The velocity of the water coming out of the nozzle can be calculated using the conservation of mass principle, by equating the flow rates in the garden hose and the nozzle and then solving for the exit velocity.
To calculate the velocity of water coming out of the spray nozzle, we can use the principle of conservation of mass, which implies that the flow rate through the garden hose must equal the flow rate through the nozzle (assuming incompressible, non-viscous fluid and steady flow). The flow rate can be found by multiplying the cross-sectional area of the hose or nozzle by the velocity of the water. Using the given radius of the garden hose (1 cm) and the velocity (0.1 m/s), we can calculate the flow rate and then use the radius of the nozzle (1 mm) to find the exit velocity using the equation A1∙V1=A2∙V2.
First, find the area of the hose, A1 = π∙r1² = π∙(1 cm)², and likewise for the nozzle, A2 = π∙r2² = π∙(1 mm)². After calculating the flow rate, Q = A1∙V1, we find the nozzle velocity by rearranging the equation to V2 = Q/A2.
Since the radii and velocity are in different units (centimeters for the hose and millimeters for the nozzle), it's important to use consistent units for this calculation.