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Problem 1 AUS In The power required to drive a propeller, P, is a found to be a function of the freestream velocity U, fluid density P, fluid viscosity (in the unit of Pa-s), the propeller diameter D, and the angular velocity of the propeller (in the unit of rad /s; note that radian is dimensionless). (a) Make this relation dimensionless using the Buckingham-Pi Theorem (you must identify all x-groups for pullivery (b) A full-scale propeller with a diameter of 1m is working under water with P. = 1000kg/m³. = 0.001Pa-s, flowing at a freestream velocity of 1m/s. You want to build an experimental model using air as the working fluid with Par = 1.225kg / m³, H=1.8×10 Pa-s, flowing at a freestream velocity of 5m/s. Assume the so-called Strouhal number @D/U for the two flows are already matched, what should be the diameter of the experimental model? (Apply dynami similarity condition by matching the Reynolds numbers),-. (c) The measured power required to drive the experimental model is 20kW. What is the power required to drive the full-scale propeller? (

Problem 1 AUS In The power required to drive a propeller, P, is a found to be a function of the freestream velocity U, fluid density P, fluid viscosity (in the unit of Pa-s), the propeller diameter D, and the angular velocity of the propeller (in the unit of rad /s; note that radian is dimensionless). (a) Make this relation dimensionless using the Buckingham-Pi Theorem (you must identify all x-groups for pullivery (b) A full-scale propeller with a diameter of 1m is working under water with P. = 1000kg/m³. = 0.001Pa-s, flowing at a freestream velocity of 1m/s. You want to build an experimental model using air as the working fluid with Par = 1.225kg / m³, H=1.8×10 Pa-s, flowing at a freestream velocity of 5m/s. Assume the so-called Strouhal number @D/U for the two flows are already matched, what should be the diameter of the experimental model? (Apply dynami similarity condition by matching the Reynolds numbers),-. (c) The measured power required to drive the experimental model is 20kW. What is the power required to drive the full-scale propeller? (

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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Problem The power required to drive a propeller, P, is a found to be a function of the freestream velocity U, fluid density P, fluid viscosity (in the unit of Pa-s), the propeller diameter D, and the angular velocity of the propeller (in the unit of rad /s; note that radian is dimensionless). (a) Make this relation dimensionless using the Buckingham-Pi Theorem (you must identify all z-groups M La punne (b) A full-scale propeller with a diameter of 1m is working under water with P=1000kg/m³, = 0.001Pa-s, flowing at a freestream velocity of 1m/s. You want to build an experimental model using air as the working fluid with Par=1.225kg/m, 1.8x10 Pa-s, flowing at a freestream velocity of 5m/s. Assume the so-called Strouhal number @D/U for the two flows are already matched, what should be the diameter of the experimental model? (Apply dynamic similarity condition by matching the Reynolds numbers),-. (c) The measured power required to drive the experimental model is 20kW. What is the power required to drive the full-scale propeller?
Transcribed Image Text:Problem The power required to drive a propeller, P, is a found to be a function of the freestream velocity U, fluid density P, fluid viscosity (in the unit of Pa-s), the propeller diameter D, and the angular velocity of the propeller (in the unit of rad /s; note that radian is dimensionless). (a) Make this relation dimensionless using the Buckingham-Pi Theorem (you must identify all z-groups M La punne (b) A full-scale propeller with a diameter of 1m is working under water with P=1000kg/m³, = 0.001Pa-s, flowing at a freestream velocity of 1m/s. You want to build an experimental model using air as the working fluid with Par=1.225kg/m, 1.8x10 Pa-s, flowing at a freestream velocity of 5m/s. Assume the so-called Strouhal number @D/U for the two flows are already matched, what should be the diameter of the experimental model? (Apply dynamic similarity condition by matching the Reynolds numbers),-. (c) The measured power required to drive the experimental model is 20kW. What is the power required to drive the full-scale propeller?
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