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Water enters a perforated irrigation pipe (Length L, diameter D) with a uniform velocity Uin=10m/s. The water exits at the outlet with an average velocity Uout =8m/s and through N=10 perforations that all have the same diameter (d). The perforations are distributed at equidistant lengths, with the first one and last one located at a distance lo from the inlet and the outlet, respectively. It will be assumed that the average velocity through the perforations decreases linearly as one moves down the perforations. The flow rates through the different perforations have to be controlled to ensure proper irrigation of different plants. (a) Determine the diameters ratio (d/D) so that the average velocity at the first perforation id Vp1=Uin/5 and that at the last perforation is VpN = Vp1/10. (b) Generalize the previous analysis to obtain an expression of (d/D) in terms of a= Uout/ Uin, ß = Vpl/VpN, λ= Uin/Vpl, and N. (c) What is the ratio (d/D) that will ensure that all water exits through the perforations only?

Water enters a perforated irrigation pipe (Length L, diameter D) with a uniform velocity Uin=10m/s. The water exits at the outlet with an average velocity Uout =8m/s and through N=10 perforations that all have the same diameter (d). The perforations are distributed at equidistant lengths, with the first one and last one located at a distance lo from the inlet and the outlet, respectively. It will be assumed that the average velocity through the perforations decreases linearly as one moves down the perforations. The flow rates through the different perforations have to be controlled to ensure proper irrigation of different plants. (a) Determine the diameters ratio (d/D) so that the average velocity at the first perforation id Vp1=Uin/5 and that at the last perforation is VpN = Vp1/10. (b) Generalize the previous analysis to obtain an expression of (d/D) in terms of a= Uout/ Uin, ß = Vpl/VpN, λ= Uin/Vpl, and N. (c) What is the ratio (d/D) that will ensure that all water exits through the perforations only?

Elements Of Electromagnetics
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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Water enters a perforated irrigation pipe (Length L, diameter D) with a uniform velocity Uin=10m/s. The water exits at the outlet with an average velocity Uout =8m/s and through N=10 perforations that all have the same diameter (d). The perforations are distributed at equidistant lengths, with the first one and last one located at a distance lo from the inlet and the outlet, respectively. It will be assumed that the average velocity through the perforations decreases linearly as one moves down the perforations. The flow rates through the different perforations have to be controlled to ensure proper irrigation of different plants. (a) Determine the diameters ratio (d/D) so that the average velocity at the first perforation id Vp1 Uin/5 and that at the last perforation is VpN = Vp1/10. (b) Generalize the previous analysis to obtain an expression of (d/D) in terms of a= Uout/ Uin, ß = Vp1/VpN, λ= Uin/Vp1, and N. (c) What is the ratio (d/D) that will ensure that all water exits through the perforations only?
Transcribed Image Text:Water enters a perforated irrigation pipe (Length L, diameter D) with a uniform velocity Uin=10m/s. The water exits at the outlet with an average velocity Uout =8m/s and through N=10 perforations that all have the same diameter (d). The perforations are distributed at equidistant lengths, with the first one and last one located at a distance lo from the inlet and the outlet, respectively. It will be assumed that the average velocity through the perforations decreases linearly as one moves down the perforations. The flow rates through the different perforations have to be controlled to ensure proper irrigation of different plants. (a) Determine the diameters ratio (d/D) so that the average velocity at the first perforation id Vp1 Uin/5 and that at the last perforation is VpN = Vp1/10. (b) Generalize the previous analysis to obtain an expression of (d/D) in terms of a= Uout/ Uin, ß = Vp1/VpN, λ= Uin/Vp1, and N. (c) What is the ratio (d/D) that will ensure that all water exits through the perforations only?
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