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° above the horizontal and covers a radius of 6.0 m. (a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.) (b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second? (c) How fast is the water flowing inside the 1.9-cm-diameter pipe?

A) Vo = 9.36 m/s

B) Volumetric flow rate = 2.65 l/s

C) Water velocity = 0.933 m/s

Step-by-step explanation:

We are given;

Vertical distance Δx= 6m

Angle = 35°

Output diameter of each head = 3mm = 0.003m

A) Let Vo be the velocity of water from each sprinkler

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 8.4 m from sprinkler head is given as t = 2Voy/g. Thus, t = 2Vo sin 35/g

Distance water reaches from sprinkler head = (t)(Vox) = 2Vo sin 35/g (Vo cos 35)

Thus;

[2Vo²(sin 35)(cos 35)]/g = 8.4

Vo² = (8.4 x 9.81)/(2)(sin 35)(cos 35) =√87.6927

Vo = 9.36 m/s

B) Area of sprinkler head (A) = πD²/4 = π(0.003)²/4 = 7.0686 x 10^(-6) m²

volume rate of flow thru one sprinkler head is given as;

VoA

Thus;

= (9.36)(7.0686 x 10^(-6)) = 66.16 x 10^(-6) m³/s

Question asks for unit in l/s. Thus, let's convert 66.16 x 10^(-6) m³/s to l/s. So, 66.16 x 10^(-6) m³/s = 66.16 x 10^(-6) x 1000 = 0.0662 liter/s

This is for just one sprinkler

Therefore, for total amount of liters/s flowing in all 4 sprinklers, we have; flow rate = 4 x 0.662 = 2.65 l/s

C) Area of 1.9 cm or 0.019m diameter pipe is;

πD²/4 = π(0.019)²/4 = 2.835 x 10^(-4) m²

From last answer,we saw that flow rate across one sprinkler = 66.16 x 10^(-6) m³/s and for 4 in m³/s will be; 4 x 66.16 x 10^(-6) m³/s = 264.6 x 10^(-6) m³/s

water velocity in pipe is given by; velocity = volumetric flow rate/Area.

Thus,

Velocity = 264.6 x 10^(-6)/2.835 x 10^(-4) = 0.933 m/s

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

answer: ouch. thats difficult

step-by-step explanation: