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A velocity field is represented by the expression
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Chapter 5 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
- 5. Determine the 1, in order that the velocity constants т, and m x+lr y+mr z + nr where r = x² +y² +z° may satisfy the equation of V = r(x+r)'r(x+r)´ r(x+r)] continuity for a fluid motion.arrow_forward5. The velocity field of an incompressible flow is given by V = (a1x + a2y + azz) i + (b1 x + b2y + b3 z)j + (c1x + c2y + c32)k, where a1=2 and c3=-4. The value of b2 isarrow_forward1-Consider the flow of a fluid in rectangular coordinates VX=XY2, VY=-X2Y, VZ=0 and ρ=xy. Make sure the velocity and density represent a physically possible flow. Remarks: For resolution, use the continuity equation. Furthermore, it is important to look in the literature for what flow is possible from the continuity equation together with the substitution of rectangular coordinate values.arrow_forward
- B/ Two components of velocity in an incompressible fluid flow are given by v=z³y³ determine the third component. u= x² - y³ and Do the velocity field U = 5xi + (3y + ty2)j represent physically possible flow?arrow_forward1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.arrow_forward1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where 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.arrow_forward
- The velocity field is given as u=y-1 and v=y-2. The units of u and v are m/s and the units of x and y are meters. a) Draw the stream line passing through the point (x,y)=(4.3). b) Determine the streakline passing through the point (x, y) = (4,3) and compare it with the streamline. c) Determine whether the current is revolving or not.arrow_forward1. An idealized velocity field is given by the formula, V = 4txi – 2t²yj + 4xzk At the point (x, y, z) =(-1, +1, 0), compute the acceleration vector and magnitude of the acceleration.arrow_forwardA two-dimensional velocity field is given by v = xyi +3xtj, where x and y are in metres, t is in seconds and v is in metres per second. The magnitude of the acceleration at x = 1 m, y = 0.5 m and t = 2 secs isarrow_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_forwardy = 2r'sin20 (2) 0.5 m A 20 inviscid incompressible In addition, if Y=1, draw a streamline. Also plot some polar coordinates (r, 0) passing through the streamline, and indicate the direction of the velocity fluid flow around a corner is described by the stream function as shown. The fluid density is 1000kg/m3, and the plane is horizontal, determine the velocity potential. If the pressure at (1) is 30 kPa, what the pressure at (2)? vector.arrow_forwardChapter 6 Problems Euler's Equation 6.1 An incompressible frictionless flow field is given by V = (Ax +By)i+ (Bx-Ay)j where A=2s and B=2s and x and y are in meters. The fluid is water and g=gj . Determine the magnitude and acceleration of a fluid particle and the pressure gradient at (x.y) (2,2).arrow_forward
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