Vessel Speed given Froude Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vessel Speed = Froude Number*sqrt([g]*Water Depth)
Vs = Fr*sqrt([g]*D)
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Vessel Speed - (Measured in Meter per Second) - Vessel Speed influencing individual wave celerity [length/time].
Froude Number - Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.
Water Depth - (Measured in Meter) - Water depth means the depth as measured from the water level to the bottom of the considered water body.
STEP 1: Convert Input(s) to Base Unit
Froude Number: 10 --> No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vs = Fr*sqrt([g]*D) --> 10*sqrt([g]*12)
Evaluating ... ...
Vs = 108.480320795986
STEP 3: Convert Result to Output's Unit
108.480320795986 Meter per Second --> No Conversion Required
FINAL ANSWER
108.480320795986 108.4803 Meter per Second <-- Vessel Speed
(Calculation completed in 00.020 seconds)

Credits

Created by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
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National Institute of Technology Karnataka (NITK), Surathkal
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17 Flushing/Circulation Processes and Vessel Interactions Calculators

Vessel Speed given Return Flow Velocity
Go Vessel Speed = Return Flow Velocity/(((Channel Width corresponding to Mean Water Depth*Water Depth)/(Channel Width corresponding to Mean Water Depth*(Water Depth-Water Surface Drawdown)-Vessel’s midsection wetted Cross-Sectional Area))-1)
Return Flow Velocity
Go Return Flow Velocity = Vessel Speed*(((Channel Width corresponding to Mean Water Depth*Water Depth)/(Channel Width corresponding to Mean Water Depth*(Water Depth-Water Surface Drawdown)-Vessel’s midsection wetted Cross-Sectional Area))-1)
Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio
Go Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2))
Vessel Blockage Ratio
Go Vessel Blockage Ratio = Vessel’s midsection wetted Cross-Sectional Area/(Water Depth at Breaking*Channel Width corresponding to Mean Water Depth)
Channel Depth given Vessel Blockage Ratio
Go Channel Depth = Vessel’s midsection wetted Cross-Sectional Area/(Vessel Blockage Ratio*Channel Width corresponding to Mean Water Depth)
Channel Width given Vessel Blockage Ratio
Go Channel Width corresponding to Mean Water Depth = Vessel’s midsection wetted Cross-Sectional Area/(Vessel Blockage Ratio*Water Depth)
Vessel's Midsection Wetted Cross-Sectional Area given Vessel Blockage Ratio
Go Vessel’s midsection wetted Cross-Sectional Area = Vessel Blockage Ratio*Channel Width corresponding to Mean Water Depth*Water Depth
Average per Cycle Exchange Coefficient
Go Average per cycle exchange coefficient = 1-(Concentration of substance after i Tidal Cycles/Initial concentration)^1/Tidal Cycles
Initial Concentration of Substance in Harbor Water
Go Initial concentration = Concentration of substance after i Tidal Cycles/(1-Average per cycle exchange coefficient)^Tidal Cycles
Concentration of Substance after i Tidal Cycles
Go Concentration of substance after i Tidal Cycles = Initial concentration*(1-Average per cycle exchange coefficient)^Tidal Cycles
Froude Number where Particle Motion in Vessel generated Waves does not Reach Bottom
Go Froude Number = Vessel Speed/sqrt([g]*Water Depth)
Vessel Speed given Froude Number
Go Vessel Speed = Froude Number*sqrt([g]*Water Depth)
Vessel Speed given Individual Wave Celerity created by Moving Vessel
Go Vessel Speed = Individual Wave Celerities/cos(Angle between sailing line)
Individual Wave Celerity created by Moving Vessel
Go Individual Wave Celerities = Vessel Speed*cos(Angle between sailing line)
Water Depth given Froude Number
Go Water Depth = ((Vessel Speed/Froude Number)^2)/[g]
Drawdown with respect to Water Depth
Go Dimensionless Drawdown = Water Surface Drawdown/Water Depth
Direction of Wave Propagation for Froude numbers up to unity
Go Direction of Wave Propagation = 35.27*(1-e^(12*(Froude Scaling-1)))

Vessel Speed given Froude Number Formula

Vessel Speed = Froude Number*sqrt([g]*Water Depth)
Vs = Fr*sqrt([g]*D)

What is Froude law?

This is Froude's Law, that the speed attainable by a creature or a ship is proportional to the square root of its scale. Froude number (Fr), in hydrology and fluid mechanics, dimensionless quantity used to indicate the influence of gravity on fluid motion.

How to Calculate Vessel Speed given Froude Number?

Vessel Speed given Froude Number calculator uses Vessel Speed = Froude Number*sqrt([g]*Water Depth) to calculate the Vessel Speed, Vessel Speed given Froude Number, at increasing distances from vessel, diffraction causes wave crest lengths to continually increase and resulting wave heights to continually decrease. Vessel Speed is denoted by Vs symbol.

How to calculate Vessel Speed given Froude Number using this online calculator? To use this online calculator for Vessel Speed given Froude Number, enter Froude Number (Fr) & Water Depth (D) and hit the calculate button. Here is how the Vessel Speed given Froude Number calculation can be explained with given input values -> 108.4803 = 10*sqrt([g]*12).

FAQ

What is Vessel Speed given Froude Number?
Vessel Speed given Froude Number, at increasing distances from vessel, diffraction causes wave crest lengths to continually increase and resulting wave heights to continually decrease and is represented as Vs = Fr*sqrt([g]*D) or Vessel Speed = Froude Number*sqrt([g]*Water Depth). Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders & Water depth means the depth as measured from the water level to the bottom of the considered water body.
How to calculate Vessel Speed given Froude Number?
Vessel Speed given Froude Number, at increasing distances from vessel, diffraction causes wave crest lengths to continually increase and resulting wave heights to continually decrease is calculated using Vessel Speed = Froude Number*sqrt([g]*Water Depth). To calculate Vessel Speed given Froude Number, you need Froude Number (Fr) & Water Depth (D). With our tool, you need to enter the respective value for Froude Number & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Vessel Speed?
In this formula, Vessel Speed uses Froude Number & Water Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Vessel Speed = Individual Wave Celerities/cos(Angle between sailing line)
  • Vessel Speed = Return Flow Velocity/(((Channel Width corresponding to Mean Water Depth*Water Depth)/(Channel Width corresponding to Mean Water Depth*(Water Depth-Water Surface Drawdown)-Vessel’s midsection wetted Cross-Sectional Area))-1)
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