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The velocity field for steady inviscid flow from left to right over a circular cylinder, of radius R is given by
Obtain expressions for the acceleration of a fluid particle moving along the stagnation streamline (θ = π) and for the acceleration along the cylinder surface (r = R). Plot ar as a function of r = R for θ = π, and as a function of θ for r = R; plot aθ as a function of θ for r = R. Comment on the plots. Determine the locations at which these accelerations reach maximum and minimum values.
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Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
- 3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian coordinates by u == AxBt. Show that x = f(x, t) in the Lagrange coordinates can be obtained from the Eulerian system. The in- itial position of the fluid particle is designated by x) and the initial time to = 0 may be assumed.arrow_forward4 = 3x2 – y represents a stream function in a two – dimensional flow. The velocity component in 'x' direction at the point (1, 3) is:arrow_forwardb. The velocity vector in a fluid flow is given as V = 4x³i – 10x²yj + 2tk . Find (i) The velocity of a fluid particle at (2, 1, 3) at time t=1. (ii) The acceleration of a fluid particle at (2,1,3) at time t =1.arrow_forward
- Given the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u Varrow_forwardThe velocity vector in a fluid flow is given by V = 2xy3i – 5x2yj + 4xyztk. Find the velocity and acceleration of a fluid particle at (1, 2, 1) at time, t = 0.arrow_forwardConsider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis isarrow_forward
- 1. For incompressible flows, their velocity field 2. In the case of axisymmetric 2D incompressible flows, where is Stokes' stream function, and u = VXS, S(r, z, t) = Uz = where {r, y, z} are the cylindrical coordinates in which the flow is independent on the coordinate and hence 1 Ꭷ r dr 1 dy r dz Show that in spherical coordinates {R, 0, 0} with the same z axis, this result reads Y(R, 0, t) R sin 0 S(R, 0, t) UR uo Y(r, z, t) r = = -eq, and Up = = 1 ay R2 sin Ꮎ ᎧᎾ 1 ƏY R sin Ꮎ ᎧR -eq 2 (1) (2) (3)arrow_forward9- V(D1)^2=V1(D2)^2 mass 10 points continuity equation O true O False 10-stream line is a line giving 10 points direction of velocity at any point. O True O Falsearrow_forward4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?arrow_forward
- Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flowarrow_forwardIn a stream line steady flow, two points A and B on a stream line are 1 m apart and the flow velocity varies uniformly from 2 m/s to 5 m/s/ What is the acceleration of fluid B?arrow_forward1. For a two-dimensional, incompressible flow, the x-component of velocity is given by u = xy2 . Find the simplest y-component of the velocity that will satisfy the continuity equation. 2. Find the y-component of velocity of an incompressible two-dimensional flow if the x-component is given by u = 15 − 2xy. Along the x-axis, v = 0.arrow_forward
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