**Problem 2**In an experiment conducted in a laboratory, the surface tension (\(\Upsilon\)) acting on a rotating square plate in a viscous fluid is a function of the external torque (\(\tau\)), plate length (\(a\)), area moment of inertia of plate (\(I\)), specific weight of the fluid (\(\gamma\)) and angular displacement of the plate (\(\Theta\)). Using Buckingham-Pi theorem, find a suitable set of pi terms (in \(M\), \(L\) and \(T\) primary dimensions). Your final answer should be written in proper functional form. Refer Table 5.1/ page-296 for secondary dimension of the variables.**PLEASE BOX YOUR ANSWERS**

buckingham'S π theorem the surface tension Y is a function depends on external torque ς,plate length a, area moment of inertia of plate I, specific weight of the fluid γ and angular displacement of the plate θ. Express the surface tension Y in terms of dimensionless parameter. here Y is the function of the ς ,a, I,γ,θ Y=f(ς, a, I, γ,θ)Y dependent variableς,a, I, γ,θ independent variablesthe funtion relationship dependent and independent variables can be written asf(Y,ς, a, I, γ,θ)=0 total number of variables n= 6 Dimensions of the variables surface tension , Y=ML0T-2 external torque, ς = ML2 T-2 length, a =M0LT0 area moment inertia, I= M0L4T0 specific weight , γ=M L-2T-2 angular displacement, θ=M0L0T0 number of fundamental dimension for the problem m=3 number of π terms= n-m =6-3=3 therefore F(π1,π2,π3)=0 π1=aa1 θb1 γc1 Yπ2=aa2 θb2 γc2 Iπ3=aa3 θb3 γc3 ς as we know π are dimensionless terms for π1 M0L0T0=M0LT0a1M0L0T0b1M L-2T-2c1ML0T-2 power of M= 0+0+c1+1=0 hence c1=-1 power of L= a1+0-2c1+0=0 hence a1=-2 power of T =0+0-2c1-2=0 hence c1=-1 for π2 M0L0T0=M0LT0a2M0L0T0b2M L-2T-2c2M0L4T0 power of M= 0+0+c2+0=0 hence c2=0 power of L=a2+0-2c2+4=0 hence a2=-4 power of T= 0+0-2c2+0=0 hence c2=0 for π3 M0L0T0=M0LT0a3M0L0T0b3M L-2T-2c3ML2 T-2 power of M=0+0+c3+1=0 hence c3=-1power of L=a3+0-2c3-2=0 hence a3=0 power of T=0+0-2c3-2=0 hence c3=-1 now π1=a-2 θb1 γ-1 Y π2=a-4 θb2 γ0 I π3=a0 θb3 γ-1 ς we know F(π1,π2,π3)=0 Fθb1Ya2 γ, θb2 Ia4,θb3ςγ= 0 θb1Ya2γ=ϕθb2Ia4, θb3ςγY=a2γθb1 ϕ(θb2Ia4, θθb3ςγ)

Engineering

Mechanical Engineering

PLEASE BOX YOUR ANSWERS Problem 2 In an experiment conducted in a laboratory, the surface tension (Y) acting on a rotating square plate in a viscous fluid is a function of the external torque (7), plate length (a), area moment of inertia of plate (I), specific weight of the fluid (7) and angular displacement of the plate (8). Using Buckingham-Pi theorem, find a suitable set of pi terms (in M, L and T primary dimensions). Your final answer should be written in proper functional form. Refer Table 5.1/ page-296 for secondary dimension of the variables.

PLEASE BOX YOUR ANSWERS Problem 2 In an experiment conducted in a laboratory, the surface tension (Y) acting on a rotating square plate in a viscous fluid is a function of the external torque (7), plate length (a), area moment of inertia of plate (I), specific weight of the fluid (7) and angular displacement of the plate (8). Using Buckingham-Pi theorem, find a suitable set of pi terms (in M, L and T primary dimensions). Your final answer should be written in proper functional form. Refer Table 5.1/ page-296 for secondary dimension of the variables.

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

**Problem 2**

In an experiment conducted in a laboratory, the surface tension (\(\Upsilon\)) acting on a rotating square plate in a viscous fluid is a function of the external torque (\(\tau\)), plate length (\(a\)), area moment of inertia of plate (\(I\)), specific weight of the fluid (\(\gamma\)) and angular displacement of the plate (\(\Theta\)). Using Buckingham-Pi theorem, find a suitable set of pi terms (in \(M\), \(L\) and \(T\) primary dimensions). Your final answer should be written in proper functional form. Refer Table 5.1/ page-296 for secondary dimension of the variables.

**PLEASE BOX YOUR ANSWERS**

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