Mass Transport Velocity to second-order Calculator

✖Height of The Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Height of The Wave [H_w]			+10% -10%
✖Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength of Wave [λ]			+10% -10%
✖Celerity of the Wave refers to the speed at which a wave propagates through a medium.ⓘ Celerity of The Wave [C]			+10% -10%
✖Distance above the Bottom expressing the local fluid velocity component.ⓘ Distance above the Bottom [D_Z+d]			+10% -10%
✖Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth for Fluid Velocity [d]			+10% -10%

✖Mass Transport Velocity is the mean drift velocity and is denoted by U(z) symbol.ⓘ Mass Transport Velocity to second-order [U_z]

⎘ Copy

👎

Formula

✖

Mass Transport Velocity to second-order

Formula

`"U"_{"z"} = (pi*"H"_{"w"}/"λ")^2*("C"*cosh(4*pi*("D"_{"Z+d"})/"λ"))/(2*sinh(2*pi*"d"/"λ")^2)`

Example

`"0.152155m/s"=(pi*"14m"/"32m")^2*("24.05m/s"*cosh(4*pi*("2m")/"32m"))/(2*sinh(2*pi*"17m"/"32m")^2)`

Calculator

LaTeX

Reset

👍

Download Coastal and Ocean Engineering Formula PDF

Mass Transport Velocity to second-order Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Transport Velocity = (pi*Height of The Wave/Wavelength of Wave)^2*(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))/(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2)
U_z = (pi*H_w/λ)^2*(C*cosh(4*pi*(D_Z+d)/λ))/(2*sinh(2*pi*d/λ)^2)
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sinh - The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function., sinh(Number)
cosh - The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2., cosh(Number)

Variables Used

Mass Transport Velocity - (Measured in Meter per Second) - Mass Transport Velocity is the mean drift velocity and is denoted by U(z) symbol.
Height of The Wave - (Measured in Meter) - Height of The Wave is the difference between the elevations of a crest and a neighboring trough.
Wavelength of Wave - (Measured in Meter) - Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave.
Celerity of The Wave - (Measured in Meter per Second) - Celerity of the Wave refers to the speed at which a wave propagates through a medium.
Distance above the Bottom - (Measured in Meter) - Distance above the Bottom expressing the local fluid velocity component.
Water Depth for Fluid Velocity - (Measured in Meter) - Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Height of The Wave: 14 Meter --> 14 Meter No Conversion Required
Wavelength of Wave: 32 Meter --> 32 Meter No Conversion Required
Celerity of The Wave: 24.05 Meter per Second --> 24.05 Meter per Second No Conversion Required
Distance above the Bottom: 2 Meter --> 2 Meter No Conversion Required
Water Depth for Fluid Velocity: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_z = (pi*H_w/λ)^2*(C*cosh(4*pi*(D_Z+d)/λ))/(2*sinh(2*pi*d/λ)^2) --> (pi*14/32)^2*(24.05*cosh(4*pi*(2)/32))/(2*sinh(2*pi*17/32)^2)

Evaluating ... ...

U_z = 0.152154520491551

STEP 3: Convert Result to Output's Unit

0.152154520491551 Meter per Second --> No Conversion Required

FINAL ANSWER

0.152154520491551 ≈ 0.152155 Meter per Second <-- Mass Transport Velocity

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Local Fluid and Mass Transport Velocity » Mass Transport Velocity » Mass Transport Velocity to second-order

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 M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Calculator and 900+ more calculators!

< 2 Mass Transport Velocity Calculators

Wave Height for Mass Transport Velocity to second-order

Go Height of The Wave = (Wavelength of Wave*((Mass Transport Velocity*(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2/(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))))^0.5)/pi)

Mass Transport Velocity to second-order

Go Mass Transport Velocity = (pi*Height of The Wave/Wavelength of Wave)^2*(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))/(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2)

Mass Transport Velocity to second-order Formula

What is Wave Celerity?

The Wave Celerity is defined as the speed at which an individual wave advances or “propagates” . The open channel Surges due to sudden changes of flow depth creates Celerity (Wave Velocity) in the flow in addition to the normal water velocity of the channels. These waves travel in the downstream and sometimes upstream of the channels depending on the various situations.

What is Wavelength?

Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave). Wavelength is inversely proportional to frequency. This means the longer the wavelength, lower the frequency.

How to Calculate Mass Transport Velocity to second-order?

Mass Transport Velocity to second-order calculator uses Mass Transport Velocity = (pi*Height of The Wave/Wavelength of Wave)^2*(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))/(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2) to calculate the Mass Transport Velocity, The Mass Transport Velocity to second-order may be measured as the ratio of the displacement of a particle to the length of the corresponding time interval provided and that the contribution from the second-order terms is large compared with that from the first- order terms. Mass Transport Velocity is denoted by U_z symbol.

How to calculate Mass Transport Velocity to second-order using this online calculator? To use this online calculator for Mass Transport Velocity to second-order, enter Height of The Wave (H_w), Wavelength of Wave (λ), Celerity of The Wave (C), Distance above the Bottom (D_Z+d) & Water Depth for Fluid Velocity (d) and hit the calculate button. Here is how the Mass Transport Velocity to second-order calculation can be explained with given input values -> 0.152155 = (pi*14/32)^2*(24.05*cosh(4*pi*(2)/32))/(2*sinh(2*pi*17/32)^2).

FAQ

What is Mass Transport Velocity to second-order?

The Mass Transport Velocity to second-order may be measured as the ratio of the displacement of a particle to the length of the corresponding time interval provided and that the contribution from the second-order terms is large compared with that from the first- order terms and is represented as U_z = (pi*H_w/λ)^2*(C*cosh(4*pi*(D_Z+d)/λ))/(2*sinh(2*pi*d/λ)^2) or Mass Transport Velocity = (pi*Height of The Wave/Wavelength of Wave)^2*(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))/(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2). Height of The Wave is the difference between the elevations of a crest and a neighboring trough, Wavelength of Wave can be defined as the distance between two successive crests or troughs of a wave, Celerity of the Wave refers to the speed at which a wave propagates through a medium, Distance above the Bottom expressing the local fluid velocity component & Water Depth for Fluid Velocity is the depth as measured from the water level to the bottom of the considered water body.

How to calculate Mass Transport Velocity to second-order?

The Mass Transport Velocity to second-order may be measured as the ratio of the displacement of a particle to the length of the corresponding time interval provided and that the contribution from the second-order terms is large compared with that from the first- order terms is calculated using Mass Transport Velocity = (pi*Height of The Wave/Wavelength of Wave)^2*(Celerity of The Wave*cosh(4*pi*(Distance above the Bottom)/Wavelength of Wave))/(2*sinh(2*pi*Water Depth for Fluid Velocity/Wavelength of Wave)^2). To calculate Mass Transport Velocity to second-order, you need Height of The Wave (H_w), Wavelength of Wave (λ), Celerity of The Wave (C), Distance above the Bottom (D_Z+d) & Water Depth for Fluid Velocity (d). With our tool, you need to enter the respective value for Height of The Wave, Wavelength of Wave, Celerity of The Wave, Distance above the Bottom & Water Depth for Fluid Velocity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search