Water flows at 0.65 m/s through a 3.0 cm diameter hose that terminates in a 0.3 cm diameter nozzle. (Recall, the density of water is 1000 kg/m3.) (a) What is the speed of the water leaving the nozzle

v2 = 65 m/s

the speed of the water leaving the nozzle is 65 m/s

Explanation:

Given;

Water flows at 0.65 m/s through a 3.0 cm diameter hose that terminates in a 0.3 cm diameter nozzle

Initial speed v1 = 0.65 m/s

diameter d1 = 3.0 cm

diameter (nozzle) d2 = 0.3 cm

The volumetric flow rates in both the hose and the nozzle are the same.

V1 = V2 ... 1

Volumetric flow rate V = cross sectional area * speed of flow

V = Av

Area = (πd^2) / 4

V = v (πd^2) / 4 ... 2

Substituting equation 2 to 1;

v1 (πd1^2) / 4 = v2 (πd2^2) / 4

v1d1^2 = v2d2^2

v2 = (v1d1^2) / d2^2

Substituting the given values;

v2 = (0.65 * 3^2) / 0.3^2

v2 = 65 m/s

the speed of the water leaving the nozzle is 65 m/s