![daemonacoster](/avatars/25877.jpg)
daemonacoster
20.03.2020 •
Mathematics
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?
Solved
Show answers
More tips
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- L Leisure and Entertainment Carving: History and Techniques for Creating Vegetable and Fruit Decorations...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
- H Health and Medicine What vaccines do children need?...
- H Health and Medicine Reasons for the Appearance of Warts: Everything You Need to Know...
- A Art and Culture How to Learn Screaming: Step-by-Step Guide for Beginners...
Answers on questions: Mathematics
- M Mathematics If a = 3, what is the value of 2 2/3?A. 6B. 12C. 18D. 36...
- M Mathematics Please fill out these charts ASAP!!...
- B Biology Some bacteria living on the ocean floor can turn sulfur (a gas) into food. How would you classify these bacteria?...
- A Arts Anyone wanna have free sex over pad-let no show face tho im 13 btw...
- A Arts I be swimming with the sharks lil ni--ga you a lobster...
Ответ:
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
Ответ:
44 no negative
Step-by-step explanation: Because I took the K12 2.13 quiz