1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
german
3 years ago
6

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 horiz

ontal 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?
Mathematics
2 answers:
Svetlanka [38]3 years ago
8 0

Answer:

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

klemol [59]3 years ago
7 0

Answer:

Step-by-step explanation:

Given:

Angle, θ = 35°

Vertical distance, Δx = 6 m

Diameter, d = 1.9 cm

= 0.019 m

A.

When the water leaves the sprinkler, it does so at a projectile motion.

Therefore,

Using equation of motion,

(t × Vox) = 2Vo²(sin θ × cos θ)/g

= Δx = 2Vo²(sin 35 × cos 35)/g

Vo² = (6 × 9.8)/(2 × sin 35 × cos 35)

= 62.57

Vo = 7.91 m/s

B.

Area of sprinkler, As = πD²/4

Diameter, D = 3 × 10^-3 m

As = π × (3 × 10^-3)²/4

= 7.069 × 10^-6 m²

V_ = volume rate of the sprinkler

= area, As × velocity, Vo

= (7.069 × 10^-6) × 7.91

= 5.59 × 10^-5 m³/s

Remember,

1 m³ = 1000 liters

= 5.59 × 10^-5 m³/s × 1000 liters/1 m³

= 5.59 × 10^-2 liters/s

= 0.0559 liters/s.

For the 4 sprinklers,

The rate at which volume is flowing in the 4 sprinklers = 4 × 0.0559

= 0.224 liters/s

C.

Area of 1.9 cm pipe, Ap = πD²/4

= π × (0.019)²/4

= 2.84 × 10^-4 m²

Volumetric flowrate of the four sprinklers = 4 × 5.59 × 10^-5 m³/s

= 2.24 × 10^-4 m³/s

Velocity of the water, Vw = volumetric flowrate/area

= 2.24 × 10^-4/2.84 × 10^-4

= 0.787 m/s

You might be interested in
The function f(x) = x^2 is reflected across the x-axis and a stretch factor of 4 is applied to create a second function, g(x). W
Anon25 [30]
C. The vertexes are the same. The functions' vertex (h,k) values were not altered, just a (stretch/compress).
8 0
3 years ago
The histogram below shows the number of sit-ups accomplished by 6th grade students in a physical fitness test.how many students
Harman [31]
I chose 40! thought it was to only logical answer

4 0
3 years ago
1,000 times 10 of the power of 3
NNADVOKAT [17]

Answer:

1,000,000

Step-by-step explanation:

10 to the power of 3 is 1,000.

1,000 x 1,000 = 1,000,000

6 0
1 year ago
Read 2 more answers
I can't seem to figure this out
antiseptic1488 [7]

Answer:

c. 4

Step-by-step explanation:

tan (30)/1 = x/7 *cross multiply*

x = 7 (tan(30))

x = 4.04

x = 4

6 0
3 years ago
Which is the best measure of central tendency for the type of data below–the mean, the median, or the mode? explain. hours of sl
djverab [1.8K]
Mean, because the outliers are limited.

There will be nights when you get more sleep or less sleep than usual, but overall, they will not be far away from the rest of the data you're comparing. 
8 0
3 years ago
Read 2 more answers
Other questions:
  • Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
    6·1 answer
  • A square rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the corre
    9·1 answer
  • HELP PLS I NEED THIS RIGHT NOW
    5·2 answers
  • Solve the equation. 2m/3-1=3/4+m (please show work)
    11·1 answer
  • Write the slope intercept form of the equation of each line<br> y+5=-4/5(x-4)
    15·1 answer
  • Pay:11.71 per hour<br>hours:11 hours per week​
    14·2 answers
  • What's the size of angle x?
    5·2 answers
  • Anyone know the answer ?
    8·1 answer
  • A number x divided by -1 is at less than 45
    8·2 answers
  • Write a division expression with a quotient between-20 and -25
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!