Four lawn sprinkler heads are fed by a 1.9 cm diameter pipe. The water comes out

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 degrees 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)

___9.02___ 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

(I already found part A but I can't figure out B or C)

Explanation / Answer

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 = (t)(Vox) = 2Vo²(sin 35)(cos 35)/g = 7.8

Vo² = 7.8g/(2)(sin 35)(cos 35)

Vo = 9.2 m/s

b) Area of sprinkler head = D²/4 = (3.0*10^-3)²/4 = 7.0686*10^-6 m² = A
VoA = volume rate of flow thru one sprinkler head = (9.2)(7.0686*10^-6) = 65.03112*10^-6 m^3/sec

1000 liters per m³
65.03112*10^-6 x 1000 = 65.03112*10^-3 liter/s = 0.0653 liter/s {for one sprinkler}

total amount of liters/s flowing = 4 x 0.0653 = 0.2612 L/sec

3) Area of 1.9 cm diameter pipe = D²/4 = (1.9*10^-2)²/4 = 2.835*10^-4 m²

volume rate of flow thru all four sprinklers = 4 x 65.3*10^-6 m³/s = 261.2*10^-6 m³/s

water velocity in pipe = 261.2*10^-6/2.835*10^-4 = 0.92 m/sec

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.