Velocity profile for a fluid with no net volume flux

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I've established a relationship between the upper horizontal boundary layer $U$ and pressure gradient $G$ where $\mu$ is dynamic viscosity and h is the height of the pipe the fluid is travelling through

$$U=\frac {Gh^2} {6\mu}$$

And I'm now asked to sketch the velocity profile... apparently its a parabola from $y=0$ to $y=h$ but h is a constant, so $U$ is a constant, so I don't understand why it varies depending on $y$

If anyone could clear up why the velocity profile for this is what it is, I'd be very grateful.

Thank in a advance