Question 4 A sprinkler system pumps water through a large pipe inlet with a diameter (d₁). The pipe then breaks into N narrow pipes (which have a diameter, d2, and a length, L2), before the water is released to the atmosphere, as shown in figure Q4. The entrance to the small pipe from the large pipe has a loss coefficient of K₁. You may assume the flow is laminar and fully developed everywhere in the system, and that any changes in height are negligible. The viscosity is not negligible a) Find an expression for the velocity of water leaving the sprinkler b) Find an expression for the gauge pressure at point A, a distance L₁ upstream of the narrow pipes. Express your answer in terms of the flowrate, Q. c) The inner diameter of the first segment of the pipe is d₁ = 10 mm, the inner diameter of the second set of pipes is d₂ = 1 mm, with N = 25. The flowrate through the sprinkler is Q = 0.2 L/s. Flow in pipes typically becomes turbulent when the Reynolds number exceeds 2000. Comment on the accuracy of our assumption that the flow could be treated as laminar everywhere. You may assume water has a density of 1000 kg/m³ and a viscosity of 1 mPa.s. a ↑ A d₁ L₁ d₂ L₂ Figure Q4: Flow in a sprinkler head.
Question 4 A sprinkler system pumps water through a large pipe inlet with a diameter (d₁). The pipe then breaks into N narrow pipes (which have a diameter, d2, and a length, L2), before the water is released to the atmosphere, as shown in figure Q4. The entrance to the small pipe from the large pipe has a loss coefficient of K₁. You may assume the flow is laminar and fully developed everywhere in the system, and that any changes in height are negligible. The viscosity is not negligible a) Find an expression for the velocity of water leaving the sprinkler b) Find an expression for the gauge pressure at point A, a distance L₁ upstream of the narrow pipes. Express your answer in terms of the flowrate, Q. c) The inner diameter of the first segment of the pipe is d₁ = 10 mm, the inner diameter of the second set of pipes is d₂ = 1 mm, with N = 25. The flowrate through the sprinkler is Q = 0.2 L/s. Flow in pipes typically becomes turbulent when the Reynolds number exceeds 2000. Comment on the accuracy of our assumption that the flow could be treated as laminar everywhere. You may assume water has a density of 1000 kg/m³ and a viscosity of 1 mPa.s. a ↑ A d₁ L₁ d₂ L₂ Figure Q4: Flow in a sprinkler head.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Question 4
A sprinkler system pumps water through a large pipe inlet with a diameter (di). The pipe
then breaks into N narrow pipes (which have a diameter, d2, and a length, L2), before the
water is released to the atmosphere, as shown in figure Q4. The entrance to the small
pipe from the large pipe has a loss coefficient of KL. You may assume the flow is laminar
and fully developed everywhere in the system, and that any changes in height are
negligible.
The viscosity is not negligible
a) Find an expression for the velocity of water leaving the sprinkler
b) Find an expression for the gauge pressure at point A, a distance L1 upstream of the
narrow pipes. Express your answer in terms of the flowrate, Q.
c) The inner diameter of the first segment of the pipe is di = 10 mm, the inner
diameter of the second set of pipes is d2 = 1 mm, with N = 25. The flowrate through
the sprinkler is Q = 0.2 L/s. Flow in pipes typically becomes turbulent when the
Reynolds number exceeds 2000. Comment on the accuracy of our assumption that
the flow could be treated as laminar everywhere.
You may assume water has a density of 1000 kg/m3 and a viscosity of 1 mPas.
d
Figure Q4: Flow in a sprinkler head.
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