Is there a contradiction between the continuity equation and Poiseuilles Law?

The continuity equation states that flow rate should be conserved in different areas of a pipe:

$Q={v}_{1}{A}_{1}={v}_{2}{A}_{2}=v\pi {r}^{2}$

We can see from this equation that velocity and pipe radius are inversely proportional. If radius is doubled, velocity of flow is quartered.

Another way I was taught to describe flow rate is through Poiseuilles Law:

$Q=\frac{\pi {r}^{4}\mathrm{\Delta}P}{8\eta L}$

So if I were to plug in the continuity equations definition of flow rate into Poiseuilles Law:

$vA=v\pi {r}^{2}=\frac{\pi {r}^{4}\mathrm{\Delta}P}{8\eta L}$

Therefore:

$v=\frac{{r}^{2}\mathrm{\Delta}P}{8\eta L}$

Now in this case, the velocity is proportional to the radius of the pipe. If the radius is doubled, then velocity is qaudrupled.

What am I misunderstanding here? I would prefer a conceptual explanation because I feel that these equations are probably used with different assumptions/in different contexts.

The continuity equation states that flow rate should be conserved in different areas of a pipe:

$Q={v}_{1}{A}_{1}={v}_{2}{A}_{2}=v\pi {r}^{2}$

We can see from this equation that velocity and pipe radius are inversely proportional. If radius is doubled, velocity of flow is quartered.

Another way I was taught to describe flow rate is through Poiseuilles Law:

$Q=\frac{\pi {r}^{4}\mathrm{\Delta}P}{8\eta L}$

So if I were to plug in the continuity equations definition of flow rate into Poiseuilles Law:

$vA=v\pi {r}^{2}=\frac{\pi {r}^{4}\mathrm{\Delta}P}{8\eta L}$

Therefore:

$v=\frac{{r}^{2}\mathrm{\Delta}P}{8\eta L}$

Now in this case, the velocity is proportional to the radius of the pipe. If the radius is doubled, then velocity is qaudrupled.

What am I misunderstanding here? I would prefer a conceptual explanation because I feel that these equations are probably used with different assumptions/in different contexts.