Given velocity fieldV(x,y,z,t) = (5xy² + t)i + (2z + 8)j +18km/s, with x,y,z in meters and it in seconds. Calculate V(9, -2, 1,4). What is the magnitude o this velocity?
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- 2. The velocity components expressed in m/s in a fluid flow is known to be: 2 u= 2yzt v=xy W=4xzt² Find the acceleration of a fluid particle at point, P (2m,1m,1m) when time is 2 s.Given a velocity field as V(x, y, z) = axî – ayĵ %3D With units of velocity in m/sec; x and y in meters; and the constant coefficient a = 0.1 sec. a) Determine the equation for the streamline passing through the point (x, y, 0) = (2, 8, 0). b) Determine the velocity of a particle at the point (2, 8, 0). c) If we mark the particle passing through the point (xo, Yo, 0) at to = 0, determine the location of the particle at time t = 20 sec. d) Show that the equation of the particle path (the pathline) matches the equation of the streamline.The two components of the velocity vector are given as Vx = –ay/(x2+ y2)1/2 and Vy = ax/(x2+ y2)1/2 where a is a constant in cm/s. Find the vorticity of a fluid element located at x = y = 1 cm. [Ans.: 1.41a k ].
- The position of an object moving along an x axis is given by x = 3t - 4t? + t, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity for the time interval from t = 2 s tot = 4 s? (g) Graph x versus t for 0Home 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 flowtwo-dimensional velocity field u =xt + 2y and v =xt^2- yt x=1 meter y= 1 meter and t= 1 second Find the acceleration where it is.?The position of an object moving along an x axis is given by x = 3t – 412 + , where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity for the time interval from t 2 s to t = 4 s? (g) Graph x versus t for 0A flow is described by velocity field, V=ayi+btj, where a=1 s-1and b=0.5 m/s2.At t=n s (Where n is 19), what are the coordinates of the particle that passed through point (1,2) at t=n-1? At t=n+1 s, what are the coordinates of the particle that passed through point (1,2) at t=n+1 s? Plot the pathline and streakline through point (1,2) and compare with the streamlines through the same point at the instants t=n-1 , n and n+1 s.Consider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis is= [2x² + y³ , flow. Is the flow irrotational? Q4) Let v xyz + 2y, xy + zy] be the velocity vector of steady fluidp) A mass of fluid is in motion so that the lines of motion lie on the surface of coaxial cylinders. Show that the equation of continuity is partial differential ap 1 a 5(pvo) + əz - (ρυ.) 0 r d0 where (v,, vg, vz) are the components of velocity in cylindrical co-ordinates and p is the density.A 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 isSEE MORE QUESTIONSRecommended textbooks for youElements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
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