Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2))
Fr = sqrt((2*D*(1-D-S)^2)/(1-(1-D-S)^2))
This formula uses 1 Functions, 3 Variables
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
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.
Dimensionless Drawdown - Dimensionless Drawdown for the continuity and energy equations.
Vessel Blockage Ratio - Vessel Blockage Ratio in The continuity and energy equations.
STEP 1: Convert Input(s) to Base Unit
Dimensionless Drawdown: 0.4 --> No Conversion Required
Vessel Blockage Ratio: 0.05 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fr = sqrt((2*D*(1-D-S)^2)/(1-(1-D-S)^2)) --> sqrt((2*0.4*(1-0.4-0.05)^2)/(1-(1-0.4-0.05)^2))
Evaluating ... ...
Fr = 0.589027507861832
STEP 3: Convert Result to Output's Unit
0.589027507861832 --> No Conversion Required
FINAL ANSWER
0.589027507861832 0.589028 <-- Froude Number
(Calculation completed in 00.020 seconds)

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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)))

Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio Formula

Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2))
Fr = sqrt((2*D*(1-D-S)^2)/(1-(1-D-S)^2))

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 Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio?

Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio calculator uses Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)) to calculate the Froude Number, The Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders. Froude Number is denoted by Fr symbol.

How to calculate Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio using this online calculator? To use this online calculator for Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio, enter Dimensionless Drawdown (D) & Vessel Blockage Ratio (S) and hit the calculate button. Here is how the Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio calculation can be explained with given input values -> 0.589028 = sqrt((2*0.4*(1-0.4-0.05)^2)/(1-(1-0.4-0.05)^2)).

FAQ

What is Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio?
The Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders and is represented as Fr = sqrt((2*D*(1-D-S)^2)/(1-(1-D-S)^2)) or Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)). Dimensionless Drawdown for the continuity and energy equations & Vessel Blockage Ratio in The continuity and energy equations.
How to calculate Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio?
The Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders is calculated using Froude Number = sqrt((2*Dimensionless Drawdown*(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)/(1-(1-Dimensionless Drawdown-Vessel Blockage Ratio)^2)). To calculate Continuity and Energy Equations given Froude Number, Drawdown and Vessel Blockage Ratio, you need Dimensionless Drawdown (D) & Vessel Blockage Ratio (S). With our tool, you need to enter the respective value for Dimensionless Drawdown & Vessel Blockage Ratio 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 Froude Number?
In this formula, Froude Number uses Dimensionless Drawdown & Vessel Blockage Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Froude Number = Vessel Speed/sqrt([g]*Water Depth)
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