Water Hose Problem Bernouili's Principle- Will Pick Best Answer?

Question

A fireman standing on a 12 m high ladder
operates a water hose with a round nozzle of
diameter 1.51 inch. The lower end of the hose
(12 m below the nozzle) is connected to the
pump outlet of diameter 2.98 inch. The gauge
pressure of the water at the pump is

P(guage of pump)= P(abs of pump)-P(atm)=81PSI=558.475 kPa

Calculate the speed of the water jet emerg-
ing from the nozzle. Assume that water is
incompressible liquid of density 1000 kg/m^3
and negligible viscosity. The acceleration of
gravity is 9.8 m/s^2. Answer in units of m/s.

Answer 1

Bernoulli's Principle predicts that

P + ρ g h + 1/2 ρ v² = Constant in any closed system

It is also useful to note that for an incompressible fluid, the velocities and cross-sectional areas are related as

v1 / v2 = A2 / A1

To solve we use the values at the bottom of the hose and at the top...

P_bottom + ρ g h_bottom + 1/2 ρ v_bottom² = P_top + ρ g h_top + 1/2 ρ v_top²

Hint: P_top = 0 since you used gauge pressure at the bottom.