GATE ME 2024 Set 1 — Question 51
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Fluid Mechanics → Dimensional Analysis & Similitude → Buckingham Pi Theorem
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Question
A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance travelled by the liquid meniscus inside the capillary in time is given bywhere is the surface tension, is the inner radius of the capillary, and is the dynamic viscosity of the liquid. If is a dimensionless constant, then the exponent is __________ (rounded off to 1 decimal place).
Correct answer
0.5 to 0.5
Solution
Using dimensional analysis:
The equation is . Substituting dimensions:
Equating powers of :
For
For
For Substitute into the equation:
Thus, the exponent is 0.5.
The equation is . Substituting dimensions:
Equating powers of :
For
For
For Substitute into the equation:
Thus, the exponent is 0.5.
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