For a given flow the velocity from time t=0 to t=5s was u=2 m/s, v=0. Then from t=5s to t=10s the velocity was u=+3 m/s, v=-4 m/s. A dye streak was started at t=0, and a path was traced from that same point at the same time. Draw to scale the streakline, pathline, and streamlines at t=10s. Please solve and explain.
I have seen the solution to this problem and am still confused at how to solve/sketch. Is there a fluids reference website that you may suggest?© BrainMass Inc. brainmass.com September 20, 2018, 4:16 pm ad1c9bdddf - https://brainmass.com/engineering/structural-engineering/sketch-a-streamline-pathline-and-streakline-8572
Because, the differential equation of stream line is given as;
dx/u = dy/v
from 0 to 5 sec:
=>dy/dx = v/u = 0/2 = 0
=> y = constant.
Let initial point is the origin (0,0)
Because, velocity along y-direction is ...
The solution is a step-by-step equation process. The attachment is an image to further understanding of the answer.