King's Dimensionless Variable Calculator

✖River or Freshwater Inflow to a Bay is the water that is less saline than marine water.ⓘ River or Freshwater Inflow to a Bay [Qr]			+10% -10%
✖Tidal Period is the time it takes for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.ⓘ Tidal Period [T]			+10% -10%
✖Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.ⓘ Ocean Tide Amplitude [a_o]			+10% -10%
✖Surface Area of Bay is defined as a small body of water set off from the main body.ⓘ Surface Area of Bay [A_b]			+10% -10%

✖King’s Dimensionless Variable for Freshwater is a metric used in fluid dynamics to characterize flow patterns in freshwater environments succinctly.ⓘ King's Dimensionless Variable [Qr']

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Formula

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King's Dimensionless Variable

Formula

`"Qr'" = "Qr"*"T"/(2*pi*"a"_{"o"}*"A"_{"b"})`

Example

`"0.574688"="10m³/min"*"130s"/(2*pi*"4.0m"*"1.5001m²")`

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Download Bay Superelevation, Effect of Freshwater Inflow, Multiple Inlets and Wave-Current Interaction Formulas PDF

King's Dimensionless Variable Solution

STEP 0: Pre-Calculation Summary

Formula Used

King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay)
Qr' = Qr*T/(2*pi*a_o*A_b)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

King’s Dimensionless Variable for Freshwater - King’s Dimensionless Variable for Freshwater is a metric used in fluid dynamics to characterize flow patterns in freshwater environments succinctly.
River or Freshwater Inflow to a Bay - (Measured in Cubic Meter per Second) - River or Freshwater Inflow to a Bay is the water that is less saline than marine water.
Tidal Period - (Measured in Second) - Tidal Period is the time it takes for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.
Ocean Tide Amplitude - (Measured in Meter) - Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.
Surface Area of Bay - (Measured in Square Meter) - Surface Area of Bay is defined as a small body of water set off from the main body.

STEP 1: Convert Input(s) to Base Unit

River or Freshwater Inflow to a Bay: 10 Cubic Meter per Minute --> 0.166666666666667 Cubic Meter per Second (Check conversion here)
Tidal Period: 130 Second --> 130 Second No Conversion Required
Ocean Tide Amplitude: 4 Meter --> 4 Meter No Conversion Required
Surface Area of Bay: 1.5001 Square Meter --> 1.5001 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Qr' = Qr*T/(2*pi*a_o*A_b) --> 0.166666666666667*130/(2*pi*4*1.5001)

Evaluating ... ...

Qr' = 0.574687870862677

STEP 3: Convert Result to Output's Unit

0.574687870862677 --> No Conversion Required

FINAL ANSWER

0.574687870862677 ≈ 0.574688 <-- King’s Dimensionless Variable for Freshwater

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Hydrodynamics of Tidal Inlets-1 » Inlet Hydrodynamics » Bay Superelevation, Effect of Freshwater Inflow, Multiple Inlets and Wave-Current Interaction » Effect of Freshwater Inflow » King's Dimensionless Variable

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< 5 Effect of Freshwater Inflow Calculators

Surface Area of Bay or Basin using King's Dimensionless Variable

Go Surface Area of Bay = (River or Freshwater Inflow to a Bay*Tidal Period)/(King’s Dimensionless Variable for Freshwater*2*pi*Ocean Tide Amplitude)

Ocean Tide Amplitude using King's Dimensionless Variable

Go Ocean Tide Amplitude = (River or Freshwater Inflow to a Bay*Tidal Period)/(King’s Dimensionless Variable for Freshwater*2*pi*Surface Area of Bay)

River or Freshwater Inflow to Bay using King's Dimensionless Variable

Go River or Freshwater Inflow to a Bay = (King’s Dimensionless Variable for Freshwater*2*pi*Ocean Tide Amplitude*Surface Area of Bay)/Tidal Period

Tidal Period using King's Dimensionless Variable

Go Tidal Period = (King’s Dimensionless Variable for Freshwater*2*pi*Ocean Tide Amplitude*Surface Area of Bay)/River or Freshwater Inflow to a Bay

King's Dimensionless Variable

Go King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay)

King's Dimensionless Variable Formula

King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay)
Qr' = Qr*T/(2*pi*a_o*A_b)

What is Ocean Tide?

Tides are caused by gravitational pull of the moon and the sun. Tides are very long-period waves that move through the oceans in response to the forces exerted by the moon and sun. Tides originate in the oceans and progress toward the coastlines where they appear as the regular rise and fall of the sea surface.

Can ocean tides vary in amplitude?

The amplitude (difference in height between high and low tide) varies through the month with the phases of the Moon, and also varies dramatically around the world. The Bay of Fundy in Canada has the largest tides, while the Mediterranean Sea has very small tides.

How to Calculate King's Dimensionless Variable?

King's Dimensionless Variable calculator uses King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay) to calculate the King’s Dimensionless Variable for Freshwater, The King's Dimensionless Variable is defined as a parameter that characterizes fluid flow properties, independent of scale, crucial in fluid dynamics and heat transfer analyses. King’s Dimensionless Variable for Freshwater is denoted by Qr' symbol.

How to calculate King's Dimensionless Variable using this online calculator? To use this online calculator for King's Dimensionless Variable, enter River or Freshwater Inflow to a Bay (Qr), Tidal Period (T), Ocean Tide Amplitude (a_o) & Surface Area of Bay (A_b) and hit the calculate button. Here is how the King's Dimensionless Variable calculation can be explained with given input values -> 0.574726 = 0.166666666666667*130/(2*pi*4*1.5001).

FAQ

What is King's Dimensionless Variable?

The King's Dimensionless Variable is defined as a parameter that characterizes fluid flow properties, independent of scale, crucial in fluid dynamics and heat transfer analyses and is represented as Qr' = Qr*T/(2*pi*a_o*A_b) or King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay). River or Freshwater Inflow to a Bay is the water that is less saline than marine water, Tidal Period is the time it takes for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day, Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun & Surface Area of Bay is defined as a small body of water set off from the main body.

How to calculate King's Dimensionless Variable?

The King's Dimensionless Variable is defined as a parameter that characterizes fluid flow properties, independent of scale, crucial in fluid dynamics and heat transfer analyses is calculated using King’s Dimensionless Variable for Freshwater = River or Freshwater Inflow to a Bay*Tidal Period/(2*pi*Ocean Tide Amplitude*Surface Area of Bay). To calculate King's Dimensionless Variable, you need River or Freshwater Inflow to a Bay (Qr), Tidal Period (T), Ocean Tide Amplitude (a_o) & Surface Area of Bay (A_b). With our tool, you need to enter the respective value for River or Freshwater Inflow to a Bay, Tidal Period, Ocean Tide Amplitude & Surface Area of Bay 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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