GATE ME 2023 Set 1 — Question 65
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Fluid Mechanics → Dimensional Analysis & Similitude → Buckingham Pi Theorem
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Question
An explosion at time releases energy at the origin in a space filled with a gas of density . Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure.Let denote the radius of the front of the hemispherical blast wave. The radius follows the relationship , where is a dimensionless constant. The value of exponent is __________.(Rounded off to one decimal place)
Correct answer
0.39 to 0.41
Solution
We use dimensional analysis to find the exponent . The dimensions of the variables are:
Equating the exponents for , , and :
1) For :
2) For :
3) For : Thus, the value of exponent is .
- Radius
- Time
- Energy
- Density
Equating the exponents for , , and :
1) For :
2) For :
3) For : Thus, the value of exponent is .
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