What happens to pipe length when the pipe diameter changes?

Intuitively, when the diameter of pipe is decreased, there will be more friction loss, more water pressure, and a higher flow rate. Is there a direct relationship/equation derived to see the affect of the pipe lengths?

Deriving from Hagen-Poiseuille's equation, we get:

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

where :

$Q=$ flow rate

$\mathrm{\Delta}\text{}P=$ change in fluid pressure

$r=$ radius of pipe,

$\mu =$ dynamic viscosity of fluid,

$L=$ length of pipe

To keep similar flow rates, are we able to use Poiseuille's derived formula to find the new lengths of pipe with a change in $r$ (pipe radius)?

Intuitively, when the diameter of pipe is decreased, there will be more friction loss, more water pressure, and a higher flow rate. Is there a direct relationship/equation derived to see the affect of the pipe lengths?

Deriving from Hagen-Poiseuille's equation, we get:

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

where :

$Q=$ flow rate

$\mathrm{\Delta}\text{}P=$ change in fluid pressure

$r=$ radius of pipe,

$\mu =$ dynamic viscosity of fluid,

$L=$ length of pipe

To keep similar flow rates, are we able to use Poiseuille's derived formula to find the new lengths of pipe with a change in $r$ (pipe radius)?