Sol. For the straight-line assumption, the relation between velocity v and distance y is v = 15y, dv = 15dy. The velocity gradient = dv/dy = 15. Since µ = τ (dv/dy), τ = µ (dv/dy). For y = 0 (i.e., at the boundary), v = 0 and dv/dy = 15 s –1 ; τ = (0.0010) (15) = 0.015 lb/ft 2 . For y = 1 in, 2 in, and 3 in, dv/dy and τ are also 15 s –1 and 0.015 lb/ft 2 , respectively.

For the parabolic assumption, the parabola pases through the points v = 0 when y = 0 and v = 45 when y = 3. The equation of this parabola is v = 45 – 5(3 – y) 2 , dv/dy = 10(3 – y), τ = 0.0010 (dv/dy). For y = 0 in, v = 0 in/s, v = 0 in/s, dv/dy = 30 s –1 , and τ = 0.030 lb/ft 2 . For y = 1 in, v = 25 in/s, dv/dy = 20 s –1 , and τ = 0.020 lb/ft 2 . For y = 2 in, v = 40 in/s, dv/dy = 10 s –1 , and τ = 0.010 lb/ft 2 . For y = 3 in, v = 45 in/s, dv/dy = 0 s –1 , and τ = 0 lb/ft 2 .