Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2023
Hard
An explosion at time t=0 releases energy E at the origin in a space filled with a gas of density ρ. A hemispherical blast wave subsequently propagates radially outward with front radius R following R=k·tᵃ·Eᵇ·ρᶜ, where k is a dimensionless constant. The value of exponent a is ______. (Rounded to one decimal place)
0.4(± 0.05 accepted)
Explanation
Dimensions: R=[L], t=[T], E=[ML²T⁻²], ρ=[ML⁻³]. Matching [L]=[T]ᵃ[ML²T⁻²]ᵇ[ML⁻³]ᶜ: for M, b+c=0; for L, 2b−3c=1; for T, a−2b=0. Solving: c=−b, so 2b+3b=1 → b=0.2, then a=2b=0.4.
Source: GATE ME 2023 Official Paper (2023)
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