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Question 3 (20 marks): Solution of Stream Function to Planar 2D Jet It turns out that the ODE and associated set of boundary conditions for the2Dplanar jet above can actually be solved analytically to yield a closed form solution! All it takes is a couple of integrations of the ODE. 1. Prove that the ODE above can be solved to yield: \[ f(\eta)=C \tanh C \eta \quad(10 \text { marks }) \] Hint: You will need the following: \[ \frac{d}{d x} \tanh ^{-1} x=\frac{1}{1-x^{2}} \] 2. What is the stream function(x,y)for the 2D planar jet? (2 marks) 3. If=1.0105[m2/s],U0=3.5[m/s],h=1[cm], and depth into the pageb=20[cm], what must be the value of constantCinf()?( 8 marks)

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