Superelevation due to Varying Entrance Channel Cross-Section Calculator

✖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%
✖Bay Tide Amplitude is the average difference between water levels at high and low tide.ⓘ Bay Tide Amplitude [a_B]			+10% -10%
✖Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.ⓘ Channel Depth [D_t]			+10% -10%
✖Bank Slope defined as the angle, measured in degrees of deviation from the horizontal, at which earthy or rock material will stand [length-rise/length-run].ⓘ Bank Slope [m]			+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%
✖Phase Lag is called the local epoch in order to distinguish it from other forms of epochs.ⓘ Phase Lag [k]			+10% -10%

✖Superelevation is the amount of raise of outer edge with respect to the inner edge of the road surface. In case of railways the amount by which the outer rail is raised is known as superelevation.ⓘ Superelevation due to Varying Entrance Channel Cross-Section [S]

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Superelevation due to Varying Entrance Channel Cross-Section

Formula

`"S" = "a"_{"o"}*(1-((("a"_{"B"}/"a"_{"o"})^2)/(4*("D"_{"t"}/"a"_{"o"})))-("a"_{"o"}/("m"*"W"))*(0.5-("a"_{"B"}/"a"_{"o"})*cos("k")-((3/2)*("a"_{"B"}/"a"_{"o"})^2)+4*("D"_{"t"}/"a"_{"o"})^2))`

Example

`"2.000651m"="4.0m"*(1-((("3.7"/"4.0m")^2)/(4*("5.01m"/"4.0m")))-("4.0m"/("1.5"*"52m"))*(0.5-("3.7"/"4.0m")*cos("22")-((3/2)*("3.7"/"4.0m")^2)+4*("5.01m"/"4.0m")^2))`

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

Superelevation due to Varying Entrance Channel Cross-Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2))
S = a_o*(1-(((a_B/a_o)^2)/(4*(D_t/a_o)))-(a_o/(m*W))*(0.5-(a_B/a_o)*cos(k)-((3/2)*(a_B/a_o)^2)+4*(D_t/a_o)^2))
This formula uses 1 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Superelevation - (Measured in Meter) - Superelevation is the amount of raise of outer edge with respect to the inner edge of the road surface. In case of railways the amount by which the outer rail is raised is known as superelevation.
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.
Bay Tide Amplitude - Bay Tide Amplitude is the average difference between water levels at high and low tide.
Channel Depth - (Measured in Meter) - Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.
Bank Slope - Bank Slope defined as the angle, measured in degrees of deviation from the horizontal, at which earthy or rock material will stand [length-rise/length-run].
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.
Phase Lag - Phase Lag is called the local epoch in order to distinguish it from other forms of epochs.

STEP 1: Convert Input(s) to Base Unit

Ocean Tide Amplitude: 4 Meter --> 4 Meter No Conversion Required
Bay Tide Amplitude: 3.7 --> No Conversion Required
Channel Depth: 5.01 Meter --> 5.01 Meter No Conversion Required
Bank Slope: 1.5 --> No Conversion Required
Channel Width corresponding to Mean Water Depth: 52 Meter --> 52 Meter No Conversion Required
Phase Lag: 22 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = a_o*(1-(((a_B/a_o)^2)/(4*(D_t/a_o)))-(a_o/(m*W))*(0.5-(a_B/a_o)*cos(k)-((3/2)*(a_B/a_o)^2)+4*(D_t/a_o)^2)) --> 4*(1-(((3.7/4)^2)/(4*(5.01/4)))-(4/(1.5*52))*(0.5-(3.7/4)*cos(22)-((3/2)*(3.7/4)^2)+4*(5.01/4)^2))

Evaluating ... ...

S = 2.0006506234825

STEP 3: Convert Result to Output's Unit

2.0006506234825 Meter --> No Conversion Required

FINAL ANSWER

2.0006506234825 ≈ 2.000651 Meter <-- Superelevation

(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 » Bay Superelevation » Superelevation due to Varying Entrance Channel Cross-Section

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< 4 Bay Superelevation Calculators

Superelevation due to Varying Entrance Channel Cross-Section

Go Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2))

Tidal Amplitude in Ocean

Go Ocean Tide Amplitude = Bay Superelevation/(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))

Superelevation

Go Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))

Depth given Water Surface Slope

Go Eckman Constant Depth = (Coefficient of Eckman*Shear Stress at the Water Surface)/(Water Surface Slope*Water Density*[g])

Superelevation due to Varying Entrance Channel Cross-Section Formula

What is Bay Superelevation?

A Superelevation of the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams. The effect of long-term (months or years) rises in sea level causing a long-term rise in bay level is not included in this definition of bay superelevation, since both sea and bay are responding simultaneously. The bay may not rise at the same rate as the sea due to possible circulation effects if multiple inlets connect the bay to the ocean.

What is Ocean Dynamics & Ocean Tide?

Ocean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamics have traditionally been investigated by sampling from instruments in situ.
Tides are caused by the 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.

How to Calculate Superelevation due to Varying Entrance Channel Cross-Section?

Superelevation due to Varying Entrance Channel Cross-Section calculator uses Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2)) to calculate the Superelevation, The Superelevation due to Varying Entrance Channel Cross-Section formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams. Superelevation is denoted by S symbol.

How to calculate Superelevation due to Varying Entrance Channel Cross-Section using this online calculator? To use this online calculator for Superelevation due to Varying Entrance Channel Cross-Section, enter Ocean Tide Amplitude (a_o), Bay Tide Amplitude (a_B), Channel Depth (D_t), Bank Slope (m), Channel Width corresponding to Mean Water Depth (W) & Phase Lag (k) and hit the calculate button. Here is how the Superelevation due to Varying Entrance Channel Cross-Section calculation can be explained with given input values -> 2.004418 = 4*(1-(((3.7/4)^2)/(4*(5.01/4)))-(4/(1.5*52))*(0.5-(3.7/4)*cos(22)-((3/2)*(3.7/4)^2)+4*(5.01/4)^2)).

FAQ

What is Superelevation due to Varying Entrance Channel Cross-Section?

The Superelevation due to Varying Entrance Channel Cross-Section formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams and is represented as S = a_o*(1-(((a_B/a_o)^2)/(4*(D_t/a_o)))-(a_o/(m*W))*(0.5-(a_B/a_o)*cos(k)-((3/2)*(a_B/a_o)^2)+4*(D_t/a_o)^2)) or Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2)). Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun, Bay Tide Amplitude is the average difference between water levels at high and low tide, Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit, Bank Slope defined as the angle, measured in degrees of deviation from the horizontal, at which earthy or rock material will stand [length-rise/length-run], 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 & Phase Lag is called the local epoch in order to distinguish it from other forms of epochs.

How to calculate Superelevation due to Varying Entrance Channel Cross-Section?

The Superelevation due to Varying Entrance Channel Cross-Section formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams is calculated using Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2)). To calculate Superelevation due to Varying Entrance Channel Cross-Section, you need Ocean Tide Amplitude (a_o), Bay Tide Amplitude (a_B), Channel Depth (D_t), Bank Slope (m), Channel Width corresponding to Mean Water Depth (W) & Phase Lag (k). With our tool, you need to enter the respective value for Ocean Tide Amplitude, Bay Tide Amplitude, Channel Depth, Bank Slope, Channel Width corresponding to Mean Water Depth & Phase Lag 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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