A,B The overall streamfunction for a particular inviscid 2D flow field is ...Вy = f(r,0)= A0+²sin 0in which y has units of ft2/s when r has units of feet. A and B are constantsthat are not a function of r or 0. The fluid in this flow field is water(incompressible) and you may neglect any effects of gravity.The velocities are known at this location ( r1 = 6.0 ft, 0 = t/5 )...Vr = 12 ft/sandve=4 ft/s(2.a) Show that this flow field is irrotational.(2.b) Find the equation for the equipotential ø= f(r,0) for this flow field.Your answer will contain one/both of the constants -----(2.c) Determine the numerical values for A and B.Consider a second location ( r2 = 3 ft, 2 = 5Tt/6 ).(2.d) Find the pressure difference [ psi ] P1 – P2.

Given a stream function for 2D flow ψ=fr,θ = Aθ+Brsinθ in which A and B are constants that are not functions of r and θ To determine: (i) show that flow field is irrotational (ii) Find the the equation for the equipotential ∅=fr,θ for this flow field(I) For the flow to be irrotational 1rr∂rr∂ψ∂r + 1r2∂2ψ∂θ2 = 0 ----(i) ∂ψ∂r=-Br2sinθ and ∂2ψ∂θ2= -Brsinθ Substituting these values in the equation (i) 1r∂∂r-Brsinθ + 1r2-Brsinθ = Br3sinθ - Br3sinθ = 0 Hence the flow is irrotational (ii) Equation for equipotential According to Cauchy Reiman equations in cylindrical polar coordinates ∂ϕ∂r= ∂ψr∂θ and ∂ϕr∂θ= -∂φ∂r On differentiating ψ with respect to θ, ∂ϕ∂r= 1rA+Brcosθ On integrating with respect to r, ϕ=Alnr -Brcosθ which is the equation for the flow field.