), Density of Water (ρ) & Latitude of the line (L) and hit the calculate button. Here is how the Angular velocity of Earth for velocity at surface calculation can be explained with given input values -> 0.000901 = (pi*0.6/0.5)^2/(2*6*1000*sin(20)).

FAQ

What is Angular velocity of Earth for velocity at surface?
Angular velocity of Earth for velocity at surface also known as angular frequency vector, is vector measure of rotation rate, that refers to how fast object rotates or revolves relative to another point and is represented as ΩE = (pi*τ/Vs)^2/(2*D*ρ*sin(L)) or Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Density of Water*sin(Latitude of the line)). Shear Stress at the Water Surface, shear stress describes the force of water that is trying to drag the channel surface downstream with it, Velocity at the Surface is the speed of an object or fluid at the immediate boundary with another medium, Depth of Frictional Influence called by Eckman is the depth over which the turbulent eddy viscosity is important. At this depth velocity is 1/23 of its value at surface, The Density of Water is mass per unit of water & Latitude of the line is the projection of the specific line in north-south direction.
How to calculate Angular velocity of Earth for velocity at surface?
Angular velocity of Earth for velocity at surface also known as angular frequency vector, is vector measure of rotation rate, that refers to how fast object rotates or revolves relative to another point is calculated using Angular Speed of the Earth = (pi*Shear Stress at the Water Surface/Velocity at the Surface)^2/(2*Depth of Frictional Influence*Density of Water*sin(Latitude of the line)). To calculate Angular velocity of Earth for velocity at surface, you need Shear Stress at the Water Surface (τ), Velocity at the Surface (Vs), Depth of Frictional Influence (D), Density of Water (ρ) & Latitude of the line (L). With our tool, you need to enter the respective value for Shear Stress at the Water Surface, Velocity at the Surface, Depth of Frictional Influence, Density of Water & Latitude of the line 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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