A fireman's hose full of water has cross-sectional area $A_{0}$, apart from a smooth contraction to the outlet nozzle which has cross-sectional area $A_{1}<A_{0}$. The volume flow rate of water through the hose is $Q$.

Use Bernoulli's equation to calculate the pressure in the main part of the tube (relative to atmospheric pressure). Then use the integral momentum equation in the direction of the flow to show that the force $F$ that the fireman has to exert on the nozzle to keep it still is given by

$$F=\frac{\rho Q^{2}}{2 A_{0}}\left(\frac{A_{0}}{A_{1}}-1\right)^{2}$$

where $\rho$ is the density of water.