The velocity components in a steady, incompressible, 2-dimensional flow field are given by V = U i + 0 j.
a. Determine the corresponding stream function, ψ, and velocity potential, φ.
b. If U = 1 m/s, determine the value of ψ at y = 0.1 m and the value of φ at x = 0.1 m.
c. If ψ2 is a horizontal line at y = 0.5 m and the value of ψ along the x-axis is zero, calculate the volume flow rate per unit width between these two streamlines when U = 5 m/s.
17. Define briefly the following terms.
a. Streamline: A streamline is a line that is tangent to the velocity vector at every point in a flow field. It represents the path followed by a fluid particle in steady flow.
b. Equipotential line: An equipotential line is a line in a flow field where the velocity potential is constant. It represents a line of equal potential in the flow.
c. Irrotational flow: Irrotational flow is a flow field in which the fluid particles do not rotate as they move. This means that the vorticity, which represents the local rotation of fluid particles, is zero everywhere in the flow field.