Question

Four lawn sprinkler heads are fed by a 1.9 cm diameter pipe. The water comes out of the heads at an angle of 35° to the horizontal and covers a radius of 7.8 m.

(a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.)
m/s
(b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second?
L/s
(c) How fast is the water flowing inside the 1.9 cm diameter pipe?
m/s

Answer 1

let Vo be the velocity of water from each sprinkler g 9.8 m/s2 Voy- initial vertical component of water velocity from sprinkler head Vo sin 35 Vox- initial horizontal component of water velocity from sprinkler head Vo cos 35 time for water to reach 7.8 m from sprinkler head-t-2Voy/g 2Vo sin 35/g distance water reaches from sprinkler head-(tox) 2Vo(sin 31)(cos 31) g 7.8 Vo2-7.8g/(2)(sin 35)(cos 35)81.34 Vo 9.01 m/s-answ Area of sprinkler headD/43.0e-3)/47.0686e-6 m2-A VoA volume rate of flow thru one sprinkler head- 9.3) (7.0686e-6) 66.2e-6 m/s 1000 liters per m* 66.2e-6 x 1000 66.2e-2 iter/s-0.662 liter/s ffor one sprinkler) total amount of liters/s flowing 4 x 0.662 -2.6 liters/s -answer b Area of 1.9 cm diameter pipe-rD2/4-аџ.9e-29/4-2.83 564 m2 volume rate of flow thru all four sprinklers 4 x 66.2e-6 m/s 265e-6 m/s water velocity in pipe 265e-6/2.835e-4- 93.5e-2 - 0.935 m/s-answer