Answer
8200 Pa.
Work Step by Step
Use Poiseuille’s equation to find the pressure difference.
$$Q=\frac{\pi R^4 (P_1-P_2)}{8 \eta \mathcal{l}}$$
$$ P_1-P_2=\frac{8Q \eta \mathcal{l}}{\pi R^4}$$
Convert the flow rate Q to $1.033 \times10^{-7}\;m^3/s$.
$$ P_1-P_2=\frac{8(1.033 \times10^{-7}\;m^3/s) (0.2\;Pa \cdot s) (0.102\;m)}{\pi (0.0009\;m)^4}$$
$$ P_1-P_2=8200\;Pa$$