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(3.a) Develop a set of pi groups using W and Q as the 'king' variables.

(3.a) Develop a set of pi groups using W and Q as the 'king' variables.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Consider a rotating fan with blades of diameter D fitted inside a circular duct, pushing air through the duct with flowrate Q. mechanical power required for the motor to spin the blades, W, is a function of the fan diameter D, the air density p, the fan rotational speed o and the flowrate Q. Assume that the (3.a) Develop a set of pi groups using W and Q as the 'king' variables. (3.b) Suppose that my actual ducted fan is driven by a 100 Watt motor, has D = 0.2 m, rotates at o = 100 sec', and generates Q = 0.01 m³/sec in service. I build a scale model of the ducted fan that also operates on air, has half the blade diameter of the actual fan, and operates at one eighth of the flowrate Qmodel = 0.00125 m³/sec. What is the rotational speed of the of the model fan? What is the power required to turn the model blades?
Transcribed Image Text:Consider a rotating fan with blades of diameter D fitted inside a circular duct, pushing air through the duct with flowrate Q. mechanical power required for the motor to spin the blades, W, is a function of the fan diameter D, the air density p, the fan rotational speed o and the flowrate Q. Assume that the (3.a) Develop a set of pi groups using W and Q as the 'king' variables. (3.b) Suppose that my actual ducted fan is driven by a 100 Watt motor, has D = 0.2 m, rotates at o = 100 sec', and generates Q = 0.01 m³/sec in service. I build a scale model of the ducted fan that also operates on air, has half the blade diameter of the actual fan, and operates at one eighth of the flowrate Qmodel = 0.00125 m³/sec. What is the rotational speed of the of the model fan? What is the power required to turn the model blades?
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