Question

A 15 m long garden hose han an inner diameter of 2.5 cm. One end is connected to a spigot; 20 C water flows from the other end at a rate of 1.2 L/s. What is the gauge pressure at the spigot end of the hose

Answer 1

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.
$\Delta P= \frac{8\mu QL}{\pi R^4}$
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 $\mu$ is dynamic viscosity.
Dynamic viscosity of water at 20 Celsius is 0.001 PaS. 
Now we can calculate the pressure drop:
$\Delta P= \frac{8\cdot 0.001\cdot 15 \cdot 0.015}{\pi 3.9\cdot 10^{-7}}=1469.12 Pa$