Shallow-water velocity equationa. Confirm that the linear approximation to f(x) = tanh x ata = 0 is L(x) = x.b. Recall that the velocity of a surface wave on the ocean2ndtanh -In fluid dynamics, shallowis v =water refers to water where the depth-to-wavelength ratiod/A < 0.05. Use your answer to part (a) to explain why theshallow water velocity equation is v = Vgd.c. Use the shallow-water velocity equation to explain whywaves tend to slow down as they approach the shore.

a. Suppose that is 'f' differentiable on an interval l containing the point α. The linear…

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Fluid mechanics question Can you give a problem with solution about specific volume property
Define and briefly explain the_terms listed below, support your elaboration with mathematicalequations and illustrations where necessary:1. Viscous flow, inviscid flow, compressible and incompressible flow2. Laminar flow, tubulent flow, steady and unsteady tlow3. Reynolds number and Mach number4. VIScOSty, specific gravity, specitic densityBuoyancy., centre of gravity and center of pressure. Bemoulli's equation
% ParametersD = 0.1; % Diameter of the tube (m)L = 1.0; % Length of the tube bundle (m)N = 8; % Number of tubes in the bundleU = 1.0; % Inlet velocity (m/s)rho = 1.2; % Density of the fluid (kg/m^3)mu = 0.01; % Dynamic viscosity of the fluid (Pa.s) % Define the grid size and time stepdx = D/10; % Spatial step size (m)dy = L/10; % Spatial step size (m)dt = 0.01; % Time step size (s) % Calculate the number of grid points in each directionnx = ceil(D/dx) + 1;ny = ceil(L/dy) + 1; % Create the velocity matrixU_matrix = U * ones(nx, ny); % Perform the iterationsfor iter = 1:100 % Calculate the velocity gradients dUdx = (U_matrix(:, 2:end) - U_matrix(:, 1:end-1)) / dx; dUdy = (U_matrix(2:end, :) - U_matrix(1:end-1, :)) / dy; % Calculate the pressure gradients dpdx = -mu * dUdx; dpdy = -mu * dUdy; % Calculate the change in velocity dU = dt * (dpdx / rho); % Update the velocity matrix U_matrix(:, 2:end-1) = U_matrix(:, 2:end-1) + dU; % Apply…
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Fluid mechanics question Can you give a problem and solution about specific gravity property
1. Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. a) Is the flow field incompressible at all times? b) Compute the convective derivative of each velocity component: Du/Dt and Dv/Dt. c) By considering the velocity gradients, determine whether the fluid elements experience any deformation. What type(s) of deformation do they experience? d) Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational. e) Given that the density of the fluid does not vary spatially and changes only with time, what differential equation for the density, p(t), must be satisfied for this scenario to represent a physical, compressible flow field? f) At time t = 0, the density everywhere is p = Po. Determine how the density changes with time, given the situation does represent a physical, compressible flow field.
03:31 Given-Assign... External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: PND? and a, = b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750 kg/m and the dynamic viscosity is 0.2 N.s/ m² . For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s / m². IN =1 kgm
a) Consider steady and incompressible two-dimensional fluid flow field with a radial velocity component, Ur. The equation for the radial velocity component is: Ur = 5r² sine Determine the expression for the corresponding tangential velocity component, U required to satisfy the conservation of mass.
Don't use chat gpt are any ai, plz i vill upvote u for right answer... Needs Complete typed solution with 100 % accuracy.
3.11 For a 2D flow, the velocity potential function is given by =x - y, find the velocity at points (2, 2) and (2, 4). In addition, determine the flow rate between the streamlines passing through these points. [Ans: 4/2 units, 4/5 units, 8 units] 0 10
1. The potential function of fluid flow motion is given by, [(x+c)2+y²7 p = log la-e)2+y². a) Prove that, fluid is incompressible, b) Find the velocity field, c) Find the geometric location of the providing IV? = constant. %3D

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