Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.25 cm.If the nozzle has an opening of diameter 1.30 cm,and if the water leaves the nozzle at a speed of 14.0 m/s,what is the speed of the water inside the hose?
A)4.67 m/s
B)41.9 m/s
C)2.38 m/s
D)5.67 m/s
E)also 14.0 m/s

Question

Quizplus · Accepted Answer

The speed of the water inside the hose can be found using the principle of conservation of mass, which implies that the flow rate (volume per time) must be constant throughout the hose. This can be expressed as $A_1v_1 = A_2v_2$, where $A_1$ and $A_2$ are the cross-sectional areas of the hose and nozzle, respectively, and $v_1$ and $v_2$ are the velocities of the water in the hose and nozzle, respectively. Given that $v_2 = 14.0 \, \text{m/s}$ and the diameters of the hose and nozzle, we can find $v_1$ by calculating the areas and rearranging the equation to solve for $v_1$. The area of a circle is given by $\pi r^2$, so the areas of the hose and nozzle can be calculated using their respective diameters ($d = 2r$). Substituting the given values and solving for $v_1$ yields a speed of 4.67 m/s inside the hose.

Water Is Being Sprayed from a Nozzle at the End