Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation between dimensionless power (1) and w (n2); (b,c) a small 1/3 scale model is used in water to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b) the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the predicted ratio of powers Pwater/ Pactual. = expecting unit: (a) π1 - D; π^2 - D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual = 10^-3 SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; μwater - 10^-3 N•s/m^2; Hair - 2 x 10^-5 Nes/m^2; g = 9.8 m/s^2

Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation between dimensionless power (1) and w (n2); (b,c) a small 1/3 scale model is used in water to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b) the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the predicted ratio of powers Pwater/ Pactual. = expecting unit: (a) π1 - D; π^2 - D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual = 10^-3 SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; μwater - 10^-3 N•s/m^2; Hair - 2 x 10^-5 Nes/m^2; g = 9.8 m/s^2

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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Question

Buckingham Pi. A mechanical stirrer is used to mix chemicals in a large tank. The required
shaft power P is a function of liquid density p, viscosity μ, stirrer blade diameter D, and
angular speed w of the spinning blades. (a) use repeating variables p, D, u to find a relation
between dimensionless power (1) and w (m2); (b,c) a small 1/3 scale model is used in water
to predict the actual required power in a viscous liquid with SG =2 and μ = 12μwater. Find (b)
the ratio of speeds, wwater/ wactual, necessary for dynamic similarity and then (c) the
predicted ratio of powers Pwater/ Pactual.
expecting unit : (a) π1 ~ D ; π^2 ~ D^2; (b) wwater/ wactual: 10^0; (c) Pwater/ Pactual
10^-3
SI constant Patm = 10^5 Pa; pwater - 1000 kg/m^3; pair ~ 1.2kg/m^3; µwater ~ 10^-3
N•s/m^2; pair - 2 x 10^-5 N•s/m^2 ; g = 9.8 m/s^2
=

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