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With the help of Buckingham $\pi$-theorem show that for a forced convection

$Nu= C.Re^m.Pr^n$


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Step 1: Determination of dimension of all variables

Variables Units Dimensiond
ρ kg/m3 ML-3
v m/s LT-1
μ N.sm2=kg.ms2×sm2=kgm.s ML-1T-1
l m L
h Wm2K=Nms×1m2K,=kg.ms2×ms×1m2K=kgs3K MT-3θ-1
K WmK=Nms×1mK,=kg.ms2×ms×1mK=kg.ms3K MLT-3θ-1
Cp JkgK=Nmkg.K×kg.ms2×mkg.K L2T-2θ-1

Step 2: Number of variables (m) = 7

Step 3: Number of basic dimension (n) = 4 …

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