We can solve this problem using Hagen–Poiseuille equation. Derivation of this equation is a bit complicated so I will just write down the equation.
[tex]\Delta P= \frac{8\mu QL}{\pi R^4}[/tex]
This equation gives you the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of the constant cross section.
L is the length of the cylinder, Q is the volumetric flow rate, R is the radius of the pipe, and [tex] \mu [/tex] is dynamic viscosity.
Dynamic viscosity of water at 20 Celsius is 0.001 PaS.
Now we can calculate the pressure drop:
[tex]\Delta P= \frac{8\cdot 0.001\cdot 15 \cdot 0.015}{\pi 3.9\cdot 10^{-7}}=1469.12 $Pa[/tex]
