Answer
$4.4\times 10^5Pa$
Work Step by Step
The required pressure difference can be determined as follows:
$A=\frac{\pi d^2}{4}$
$A=\frac{\pi(0.00026)^2}{4}=5.31\times 10^{-8}m^2$
As $v=\frac{\Delta m/\Delta t}{(1000)(5.31\times 10^{-8})}=28.2\frac{m}{s}$
Now $\Delta P=8\pi \eta \frac{vL}{A}$
We plug in the known values to obtain:
$\Delta P=8\pi (0.00101)\frac{(28.2)(0.033)}{5.31\times 10^{-8}}$
$\Delta P=4.4\times 10^5Pa$
