Vessel Speed given Return Flow Velocity Calculator

✖Return Flow Velocity is the velocity that develops between the vessel hull and the channel bottom and sides [length/time].ⓘ Return Flow Velocity [V_r]			+10% -10%
✖Channel Width corresponding to Mean Water Depth is the distance between banks in a water body and is measured perpendicular to the mean water depth.ⓘ Channel Width corresponding to Mean Water Depth [W]			+10% -10%
✖Water depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [D]			+10% -10%
✖Water Surface Drawdown ∆d, taken as the vessel sinkage.ⓘ Water Surface Drawdown [Δd]			+10% -10%
✖Vessel’s midsection wetted Cross-Sectional Area [length^2] is the perimeter of the cross sectional area that is wet.ⓘ Vessel’s midsection wetted Cross-Sectional Area [A_m]			+10% -10%

✖Vessel Speed influencing individual wave celerity [length/time].ⓘ Vessel Speed given Return Flow Velocity [V_s]

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Vessel Speed given Return Flow Velocity

Formula

`"V"_{"s"} = "V"_{"r"}/((("W"*"D")/("W"*("D"-"Δd")-"A"_{"m"}))-1)`

Example

`"84.25552m/s"="87m/s"/((("52m"*"12m")/("52m"*("12m"-"5.5m")-"31m²"))-1)`

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Vessel Speed given Return Flow Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V_s = V_r/(((W*D)/(W*(D-Δd)-A_m))-1)
This formula uses 6 Variables

Variables Used

Vessel Speed - (Measured in Meter per Second) - Vessel Speed influencing individual wave celerity [length/time].
Return Flow Velocity - (Measured in Meter per Second) - Return Flow Velocity is the velocity that develops between the vessel hull and the channel bottom and sides [length/time].
Channel Width corresponding to Mean Water Depth - (Measured in Meter) - Channel Width corresponding to Mean Water Depth is the distance between banks in a water body and is measured perpendicular to the mean water depth.
Water Depth - (Measured in Meter) - Water depth means the depth as measured from the water level to the bottom of the considered water body.
Water Surface Drawdown - (Measured in Meter) - Water Surface Drawdown ∆d, taken as the vessel sinkage.
Vessel’s midsection wetted Cross-Sectional Area - (Measured in Square Meter) - Vessel’s midsection wetted Cross-Sectional Area [length^2] is the perimeter of the cross sectional area that is wet.

STEP 1: Convert Input(s) to Base Unit

Return Flow Velocity: 87 Meter per Second --> 87 Meter per Second No Conversion Required
Channel Width corresponding to Mean Water Depth: 52 Meter --> 52 Meter No Conversion Required
Water Depth: 12 Meter --> 12 Meter No Conversion Required
Water Surface Drawdown: 5.5 Meter --> 5.5 Meter No Conversion Required
Vessel’s midsection wetted Cross-Sectional Area: 31 Square Meter --> 31 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_s = V_r/(((W*D)/(W*(D-Δd)-A_m))-1) --> 87/(((52*12)/(52*(12-5.5)-31))-1)

Evaluating ... ...

V_s = 84.2555205047319

STEP 3: Convert Result to Output's Unit

84.2555205047319 Meter per Second --> No Conversion Required

FINAL ANSWER

84.2555205047319 ≈ 84.25552 Meter per Second <-- Vessel Speed

(Calculation completed in 00.005 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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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 Return Flow Velocity Formula

What is Froude Law?

Froude's Law, defines 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 Return Flow Velocity?

Vessel Speed given Return Flow Velocity calculator uses 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) to calculate the Vessel Speed, Vessel Speed given Return Flow Velocity, 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 V_s symbol.

How to calculate Vessel Speed given Return Flow Velocity using this online calculator? To use this online calculator for Vessel Speed given Return Flow Velocity, enter Return Flow Velocity (V_r), Channel Width corresponding to Mean Water Depth (W), Water Depth (D), Water Surface Drawdown (Δd) & Vessel’s midsection wetted Cross-Sectional Area (A_m) and hit the calculate button. Here is how the Vessel Speed given Return Flow Velocity calculation can be explained with given input values -> 84.25552 = 87/(((52*12)/(52*(12-5.5)-31))-1).

FAQ

What is Vessel Speed given Return Flow Velocity?

Vessel Speed given Return Flow Velocity, at increasing distances from vessel, diffraction causes wave crest lengths to continually increase and resulting wave heights to continually decrease and is represented as V_s = V_r/(((W*D)/(W*(D-Δd)-A_m))-1) or 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 is the velocity that develops between the vessel hull and the channel bottom and sides [length/time], Channel Width corresponding to Mean Water Depth is the distance between banks in a water body and is measured perpendicular to the mean water depth, Water depth means the depth as measured from the water level to the bottom of the considered water body, Water Surface Drawdown ∆d, taken as the vessel sinkage & Vessel’s midsection wetted Cross-Sectional Area [length^2] is the perimeter of the cross sectional area that is wet.

How to calculate Vessel Speed given Return Flow Velocity?

Vessel Speed given Return Flow Velocity, 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 = 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). To calculate Vessel Speed given Return Flow Velocity, you need Return Flow Velocity (V_r), Channel Width corresponding to Mean Water Depth (W), Water Depth (D), Water Surface Drawdown (Δd) & Vessel’s midsection wetted Cross-Sectional Area (A_m). With our tool, you need to enter the respective value for Return Flow Velocity, Channel Width corresponding to Mean Water Depth, Water Depth, Water Surface Drawdown & Vessel’s midsection wetted Cross-Sectional Area 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 Return Flow Velocity, Channel Width corresponding to Mean Water Depth, Water Depth, Water Surface Drawdown & Vessel’s midsection wetted Cross-Sectional Area. 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 = Froude Number*sqrt([g]*Water Depth)

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