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Water is flowing from a hose attached to water main at 400 kPa(guage). A child places a thumb to cover most of the hose outlet, causing a thin jet of high speed water to emerge.

If the hose is held vertical upward, what is maximum height that jet could achieve. Assume flow is steady, incompressible and laminar.

fluid dynamics • 1.7k  views
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Data:- $P_1=400kPa=400\times 10^3N/m^2$

To find:- $z_2-z_1=?$

Solution:

Here, outlet of hose is (1) and max height achieved by jet is (2)

Applying Bernoulis equation between (1) and (2)

$\frac{P_1}{\rho g}+\frac{v_1^2}{2g}+z_1=\frac{P_2}{\rho g}+\frac{v_2^2}{2g}+z_2+h_L$

$P_2=$atm pressure, $v_2=0$, $h_L=0\text{..........Neglecting loses}$

$\therefore z_2-z_1=\frac{P_1}{\rho g}$

$=\frac{400\times 10^3}{1000\times 9.81}$

$=40.77m$

$\therefore$ Max height achieved by the jet=40.77 m

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