A garden hose with an internal diameter of 2.5 cm is connected to a (stationary) lawn sprinkler that consists merely of a container with 28 holes, each 0.20 cm in diameter. If the water in the hose has a speed of 0.85 m/s, at what speed does it leave the sprinkler holes?

Respuesta :

Answer:

4.7433 m/sec

Step-by-step explanation:

Given data

the internal diameter of garden =2.5 cm =0.025 m

radius [tex]r_1[/tex]=  0.0125 m

it contains 28 holes each of diameter 0.20 cm =0.002 m

radius [tex]r_2[/tex] =0.001 m

from continuity equation

[tex]A_1V_1=nA_2V_2[/tex]

where A is area and V is velocity

0.85×[tex]A_1[/tex]=28 ×[tex]A_2[/tex]×[tex]V_2[/tex]

[tex]V_2=\frac{A_1}{28A_2}\times V_1=\frac{r_1^2}{28r_2^2}\times 0.85=4.7433 m/sec[/tex]

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