a garden hose with an internal diameter of 1.9 cm is connected to a (stationary) lawn sprinkler that consists merely of an enclosure with 24 holes,each 0.13 cm in diameter. If the water in the hose has a speed of 0.91 m/s,at what speed does it leave the sprinkler holes?

leta us consider the velocity of sprinkler is V2
rate of mass flow will same at a time so
incoming mass flow = outgoing mass flow
so from the principle of continuity
A1 V1 = A2V2
since sprinkler is is N = 24 then
A1V1 = NA2V2
pi* (D1 / 2)^2 *V1= pi*(D2/2)^2*V2
V2 = D1^2*V1 / ND^2
V2 = (1.9x10^-2)^2 *0.91 / 24*(0.13x10^-2)^2
V2 = 8.1 m/s^2
Thanks & Regards,
Nirmal Singh
Askiitians Faculty