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A velocity field is represented by the expression
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Fox and McDonald's Introduction to Fluid Mechanics
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- The velocity components of an incompressible, two-dimensional field are given bythe following equations: u(x,y) =y^2 -x (1+x) v(x,y) = y(2x+1) Show that the flow field is (a) irrotational and (b) satisfies conservation of mass.arrow_forward1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?arrow_forwardConsider the flow field shown. Coordinates are measured in meters. For the particle that passes through the point ðx, yÞ = ð1, 2Þ at the instant t = 0, plot the pathline during the time interval from t = 0 to 3 s. Compare this pathline with the streakline through the same point at the instant t=3s.arrow_forward
- A 2D incompressible velocity field is defined by . If both u and v are 0 at point (x = 0, y = 0), determine a) v component of the velocity and b) an expression for pressure field. Assume gravity is in the – y-direction and pressure is 0 at point (x=0, y=0). The flow is defined by: u=2(x2-y2)arrow_forwardA venturi tube is used to determine the airspeed at the throat/test section. During the test, a raise of 4.8 inches of water was recorded in the instrument. Determine the velocity of the at the (a) smallest and (b) largest section, when the ratio of the area between the largest and smallest section is 75:30. Assume incompressible flow and standard sea-level conditions.arrow_forwardThe expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.arrow_forward
- The velocity for the 2-dimensional flow is defined by V =(3y2 i+4xj) m/s, where y is in meters. Determine the equation of the streamline that passes through point (2 m, 1 m). only HANDWRITTEN answer needed ( NOT TYPED)arrow_forwardThe velocity field for an incompressible flow is given by V = 5x ^ 2i- 20 xyj + 100tk. Explain whether this flow is steady or not. Is the flow two or three dimensional? Determine the magnitude and direction of the velocity and acceleration of a flow particle at t = 0.2 and position (1, 2, 3).arrow_forwardchoose the correct answer 3- when the flow is happened without change in its quantity or velocity with time , then the flow is: * a) Unsteady b) Uniform c) Steady d-None of all above 4- Reynolds number represents: * a) Viscosity force to inertia force b) Inertia force to viscosity force c) Equality between inertia and viscosity forces d-None of all abovearrow_forward
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