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

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

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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