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Answer:
Step 1
Given: A tank is drained through an orifice from initial liquid level (h₀). The time(r), to drain the tank, depends on tank diameter (D), orifice diameter (d), acceleration due to gravity (g), liquid density (ρ) and liquid viscosity (μ).
r = f (h₀, D, d, g, ρ, μ)
Step 2
There are totally seven parameters r, h₀, D, d, g, ρ and μ
∴ n = 7
The primary variables are M, L, T
∴ m = 3
So, the number of repeating variables are, r = 3
Select the three repeating variables are ρ, d, g
Then according to Buckingham, there will be n-m (⇒ 7-3 = 4) dimensionless groups given by π₁, π₂, π₃ and π₄
So, The number of π terms = 4
Explanation:
See attached images for step 3 to 7
