Question: How to solve substitution?

I have a PDE

eq1 := du/dx+dv/dy = 0; eq2 := du/dt+u*du/dx+v*du/dy-nu*d^2*u/dy^2 = 0

where u(x, y, t), v(x, y, t) and

eta(x, y, t):=y/((nu*t*cos(alpha)+(nu*x)/(U[w])*sin(alpha))^(1/(2)));

psi(x, y, t):=U[w]*(nu*t*cos(alpha)+(nu*x)/(U[w])*sin(alpha))^(1/(2))*f(eta(x,y,t));

u = diff(psi, y); v= -diff(psi, x).

How to substitiute u = diff(psi, y); v= -diff(psi, x) in eq1 and eq2, Also find the value of nu.

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