**Flow Field Analysis**Consider the flow field formed by combining a uniform flow in the positive \( x \)-direction and a source located at the origin. Let \( U = 30 \, \text{m/s} \) and \( m = 150 \, \text{m}^2/\text{s} \).1. **Plotting Velocity Ratios:** - Plot the ratio of local velocity to the freestream velocity as a function of \( \theta \) along the stagnation streamline.2. **Identifying Maximum Velocity:** - Locate the points on the stagnation streamline where the velocity reaches its maximum value.3. **Calculating Gage Pressure:** - Find the gage pressure at these points if the fluid density is \( 1.2 \, \text{kg/m}^3 \).**Note:** Any associated graphs or diagrams for visualizing these relationships should illustrate the velocity distribution along the streamline and highlight the points of maximum velocity and corresponding gage pressure calculations.

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Answered: Consider the flow field formed by…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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4. Consider a viscous flow inside an annular pipe. The inner surface of the pipe is located at r = R₁ and is stationary. The outer surface is located at r = Ro and moves to the right with speed Upipe. The pressure inside the pipe is constant. The fluid inside the pipe has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, axisymmetric, non-rotating, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity inside the pipe in terms of Upipe, R₁, Ro, and r. b. Determine the average velocity inside the pipe in terms of Upipe, R₁, and Ro. C. Determine the shear stress acting on the inner annulus in terms of Upipe, Ri, Ro, and u. Upipe er R₁ fluid
For a flow in the xy plane, the x component of the velocity is u=3x2y-y3is given. Determine the y component for steady state and incompressible flow. Does this result also apply to unstable, incompressible flow? Why is that? How many possible y components are there? Discuss.
An incompressible Newtonian fluid having a thickness of h, flows steadily in the x- direction along a fixed wall of infinite extent by the influence of the gravitational force (g=9.81 m/s²). There is no pressure change in the flow direction and air friction is negligible. Using the given parameter values; a determine the velocity function, b. calculate the shear stress that will occur along the wall. Z fixed wall air h 0 16.0 ↓
An incompressible viscous flow is contained between two parallel plates separated from each other by distance b. as shown in Figure 1. The flow is caused by the movement of the upper plate which has a velocity U, while the bottom plate is fixed. If U =7 m/s and b= 1 cm, and there is no pressure gradient in the flow direction. A.) Start with Navier-Stokes equations and determine the velocity at the point x = 3 cm and y= 0.41 cm. The value of the velocity is.B.) Calculate the magnitude of the vorticity at the same point. The magnitude value of vorticity. C.) Calculate the rate of angular deformation at the same point. The angular deformation value
Consider an airplane flying with a velocity of 50m/s at a standard altitude of 11km. At a point on the wing, the airflow velocity is 60 m/s. Calculate the pressure at this point. Assume incompressible flow.
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For the flow defined by the stream function ψ = V0y: (a) Plot the streamlines. (b) Find the x and y components of the velocity at any point. (c) Find the volume flow rate per unit width flowing between the streamlines y = 1 and y = 2.
5.6 The x component of velocity for a flow field is given as u = Ax²y² where A = 0.3 m3 s and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Determine the equation of the streamline and plot the streamline that goes thrquek. the noint (x.y)=(1,4).
Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.
Problem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by the following velocity components: V =16y-x and v, =16x + y %3D Determine the equation for the stream function and make sure continuity is satisfied.

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