1. Stagnation PointsA steady incompressible three dimensional velocity field is given by:V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)kWhere the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s].a) Determine coordinates of possible stagnation points in the flow.b) Specify a region in the velocity flied containing at least one stagnation point.c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal-distance from your specified stagnation point.

given data stagnation point it is the point at which the velocity of flow remains zero or cionstant…

Answered: 1. Stagnation Points A steady…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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An omnidirectional robot is equipped with 3 Swedish wheels with radii r = r₂ = ₁ = r. The angle between X, and XR is 0. Suppose that robot's local reference frame, {R}, is aligned such that the robot moves forward along +XR. What is the velocity vector, ? Y₁ wo(t) Ꮎ v(t) X₁
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.
When a valve is opened, a certain fluid flows through the choke duct or valve (see figure), according to the relationship: V= V (1 + x/L) i Determine a) If the flow is stationary or transient. b) The acceleration (ax) of the fluid applying Euler's approach. c) The position of the particle as a function of time at x = 0 and t = 0. d) Determine the acceleration of the particle as a function of time.
2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂
X2 = 5x1 + 5x2 - 7x3
4. Fluid Dynamics: Blood in a new pediatric blood cannula can be described by Equation 1 below. We assume that flow conditions are steady (time independent), fully developed (fluid layers moving consistently), with laminar flow properties (no mixing or rotational fluid dynamic properties). This fluid flow is often referred to as Poiseuille flow. The figure below illustrates the concept of Poiseuille flow and the characteristic parabolic velocity distribution. X 154 AL The governing fluid momentum equation in the x-flow direction is as follows: nd dv ΔΡ 74(*)= [1] r dr dr AL is the fluid viscosity, r refers to the radial position, and AP/AL signifies the where v corresponds to the velocity, imposed pressure gradient driving flow. a. Integrated the differential equation to find v(r). Using the following boundary conditions, determine the expressions for the constants of integration in the solution to part a) and the final velocity distribution equation (parabolic shape): v must be…
1 Velocities are measured at different locations using a data logger and the field is given by the technician in the following vector form. Given that. du du ax = +u-+v. +w du du ôt əx ду əz V = 3tî +xzj+t Find the magnitude of velocity and acceleration at point (1,1,1) at time t = 1 second. Write the acceleration vector. If the fluid is incompressible, show that the flow field satisfies the conservation of mass. zj+ty²k m/s Əv dv dv Əv +u- +v +w- at Əx ду əz dw dw dw dw + w a ₂ = +u Ət Əx dy əz +v
Fluid Mechanics Problem: Part d) please. Thanks
Cauchy's ΣF ) equation of motion : pDV/Dt =pg + VT (like pa Newtonian viscous stress relations by the tensor relation : Ti j = - pôij + µ[Əvj/əxi + əvi/axj] where dij is the kroneker delta function (1 for i = T includes pressure and viscous surface forces. into Cauchy's equation, and assume constant viscosity, to get the Navier-Stokes vector eq'ns : pDV/Dt Pg -vp + μ^2 V the acceleration DV/Dt av/at+ (VV)V, which for steady state flow gives DV/Dt =(V.) V. Because (VV) V is a non-linear term on the LHS of the N-S equation Reynolds Number RepVL/μ, a measure of the ratio of inertial to viscous forces. : Patm 10^5 = = N = N = ; pwater 1000; pair 1.2; μwater 10^-3 N s/m^2 ; Hair 2 x 10^-5 N•s/m^2 ; g 9.8 m/s^2 = j; 0 for i j ); N
Find required force equation in terms of v, h, l, and delta p
t = 0

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