Answer
$6.4\times10^{5}Pa$
Work Step by Step
Let's apply Poiseuille's law to find the input pressure.
$Q=\frac{\pi R^{4}(P_{i}-P_{o})}{8\eta L}=>P_{i}-P_{o}=\frac{8Q\eta L}{\pi R^{4}}$
$P_{i}=P_{o}+\frac{8Q\eta L}{\pi R^{4}}$ ; Let's plug known values here.
$P_{i}=1.013\times10^{5}Pa+\frac{8(5.3\times10^{-5}m^{3}/s)(0.14\space Pa\space s)(37\space m)}{\pi (6\times10^{-3}m)^{4}}$
$P_{i}\approx6.4\times10^{5}Pa$
