The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ. (a) Using the Buckingham Pi theorem, show that the pressure loss is given by: Lk 4p pvz 1 = fn ( D² D² DVD) μ (b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of 0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under dynamically similar conditions. (c) Determine the corresponding pressure drop per metre length of pipe, for the air flow. The following values can be assumed: Water: Air: p = 1000 kg/m³ p=1.2 kg/m³ μ = 1 x 10³ kg/m s μ= 1.98 x 105 kg/m s
The pressure loss 4p along a pipe is known to depend on the pipe diameter D, the length of the pipe L, the wall roughness k, the flow velocity V and the fluid density p and viscosity μ. (a) Using the Buckingham Pi theorem, show that the pressure loss is given by: Lk 4p pvz 1 = fn ( D² D² DVD) μ (b) In an experiment, water flows through a pipe with a 20 mm diameter at a velocity of 0.1 m/s. The pressure drop is measured as 8 N/m² per metre length of pipe. Determine the corresponding velocity for the flow of air in a pipe with a 10 mm diameter, under dynamically similar conditions. (c) Determine the corresponding pressure drop per metre length of pipe, for the air flow. The following values can be assumed: Water: Air: p = 1000 kg/m³ p=1.2 kg/m³ μ = 1 x 10³ kg/m s μ= 1.98 x 105 kg/m s
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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