Water flows steadily through the nozzle with a volume rate Q = 3 m^3/s. Determine (a) the velocity at the exit, and (b) the acceleration at the position x.
Work:
(a) Determine the velocy at the exit
Flow is steady, incompressible and one-dimensional
The average velocity at the exit V2 is related to the average velocity at the inlet V1 by:
V2 = V1*(A1/A2), where A = area
V2 = V1*(a1/a2)^2, where a1 = radius of inlet nozzle and a2 = radius of exit nozzle
Q = V1*A1
V1 = Q/A1 = (3 m^3/s)/(6 m^2) = (1/2) m/s
a1 = 1 m and a2 = 0.5 m
V2 = (.5 m/s)*(1 m/.5 m)^2
V2 = 2 m/s
V2 = 2 m/s
(b) Determine the acceleration at the position x
a = V^2/R = (3y i + 6x j + x^2 k)^2/R