Question

A fireman standing on a 12 m high ladder operates a water hose with a round nozzle of diameter 1.18 inch. The lower end of the hose (12 m below the nozzle) is connected to the pump outlet of diameter 2.34 inch. The gauge pressure of the water at the pump is Ppump (gauge )​​=Ppump (abs)​−Patm ​=41.1PSI=283.375kPa.​ Calculate the speed of the water jet emerging from the nozzle. Assume that water is an incompressible liquid of density 1000 kg/m3 and negligible viscosity. The acceleration of gravity is 9.8 m/s2. Answer in units of m/s.

Answer 1

The speed of the water jet emerging from the nozzle, calculated using Bernoulli's principle and the equation of continuity, is 22.07 m/s.

Step-by-step explanation:

To calculate the speed of the water jet emerging from the nozzle, we can apply Bernoulli's principle and the equation of continuity given that water is an incompressible liquid. Bernoulli's principle for the pump and the nozzle level can be written as:

Ppump + ρgh + ½ρv2pump = Patm + ½ρv2nozzle

Since the pressure at the pump is given, and the atmospheric pressure is the same at the pump and nozzle with height difference 'h', we can calculate the kinetic energy at the nozzle level and then the velocity 'vnozzle'.

sing the equation of continuity for the incompressible flow we get Apumpvpump = Anozzlevnozzle, where A is the cross-sectional area. The cross-sectional area of the nozzle can be calculated using its diameter, and then the continuity equation can be used to solve for the velocity at the nozzle.

After calculations, we find that the speed of the water jet emerging from the nozzle is: