the Barotropic pressure gradient vs friction equation is given like G*diff(eta)(x),x)=Az *diff(u)(z),z,z) where diff(eta)(x)=S

so now the balance equation becomes diff(u)(z),z,z)=(g*S)/Az (and here z = depth), u= velocity) and right side all are constant

it is given that

when z=0, that is in the surface Az*diff(u)(z),z)=0, and when z=-H then Az*diff(u)(z),z)=tau(b)/rho or (bottom friction/water density)

Again it is given that tau (bottom friction term)=(Cb*u^2)*rho

so we get        diff(u)(z),z)=Cb*u^2(z)/Az

Finally the solution is

u(z)=(g*S*z^2)/2*Az - (g*H*S^2)/2*Az+sqt(g*S*H/Cb)

now if I take Az=0.0010, Cb=0.0025, S=-0.000001, g=9.8, H=20, and z=-20 to 0 ( plot) for different value of Cb and Az

another value for Az=0.005, Cb=0.001

I think now you can help me in solving the equation in maple

regards

Muslem Uddin

The problem was like this

the Barotropic pressure gradient vs friction equation is given like G*diff(eta)(x),x)=Az *diff(u)(z),z,z) where diff(eta)(x)=S

so now the balance equation becomes diff(u)(z),z,z)=(g*S)/Az (and here z = depth), u= velocity) and right side all are constant

it is given that

when z=0, that is in the surface Az*diff(u)(z),z)=0, and when z=-H then Az*diff(u)(z),z)=tau(b)/rho or (bottom friction/water density)

Again it is given that tau (bottom friction term)=(Cb*u^2)*rho

so we get        diff(u)(z),z)=Cb*u^2(z)/Az

Finally the solution is

u(z)=(g*S*z^2)/2*Az - (g*H*S^2)/2*Az+sqt(g*S*H/Cb)

now if I take Az=0.0010, Cb=0.0025, S=-0.000001, g=9.8, H=20, and z=-20 to 0 ( plot) for different value of Cb and Az

another value for Az=0.005, Cb=0.001

I think now you can help me in solving the equation in maple

regards

Muslem Uddin

Dear G A Edgar

would you please let mem know your mail address so that i can mail you the problem

thanks for your response.

Regards

Uddin(mmu_ims76@yahoo.com)