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Problem 1: The speed of shallow water waves in the ocean (e. g. seismic sea waves...
Problem 16.85 A water wave is a shallow-water wave if the water depth d is less...
Problem 16.85 A water wave is a shallow-water wave if the water depth d is less than λ/10. It is shown in hydrodynamics that the speed of a shallow-water wave is /gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 110 m, are shallow-water waves when the water depth is less than 11 m Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of...
25.The plane or depth to which waves may erode the bottom of the ocean in shallow water? 25.The plane or depth...
25.The plane or depth to which waves may erode the bottom of the ocean in shallow water?
25.The plane or depth to which waves may erode the bottom of the ocean in shallow water?
6. Use dimensional analysis to show that in a problem involving shallow water waves (Fig. P7-...
6. Use dimensional analysis to show that in a problem involving shallow water waves (Fig. P7- 87), both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density r, and fluid viscosity m. Manipulate your P's to get the parameters into the following form: pch Fr f(Re) where ReD gh ?, ?
Review | Constants Part A A water wave is a shallow-water wave if the water depth...
Review | Constants Part A A water wave is a shallow-water wave if the water depth d is less than ~ 1/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v= Vgd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 110 m , are shallow-water waves when the water depth is less than 11 m. Consider a beach where the depth increases linearly with distance from the...
III. Scaling and Modeling a. Assume that the modeling of tsumanis (waves in the ocean that...
III. Scaling and Modeling a. Assume that the modeling of tsumanis (waves in the ocean that are caused by earthquakes) can be expressed as a function of four parameters: water depth, wave speed, gravity, and pressure. Use the Buckingham-Pi theorem to produce a dimensionless number (and there is only one) that expresses the relationships of these parameters. Hint: you should end up with something that was seen in our discussion of waves) (40 points)
Question 4. (25%) Surface gravity waves: (a) Write down the expression for phase speed c for surf...
Question 4. (25%) Surface gravity waves: (a) Write down the expression for phase speed c for surface gravity waves if their wavelength λ is much shorter than the water depth. Are these 'deep- water' waves or 'shallow water' waves? Explain briefly. (b) Write the expression for wavenumber k in terms of wavelength λ. (c) Evaluate the phase speeds for a wavelength of 10 meters, and for a wavelength of 500m. (d) Using these results, suppose the waves are generated by...
What is the phase speed (celerity) for a shallow water gravity wave of length 41 m,...
What is the phase speed (celerity) for a shallow water gravity wave of length 41 m, in water depth h = 2 m? Use the shallow water approximation. Use the following values for constants (if required): g = 9.81 m/s^2,ρ = 1025 Kg/m^3, σ ′ = 0.072 N/m, π ≈ 3.14. Write your answer in m s to the nearest thousandth
2 > (25pts) In studying sand transport by ocean waves, it was postulated that the threshold...
2 > (25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom shear stress t required to move particles depends on gravity g, particle size d, particle density Pp water viscosity and water density p. Find all the dimensionless, i.e., pi groups for this problem. Consider p, g, d as repeating variables. Write all the quantities in terms of the primary dimensions, i.e. M, L, T. For example, the dimension of viscosity u is...
(25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom...
(25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom shear stress t required to move particles depends on gravity g, particle size d, particle density Pp , water viscosity u and water density p. Find all the dimensionless, i.e., pi groups for this problem. Consider p, g, d as repeating variables. Write all the quantities in terms of the primary dimensions, i.e. M, L, T. For example, the dimension of viscosity u is...
<HW 2.2 Properties of Ocean Waves How fast are the waves traveling? Express the speed e...
<HW 2.2 Properties of Ocean Waves How fast are the waves traveling? Express the speed e in meters per second using three significant figures. Review Constants Periodic Table A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.10 s for the boat to travel from its highest point to its lowest, a total distance of 0 670 m. The...
Problem 16.85 A water wave is a shallow-water wave if the water depth d is less than λ/10. It is shown in hydrodynamics that the speed of a shallow-water wave is /gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 110 m, are shallow-water waves when the water depth is less than 11 m Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of...
25.The plane or depth to which waves may erode the bottom of the ocean in shallow water?
25.The plane or depth to which waves may erode the bottom of the ocean in shallow water?
6. Use dimensional analysis to show that in a problem involving shallow water waves (Fig. P7- 87), both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density r, and fluid viscosity m. Manipulate your P's to get the parameters into the following form: pch Fr f(Re) where ReD gh ?, ?
Review | Constants Part A A water wave is a shallow-water wave if the water depth d is less than ~ 1/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v= Vgd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 110 m , are shallow-water waves when the water depth is less than 11 m. Consider a beach where the depth increases linearly with distance from the...
III. Scaling and Modeling a. Assume that the modeling of tsumanis (waves in the ocean that are caused by earthquakes) can be expressed as a function of four parameters: water depth, wave speed, gravity, and pressure. Use the Buckingham-Pi theorem to produce a dimensionless number (and there is only one) that expresses the relationships of these parameters. Hint: you should end up with something that was seen in our discussion of waves) (40 points)
Question 4. (25%) Surface gravity waves: (a) Write down the expression for phase speed c for surface gravity waves if their wavelength λ is much shorter than the water depth. Are these 'deep- water' waves or 'shallow water' waves? Explain briefly. (b) Write the expression for wavenumber k in terms of wavelength λ. (c) Evaluate the phase speeds for a wavelength of 10 meters, and for a wavelength of 500m. (d) Using these results, suppose the waves are generated by...
2 > (25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom shear stress t required to move particles depends on gravity g, particle size d, particle density Pp water viscosity and water density p. Find all the dimensionless, i.e., pi groups for this problem. Consider p, g, d as repeating variables. Write all the quantities in terms of the primary dimensions, i.e. M, L, T. For example, the dimension of viscosity u is...
(25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom shear stress t required to move particles depends on gravity g, particle size d, particle density Pp , water viscosity u and water density p. Find all the dimensionless, i.e., pi groups for this problem. Consider p, g, d as repeating variables. Write all the quantities in terms of the primary dimensions, i.e. M, L, T. For example, the dimension of viscosity u is...
<HW 2.2 Properties of Ocean Waves How fast are the waves traveling? Express the speed e in meters per second using three significant figures. Review Constants Periodic Table A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.10 s for the boat to travel from its highest point to its lowest, a total distance of 0 670 m. The...
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