Return Flow Velocity Calculator

✖Vessel Speed referred to as ship speed or boat speed, is the rate at which a vessel travels through the water.ⓘ Vessel Speed [V_s]			+10% -10%
✖Channel Width corresponding to Mean Water Depth is the width of the channel at the water surface level when the water depth is equal to the mean depth of flow.ⓘ 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 refers to the water level on a lake controlled by dam is lowered and held at a reduced level for some period of time, typically for several months.ⓘ 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%

✖Return Flow Velocity is the velocity refers to the speed at which water flows back toward the source or out to sea after being pushed inland by a force such as a wave, tide, or flood.ⓘ Return Flow Velocity [V_r]

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Formula

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Return Flow Velocity

Formula

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

Example

`"103.2573m/s"="100m/s"*((("52m"*"12m")/("52m"*("12m"-"5.5m")-"31m²"))-1)`

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Return Flow Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Return Flow Velocity - (Measured in Meter per Second) - Return Flow Velocity is the velocity refers to the speed at which water flows back toward the source or out to sea after being pushed inland by a force such as a wave, tide, or flood.
Vessel Speed - (Measured in Meter per Second) - Vessel Speed referred to as ship speed or boat speed, is the rate at which a vessel travels through the water.
Channel Width corresponding to Mean Water Depth - (Measured in Meter) - Channel Width corresponding to Mean Water Depth is the width of the channel at the water surface level when the water depth is equal to the mean depth of flow.
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 refers to the water level on a lake controlled by dam is lowered and held at a reduced level for some period of time, typically for several months.
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

Vessel Speed: 100 Meter per Second --> 100 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_r = V_s*(((W*D)/(W*(D-Δd)-A_m))-1) --> 100*(((52*12)/(52*(12-5.5)-31))-1)

Evaluating ... ...

V_r = 103.257328990228

STEP 3: Convert Result to Output's Unit

103.257328990228 Meter per Second --> No Conversion Required

FINAL ANSWER

103.257328990228 ≈ 103.2573 Meter per Second <-- Return Flow Velocity

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Flushing/Circulation Processes and Vessel Interactions » Return Flow Velocity

Credits

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

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 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)))

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 Return Flow Velocity?

Return Flow Velocity calculator uses 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) to calculate the Return Flow Velocity, The Return Flow Velocity occurs As a vessel travels in a channel, continuity of flow causes a return flow velocity to develop between the vessel hull and the channel bottom and sides. This return flow velocity Vr can be calculated for a rectangular channel and vessel cross section. Return Flow Velocity is denoted by V_r symbol.

How to calculate Return Flow Velocity using this online calculator? To use this online calculator for Return Flow Velocity, enter Vessel Speed (V_s), 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 Return Flow Velocity calculation can be explained with given input values -> 103.2573 = 100*(((52*12)/(52*(12-5.5)-31))-1).

FAQ

What is Return Flow Velocity?

The Return Flow Velocity occurs As a vessel travels in a channel, continuity of flow causes a return flow velocity to develop between the vessel hull and the channel bottom and sides. This return flow velocity Vr can be calculated for a rectangular channel and vessel cross section and is represented as V_r = V_s*(((W*D)/(W*(D-Δd)-A_m))-1) or 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). Vessel Speed referred to as ship speed or boat speed, is the rate at which a vessel travels through the water, Channel Width corresponding to Mean Water Depth is the width of the channel at the water surface level when the water depth is equal to the mean depth of flow, Water depth means the depth as measured from the water level to the bottom of the considered water body, Water Surface Drawdown refers to the water level on a lake controlled by dam is lowered and held at a reduced level for some period of time, typically for several months & Vessel’s midsection wetted Cross-Sectional Area [length^2] is the perimeter of the cross sectional area that is wet.

How to calculate Return Flow Velocity?

The Return Flow Velocity occurs As a vessel travels in a channel, continuity of flow causes a return flow velocity to develop between the vessel hull and the channel bottom and sides. This return flow velocity Vr can be calculated for a rectangular channel and vessel cross section is calculated using 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). To calculate Return Flow Velocity, you need Vessel Speed (V_s), 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 Vessel Speed, 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.

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