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 liameter of the first segment of the pipe is d₁ = 10 mm, the inner diameter of the second set of pipes is d = 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 d₁ L₁ dz Figure Q4: Flow in a sprinkler head. ^^^^^

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 liameter of the first segment of the pipe is d₁ = 10 mm, the inner diameter of the second set of pipes is d = 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 d₁ L₁ dz 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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