Question

Water is flowing from a garden hose (Fig. below). A child places his thumb
to cover most of the hose outlet, causing a thin jet of high-speed water to
emerge. The pressure in the hose just upstream of his thumb is 400 kPa. If
the hose is held upward, what is the
maximum height that the jet could achieve?

Answer 1

Maximum height will be achieved when, velocity inside the hose is low i.e $V_1=0$ , at the top of the water trajectory $V_2=0$ and the reference level $z_1=0$

Bernoulli's equation

$\frac{P_1}{\rho g}+\frac{V^2_1}{2g}+z_i=\frac{P_2}{\rho g}+\frac{V^2_2}{2g}+z_2$

Since

$\frac{V^2_1}{2g}=\frac{V^2_2}{2g}=0$

the equation reduces to

$\frac{P_1}{\rho g}=\frac{P_{atm}}{\rho g}+z_2$

Solving for $z_2$ and substituting.

$z_2=\frac{P_1-P{atm}}{\rho g}=\frac{P_1,{gauge}}{\rho g}$

$\frac{400kPa}{1000kg/m^3\times9081m/s^2}(\frac{1000N/m^2}{1kPa})(\frac{1kg.m/s^2}{1N})$

answer =$40.8m$