4.8 Determine the v velocity component such that continuity equation is satisfied if two components are u = 2y², w = 2xyz: (a) -2xy + x2y+f(y,z) (b) 4xy + x²y + f(y,z) (d) -2xy - x²y+f(y,z) (e) 4xy − x²y + f (y, z) (c) -4xy-x²y + f (y, z) 4.9 A fluid flow field is given by V = (y²x)i + (z²x)j - (2xyz + yz)k. Its acceleration at the point (2,4,4) is: (a) 361-27j + 100k (d) 361-27j (b) 361-27j - 100k (e) None of the mentioned (c) 28i27j + 100k 4.10 In a two dimensional incompressible flow, the velocity component along the x-axis is u = ax² + bxy + cy². If v = 0 at y = 0, what will be the velocity component in the y-direction? b (a) v = 2axy + by² (b) v = 2axy + by² (c) v = -2axy + y² (d) v = -2axy-y² (e) v = 2axy + by² 4.11 If U xyz³, then V²U is: = (a) 2xz33xy²z (b) 2xz³ + 6xy²z (c) 2xz3 + 3xy²z (d) 2xz³ - 6xy²z (e) None of the mentioned 4.12 If a = x²y2k, then curl(a) is: (note that curl(a) = V × a) (a) 2x²yj-2xy²k (b) 2x²yj+2xy²k (c) x²yj + 2xy²k (d) x²yj -2xy²k (e) None of the mentioned